The thesis deals ith p o le s of i e tio he e solutio s of opti izatio ethods do ot eet the o je ti es of p o le s to sol e. The p o le s p e iousl defi ed e ploit fo thei esolutio , a p o le e te di g the odel of lassi al T'I) i a a o i al fo alled "ge e alized s ste of o t adi tio s." This esea h d a s up a esolutio p o ess ased o the loop si ulatio -opti izatio -i e tio usi g oth sol i g ethods of opti izatio a d i e tio . Mo e p e isel , it odels the e t a tio of ge e alized o t a tio s f o si ulatio data as o i ato ial opti izatio p o le s a d offe s algo ith s that p o ide all the solutio s to these p o le s. I additio , it p o ides heu isti s to sele t a ia les a d its ele a t alues i ol ed i ge e alized o t adi tio s a d/o useful fo opti izatio . The o t i utio s o e theo a d p a ti e of the i e ti e desig . The thesis also e plo es oss-fe tilizatio et ee opti izatio a d T'I).

This disse tatio

as e a led due to the help of a i di iduals f o Chi a a d F a e du i g the last th ee ea s.

Fi st of all, I ould like to tha k to the Chi a " hola ship Cou il fo the fi a ial suppo t du i g PHD studies i the la o ato of desig e gi ee i g La o atoi e de GE ie de la CO eptio at the Natio al I stitute of " ie e a d Te h olog of "t as ou g IN"A de "t as ou g i f e h .

I ould like to e p ess si e e g atitude to supe iso P ofesso 'ola d De I ould also like to e p ess si e e g atitude to o-supe iso I a a 'aso ska.

Tha ks fo ou f uitful dis ussio s a d suggestio s ou ga e e he I as puzzled a d lost i thesis. I additio , I eall app e iate ou help i life, I still e e e he I fi st a i ed to "t as ou g f o Chi a a d ou a e to the ai po t

to eet e a d took e to studio a . As a fo eig e stude t ho ea l ould ot speak F e h i that ti e, e e all thi gs diffi ult fo e. Tha k ou fo all ou ha e do e fo e du i g sta i "t as ou g.

I ould also like to e p ess app e iatio to " astie Du ois. M task ould t e a o plished ithout ou help i T'I). I ha e g eatl e efited f o ou e pla atio s of the diale ti al thi ki g. I ould also like to tha k to D it Ku ha a , fo ou ou ses of T'I), hi h help e so u h i dis o e i g of T'I).

I ould espe iall like to tha k D . )ha g Qia g, D . Li Kai, D . He Hua , a d D . Ya

Wei ho ga e e a lot of suppo t fo life i F a e. Tha ks to D Tho g Chai fo sha i g the li i g e pe ie e a d idea ith e. I ould also like to tha k Chi ese f ie ds i "t as ou g, )hao Pe g, Fe g Xi , )hao E u, )a g Deji , Hao Xi , Li -Desig theo th ough o t adi tio s as the fou datio o ept of the T'I)

List of Figures

List of figu es

theo .

-P a ti al o se ue es of a e o t adi tio defi itio fo the i e ti e p o le sol i g.

-E plo atio of the elatio et ee opti izatio ethods a d T'I) i o de to de elop oss-fe tilizatio f o theo eti al a d p a ti al poi ts of ie .

To a s e these uestio s, a esea h ethod is p oposed a d uestio s a e a s e ed o pletel o pa tiall th ough the utilizatio of the p oposed algo ith s.

'eal e a ples a e the used to illust ate the p oposed algo ith s. The last pa t of this hapte is dedi ated to the thesis o ga izatio .

1-2 Ba kg ou d T o t pes of situatio s a lead to this e olutio p o ess: i easi g the s ste effi ie opti izatio of its pa a ete s o edesig i g the s ste he e pa a ete s a e i t odu ed du i g the esolutio p o ess, e.g., he a o ki g p i iple is ha ged. The h pothesis is that t o t pes of p o le sol i g te h i ues -Routi e desig p o eeds ithi a ell-defi ed state spa e, i.e. all desig a ia les a d thei possi le do ai s o a ges ei g k o a d the p o le ei g o e of possi le i sta tiatio s. The tools used a i lude opti izatio ethods.

-I ovative desig p o eeds ithi a spa e of k o solutio s hi h is e te ded de elopi g a iatio s o adaptatio s to e isti g desig s, i.e. the do ai o a ges of alues of e isti g desig a ia les is e te ded. O eo st ai ed satisfa tio ethods ould e used to sol e this t pe of p o le .

-C eative desig i plies the fo ulatio of a state spa e that a i lude a e te ded state spa e of possi le solutio s o eati g a e state spa e. Fo We a the assu e that a solutio to this p o le a e des i ed i te s of a de isio e to i the de isio spa e X. "u se ue tl , a fu tio a e de eloped that e aluates the ualit of a spe ifi solutio assig i g it a o je ti e e to i the o je ti e spa e Y Figu e . Fi st, the espo se a ia les a e t a sfo ed i to a i a s ste i o de to si plif the e t a tio p o le .

z ij =  e i   E e i ×Y :   j / z ij = E ×Y E  e i   E e i ×Y :   j / z ij = E ×Y : z ij = E ×Y E E ×Y E ×Y E ×Y
Based o this defi itio , it is possi le to sho that e isti g T'I)-ased odels a e pa ti ula odels de i ed f o the G"C. The lassi al T'I) o t adi tio s a e a pa ti ula ase of G"C see Ta le , he e: The e t a tio of the G"C i the e pe i e tatio ta le is des i ed as a set of e uatio s ha a te izi g the lo ks of the at i [ ]: To e t a t lassi al T'I) o t adi tio s, the follo i g set of e uatio s is esol ed:

a d Y i, i={ , } = , a d  i , ,  X, D i , D i / i =  Y , Y = ,  i =  Y , Y = ,
1 : ) , ( 1 : ) , ( 1 ; ) , ( 1 0 or 1 / 0 0 / 0 0 0 0 / ; /                          k i k j k j k i E e i ij k j i Y y j ij k j i ij k k j i ij Y y j E e i ij z Y E y e z Y E y e z Y E
2 1 2 2 1 1 / , / , 0 0 0 / ; / : : 1 : 1 ; ) , ( 0 0 or 1 2 1 v v v a E e v a E e z z E e z Y E y e z z ij i ij i Y y k ik Y y j ij i ij k k j i ij Y y j E e i ij k j k j k i                        
The diffe e es et ee these sets of e uatio s e ui ed to e t a t the diffe e t t pes of T'I)-ased o t adi tio s sho that the lassi al used to gai the e essa i fo atio . Fo the pu pose of ou stud , these esults e e t a sfo ed a d su a ized i to a i a e ta gula at i . The fi st step of ou app oa h is to ide tif a d e t a t the GTCs. Assu i g the GTCs a e ot elated to a tio pa a ete s, the i a at i a the e edu ed to its e aluated fo de oted as ), as sho i Figu e a .

a i ple e ted. Ide tif i g GTCs i the usto ized e pe i e tal ta le ep ese tatio e ui es defi i g the p ope ties of the GTCs. GTCs a e the ha a te ized a set of defi itio s, hi h allo the e t a tio of GTCs f o this e pe i e tal ta le.

Assu i g o e pe i e t satisfies all of the e aluatio pa a ete s at the sa e ti e, ide tif i g a GTC i su h a ta le i ol es sea hi g fo the follo i g:

 Th ee sets of e aluatio pa a ete s Y , Y , Y hose u io is the e ti e set of e aluatio pa a ete s a d hose i te se tio is a e pt set.

 Th ee sets of e pe i e ts E , E , E hose u io is the e ti e set of e pe i e ts a d hose i te se tio is a e pt set.

-

      2 , 3 , 3 2 M s C M s         2 2 , 3 , 3 2     N s C N s .
A o di g to the e uatio fo "ti li g u e s of the se o

d ki d [ ],                    k t N t t k t k k k N s 0 1 ! 1 ,   1 2 2 , 1    N N s Usi g E uatio s a d a d supposi g 3 , 3   M N
, e o tai the size of ou sea h spa e:

2 2 2 1 3 2 2 1 3                       M M N N
Clea l , the o si g of the sea h spa e is a NP-ha d p o le . The se iatio ethods [ ] offe a isual ea s of e a i i g the st u tu e of the data eo ga izi g the data to p ese t as ho oge eous a pi tu e of the data st u tu e as possi le. This isual ep ese tatio assists ith p o le i te p etatio .

2-1.3 Diffe e t possi le ethods to use i ou app oa h

The idea of se iatio is to i g si ila o s a d si ila olu s as lose to ea h 2-2 Fo ulatio of the e t a tio p o le as a i a i tege p og a I this se tio e ill fo ulate ou GTC e t a tio p o le as a uad ati i a i tege p og a i g BIP p o le . The a e hausti e sea hi g algo ith is p oposed to olle t all the solutio s. I additio , e p opose to t a sfo a uad ati i a i tege p og a to a li ea i tege p og a , hi h ill idge the e isti g i tege p og a i g algo ith to allo fo GTC sea hi g. This ill also allo fo a supple e ta app oa h he e hausti e sea hi g algo ith is u a aila le.

  0 2 1 , , Y Y Y a d   0 2 1 , , E E E , espe ti el . Ou
z ij =  e i   E e i ×Y :   j / z ij = E ×Y E  e i   E e i ×Y :   j / z ij = E ×Y : z ij = E ×Y E E ×Y E ×Y E ×Y
  N i N i i i i c c c c C ,..., , , 3 2 1 2 , 1   ,   M i M i i i i r r r r R ,..., , , 3 2 1 2 , 1   ; C 2 , 1  i ep ese ts 2 , 1  i Y , 2 , 1  i R ep ese ts 2 , 1  i E .
Fo o e ie e, e assu e that

          j j c N 1 1 ,           j j c N 2 2 ,           j j r M 1 1 , a d           j j r M 2 2 . Ou p o le
a the e t a sfo ed i to a i tege p og a i g p o le . The est i tio s ega di g lo k

1 1 Y E  a d 2 2 Y E  i di ated i Ta le a e o e a
o je ti e fu tio , as

T i i ZC
R is e ual to the su of all ele e ts i the lo k

i i Y E  . i i M N is the p odu t of the u e of o s a d olu s of the lo k   i i Y E , .Whe the lo ks   1 1 ,Y E a d   2 2 ,Y E a e full of o es , the ua tit      2 , 1 2 , 1 i i i i T i i M N ZC R is e ual
1 2 Y E  : 1 1 1 1 , 1 : 1              C c c j ij j j z N .
Usi g the sa e ethod to odel the lo k

2 1 Y E  , 2 0 Y E  a d 1 0 Y E  p o ide

2-2.1 P o le fo ulatio i fo of i tege p og a i g p o le

To su a ize, the sea h p o le su je t to the est i tio s sho i Ta le e o es a p o le of al ulati g all of the solutio s of the follo i g i tege p og a i g p o le :

De isio a ia les:

  1 1 3 1 2 1 1 1 ,... , , n c c c c C  ,   2 2 3 2 2 2 1 2 ,... , , n c c c c C  ,   1 1 3 1 2 1 1 1 ,... , , m r r r r R  ,   2 2 3 2 2 2 1 2 ,... , , m r r r r R  .
I put pa a ete : at i ) O je ti e fu tio : Fo o e ie e, e assu e that

Maximise      2 , 1 2 , 1 i i i i T i i M N ZC R su je t to 1 1 1 1 , 1 : 1              C c c j ij j j z N ,   2 2 2 , 1 | R r r i i i i     1 2 2 2 , 1 : 2              C c c j ij j j z N ,   1 1 1 , 1 | R r r i i i i     1 1 1 1 , 1 : 1              C c c j ij j j z N ,   1 1 1 2 2 2 , 0 , , 0 | R r r R r r i i i i i i       1 2 2 2 , 1 : 2              C c c j ij j j z N ,   1 1 1 2 2 2 , 0 , , 0 | R r r R r r i i i i i i         M R R 1 ,..., 1 , 1 2 1     N C C 1 ,..., 1 , 1 2 1   1 , 0 ; 1 , 0   j i j i r c 0 , , , 2 1 2 1  R R C C This BIP is o li ea e
          j j r M 1 a d that           j j c N 1 . Ou goal is to seek the lo k e p essed   1 1 ,Y E
i hi h all of the ele e ts i the lo k a e e ual to .

We a use the sa e app oa h used p e iousl to defi e the o je t fu tio :

1 1 1 1 N M ZC R T  , he e the a i u alue of hi h is ze o. Mo eo e , its a o pa i g lo k   Y E, u

de eath has at least o e ele e t e ual to fo ea h o ,

hi h a e fo ulated the i e ualities:

1 1 , 1 : 1              C c c j ij j j z N ,   1 , 1 | R r r i i i i    .
De isio a ia les:

  M M r r r R ,..., , 2 1 1  ,   N N c c c c C ,... , , 3 2 1 1  I put pa a ete : at i ); Ma i ize: 1 1 1 1 N M ZC R T 
"u je t to: The sea hi g p o edu e o sists of fi e steps:

1 1 , 1 : 1              C c c j ij j j z N ,   1 , 0 | R r r i i i i    1 , 0 ; 1 , 0   i i c r ; R   1   1 C Afte the
1. Let i = .

2. "ele t the olu s set, the ele e ts of hi h e ual i o i. . "uppose that the u e of lo ks i the sea hi g phase is S ; thus, ti e o ple it i the o pa i g phase is

    2 2 1 S O S S O         . I o lusio , the ti e o ple it is   2 2 2 S M O n  
.The p i ipal spa e ost is elated to the sto age of the lo ks i the sea hi g step.

Be ause the u e of lo ks is lo e tha N 2 , the spa e o ple it is   N O 2 .

2-2.3.3 P o le solutio

Bi a P og a i g algo ith

The o je ti e fu tio is a uad ati fu tio , it i ol es the ite s like r c o r c . I fa t, as [ ] i t odu ed, a g oup of e i a a ia les x a e i t odu ed to epla e r c su h that the i a alues o espo d the alue of r c .

Mo eo e , t o li ea o st ai ts a e added to o st ai the alue of x r and c :

∑ c + ∑ c K
K is the i i u u e of e aluatio pa a ete got i ol ed ith the GTC.

The e , the t a sfo ed li ea i a p og a i g a e sho as:

De isio a ia les:

  1 1 3 1 2 1 1 1 ,... , , n c c c c C  ,   2 2 3 2 2 2 1 2 ,... , , n c c c c C  ,   1 1 3 1 2 1 1 1 ,... , , m r r r r R  ,   2 2 3 2 2 2 1 2 ,... , , m r r r r R  .
I put pa a ete : at i ) z , O je ti e fu tio :

Maximise ∑ (z -)x + z -x , su je t to

x , r , + c , x , fo all i<M, j<N; -a d .

I the o je ti e fu tio , e a k o that the u e of e i a a ia les

x ,x is the u e of i at i ). This solutio is o ple e ta he e hausti e sea hi g is u a aila le, as the a h-a d-ut ethod has sol ed a i sta e o tai i g as a as i a a ia les [ ]. : fi i g pi ate ial plasti -, etal -;

2-3

: o e i te al dia ete high -, lo -;

: o e e te al dia ete high -, lo -;

-Illust atio of the algo ith fo the ase of the ele t i al i uit eake : fi i g pi dia ete high -, lo -;

: sp i g st aight ess high -, ediu -, lo -; a d the esults a e defi ed as the e aluatio pa a ete s as follo s:

: i uit eake dis epai satisfied -, u satisfied -;

: i uit eake eusa ilit satisfied -, u satisfied -;

: sp i g o e ou ti g satisfied -, u satisfied -;

: fi i g pi o i ou ti g satisfied -, u satisfied -;

: o al ode elease satisfied -, u satisfied -;

: fi i g pi i itial positio etu satisfied -, u satisfied -.

The s ste eha io as odelled th ough the e pe i e tal ta le a d it is sho i Ta le . The o je ti es that ha e ee esta lished to uild this e pe i e tal ta le a e as follo s:

 The satisfa tio of at least o e e aluatio pa a ete i ea h e pe i e t;

 Ea h of the a tio pa a ete s has at least o e ti e ea h of its possi le alues;

 To i i ize the u e of e pe i e ts.

E e if the assu ptio is ot totall o siste t, the a tio pa a ete s ha e ee o side ed i depe de t ithi the li its of thei defi ed do ai s.

Ta le : E pe i e tal ta le fo the i uit eake

Fi st e ide e is that o solutio a e fou d i the defi ed Ta le , as o e pe i e t e a les the satisfa tio of all the e aluatio pa a ete s. Additio all , looki g fo ge e alized s ste of o t adi tio s i su h a ta le ould lead to se e al o es, at least o e pe e aluatio pa a ete , as soo as ea h e aluatio pa a ete is at least satisfied o e.

Assu e it is that the hoi e of a tio pa a ete s is pe fo ed i su h a a that ea h e aluatio pa a ete ill e satisfied i o e e pe i e t. It is also assu ed that o solutio is fou d i the ta le; the efo e, ea h e aluatio pa a ete ill ha e at x1 x2 x3 x4 x5 y1 y2 y3 y4 y5 y6 e1 1 1 0 0 1 1 0 1 1 1 1 e2 0 1 1 1 1 0 1 0 0 1 1 e3 1 0 1 0 0 1 0 1 0 0 0 e4 1 1 0 0 0 1 1 1 1 0 0 e5 1 0 1 0 1 1 0 1 0 1 1 e6 0 1 0 1 2 0 1 0 1 1 1 e7 1 0 1 1 0 1 0 1 0 0 0 e8 1 0 0 0 1 1 0 0 1 1 1 e9 0 1 0 0 2 0 1 0 1 1 1 least o e e pe i e t i hi h it ill e satisfied a d o e e pe i e t i hi h it ill ot e satisfied. Thus, a o t adi tio ould e fo ulated fo ea h of the e aluatio pa a ete s. Ho e e , the ge e alized s ste of o t adi tio s also e a les the fo ulatio of o e o ple ge e alized s ste of o t adi tio s, the e i pl i g t o o i atio s of e aluatio pa a ete s. Thus, a set of ge e alized s ste of o t adi tio s a e fo ulated fo a desig of e pe i e t ithout a solutio . A e1 1 0 1 1 1 1 e3 1 0 1 0 0 0 e7 1 0 1 0 0 0 e5 1 0 1 0 1 1 e8 1 0 0 1 1 1 e6 0 1 0 1 1 1 e9 0 1 0 1 1 1 e2 0 1 0 0 1 1 e4 1 1 1 1 0

0 Y1 Y2 Y0 y1 y3 y2 y5 y4 y6 e1 1 1 0 1 1 1 E1 e3 1 1 0 0 0 0 e7 1 1 0 0 0 0 e5 1 1 0 1 0 1 e6 0 0 1 1 1 1 E2 e9 0 0 1 1 1 1 e2 0 0 1 1 0 1 e4 1 1 1 0 1 0 E0 e8 1 0 0 1 1 1 (a) (b)
0 1 e2 1 1 0 0 0 1 e4 1 1 0 1 1 0 e6 1 1 0 0 1 1 e6 1 0 1 0 1 1 e9 1 1 0 0 1 1 e9 1 0 1 0 1 1 e1 0 1 1 1 1 1 e1 0 1 1 1 1 1 e3 0 0 1 1 0 0 e5 0 1 1 1 0 1 e4 1 0 1 1 1 0 e3 0 1 0 1 0 0 e5 0 1 1 1 0 1 e7 0 1 0 1 0 0 e7 0 0 1 1 0 0 e8 0 0 1 1 1 1 e8 0 1 1 0 1 1 GTC #1 GTC #2 y2 y6 y3 y5 y1 y4 y2 y6 y1 y3 y4 y5 e2 1 1 0 1 0 0 e2 1 1 0 0 0 1 e6 1 1 0 1 0 1 e6 1 1 0 0 1 1 e9 1 1 0 1 0 1 e9 1 1 0 0 1 1 e1 0 1 1 1 1 1 e1 0 1 1 1 1 1 e5 0 1 1 1 1 0 e3 0 0 1 1 0 0 e3 0 0 1 0 1 0 e4 1 0 1 1 1 0 e4 1 0 1 0 1 1 e5 0 1 1 1 0 1 e7 0 0 1 0 1 0 e7 0 0 1 1 0 0 e8 0 1 0 1 1 1 e8 0 1 1 0 1 1 GTC #3 GTC #4

Chapte E t a tio of ge e alized te h i al o t adi tio

2-5 Dis ussio

The esults of the e pe i e ts f o this hapte i di ate a g eate the u e of possi le o i atio s a e possi le he the u e of te h i al pa a ete s a d e pe i e ts des i i g the te h i al s ste i eases. alues of a tio pa a ete s, V i , V i ,…, V i . The outputs of e pe i e ts e i a e ha a te ized a set of i a alue of e aluatio pa a ete s, ) i ,) i ,…, ) i , hile i is satisfied e uali g o e uali g .

Ta le : A e pe i e tal ta le

A1 … An y1 … yi … yr e1 V11 V1n Z11 Z1i Z1r e2 V21 V2n Z21 Z1i Z2r … e8 V81 V8n Z81 Z1i Z8r e9 V91 V9n Z91 Z1i Z9r
If the e is a gi e ge e alized te h i al o t adi tio ha a te ized the e pe i e t set E , E a d E , a ge e alized ph si al o t adi tio a e fo ulated.

Ide tif i g a ge e alized ph si al o t adi tio i Ta le , as the follo i g:

 Co ept : ad it the states i E , eje t states i E a d E .

 Co ept : ad it the states i E , eje t states i E a d E . o side i g all the e pe i e ts of E , the follo i g applies:

-Fo ulatio of the BIP p o le a d the e hausti e sea h algo ith

Co ept A ,A ,A ,A ,A =

A = A = A = A = A = + A = A = A = A = A = + A = A = A = A = A = ,

3-2.1 Pa a et i fo of a o ept

The pu pose of this se tio is to p opose a ge e i shape of o ept ased o a fi ite u e of pa a ete s. The efo e, defi i g the o ept is e ui ale t to defi i g the alue of its pa a ete s.

Defi itio of o ept

De The e , ith the i easi g u e of olu s, the ti e o su ptio e pe ie es a e po e tial i ease.

3-2.4 Full fa to ial e pe i e t s i o plete e pe i e t esults

Whe the e pe i e tal ta le is ot o plete, so e states i o ept a e u e tai e ause so e ge e al states a e ge e alized f o a e pe i e ts.

GSC e t a tio fo the ase stud

The fi st step of i e ti e p o le sol i g fo this ase stud is the GTC e t a tio , as the e a e o l t o e aluatio pa a ete s: a e age sto k A" a d se i e eakdo "B ; the o l GTC is a TC of A" a d "B. We defi e the ideal alue as satisf i g the alue of A" a d "B. Thus, the e a e e pe i e ts i ol ed i E fo satisf i g A" a d e pe i e ts i ol ed i E fo satisf i g "B.

The GPC e t a tio as pe fo ed du i g the full fa to ial e pe i e ts. Eight

3-4 E ploitatio of algo ith

The o e states a aila le fo o ept, the o e ph si al o t adi tio s that a e p o ided, hi h ould allo fo o e pa tial solutio s. Additio all , the s ste has

3-4.1 'elatio ship et ee u e of e pe i e ts a d states

The u e of e pe i e ts i ol ed i E a d E a e des i ed the pe e tage of hole u e of e pe i e ts l . The fi st g oup of e pe i e ts is i ega ds to the elatio ship et ee the u e of states i a o ept a d the pe e tage of l u e of e pe i e ts. We set the a tio pa a ete e ual to -E ploitatio of algo ith 9 0 0 0 0 0 8 0 0 0 0 0 7 0 0 0 0 0 6 0 0 0 0 0 5 0 0 0 0 0 4 0 0 0 0 0 3 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0  If a easo a le u e of pa a ete s ha e to e take i to a ou t, the uildi g of the e pe i e tal ta le is e i po ta t. The hoi e of the o side ed a tio pa a ete s is also u ial. A app oa h, ased o the p i ipal o po e t, fa to a al sis, a d f a tio al desig of e pe i e ts as p ese ted i [ ].

Ho e e , thei sele tio a d e t a tio of a tio pa a ete s is o l a p a ti al e gi ee ethod ithout igo , a d the efo e, a la k igo fo e e situatio .

 Fi all , o e of the ost i po ta t e ai i g uestio s is: if so a o t adi tio s a e fo ulated, ho to hoose the o e to o side p io to the othe s fo the p o le esolutio that e ai s the Q .

It is i te esti g to ote that out of the GPC that a e fo ulated, ot all of these GPCs a e e ui ale t. Thus, GPCs a e atego ized the u e of o fli ti g a tio pa a ete s i luded i its fo ulatio . Fo the e a ple, GPC e e fou d ith o l o e o fli ti g pa a ete . This i di ates e ui ale to the lassi al T'I) o t adi tio u de e tai o ditio s as defi ed the fi ed alues fo othe a tio pa a ete s. Fo e a ple, o e GPC a e fo ulated as:

if (A 2 =1)(A 3 =0)(A 4 =0), then (A 1 =1)  ((y 1 .y 3 )=1)(y 2 .y 5 .y 6 =0)) and (A 1 =0)  ((y 1 .y 3 )=0)(y 2 .y 5 .y 6 =1)).
This p a ti al poi t is i te esti g, e ause i p a ti e these o ditio s a e ot p o ided e pli itl e pe ts he a o t adi tio holds. Thus, it p o ides a fou datio fo Q usi g the ge e alized o t adi tio s i the i e ti e p o le sol i g , a d e su es p og ess to a s e i g Q usi g the ge e alized o t adi tio s to e p ess i pli it e pe t s k o ledge .

Ho e e , the o e i te esti g esult, out of this e a ple, is that pai s of ite s a e o side ed as oo fli ti g pai s as e tio ed i -. . Fo e a ple, the follo i g pai of ite s a e e t a ted out of the t o o epts:

(A 2 =1)(A 3 =1)(A 4 =1)(A 5 =1) and (A 1 =1)(A 3 =1)(A 5 =1).
This a e e og ized as a solutio o ept defi ed

A = A = A = A = A = .

4-1 I t odu tio

As e tio ed a o e the use of the e hausti e o t adi tio sea h algo ith p ese ts so e p a ti al li itatio s. Co t a to the e aluatio pa a ete s the s ste odel ould o tai a lot of a tio pa a ete s a d alues le el used i the e pe i e ts. The algo ith o putatio al o ple it is o M N , he e N is the u e of a tio pa a ete s M the u e of le els plus . That is the easo h uite ofte the e hausti e GPC sea h algo ith a ot e used ith a tual sta da d o pute ea s. We fi ed M N < , . ; hi h allo s fo i sta e t el e a tio pa a ete s ith t o alue le els. But all the a tio pa a ete s a d le els a e ot e essa fo defi i g the GPCs. This hapte p ese ts a ethod to pass this li itatio sele ti g, he it is ele a t, fe e ough pa a ete s a d alues so that the p e ious algo ith a e used; othe ise it ill let us k o hi h a tio pa a ete s a d le els a e e plai i g the pe fo a e of the a tual s ste ega di g ea h e aluatio pa a ete .

The GPC e t a tio algo ith [ ] p ese ted i Chapte p o ides all the possi le states that a defi e the o ept. The use of this algo ith i eal ases leads us to the h pothesis that i a ases o l fe a i g a tio pa a ete s a e i ol ed i a GPC. We de elop the h pothesis that the e a e e ough ases he e the u e of pa a ete s a d alues i ol ed i the GTC is lo e tha the li itatio of the a tual e t a tio algo ith . Thus, i the ase he the e is u e ous a tio pa a ete s i the odel ut o l fe a e e essa fo the GPC des iptio , e ould like to defi e the ui kl efo e o puti g the GPC ith the algo ith of Chapte .

Mo eo e , e ha e see i hapte , that i o de to defi e lassi al o ge e alized o t adi tio s ithi a gi e o te t it is ad ised to e a le to pe fo a full desig of e pe i e t. This leads us to seek k o i g the ele a t alues of the a ia les that a e i ol ed i the GPCs des iptio su h that the u e of e pe i e t is edu ed a d allo s pe fo i g a good i put fo the algo ith p ese ted i Chapte . The set E a also e i te p eted as the set of e pe i e ts he e the EP alue is satisf i g agai st the set E +E a d he e the EP alue is ot satisf i g. "i ila l E a e u de stood as the set of e pe i e ts he e the EP alue is satisf i g agai st the set E +E he e EP alue is ot satisf i g. e1 1 0 1 1 0 e2 0 0 1 1 0 e3 0 1 1 1 0 e4 0 1 0 0 1 e5 1 1 0 0 1 e6 1 1 1 0 , he e i is the eight oeffi ie t a d i is the featu e alue. Appa e tl , if take the sa ple poi t i a li ea lassifie , e a fi d that the sig of the li ea lassifie de ided the lass of the sa ple. Mo eo e , fo ea h u it of the featu e alue, if the eight oeffi ie t is la ge, it a dete i e the sig of the lassifie . Fo e a ple i Figu e

, the eight e to is , , hi h ea s that a d ha e the sa e positi e i flue e o the sig of de isio fu tio + -.

Fo a si ple e pla atio , the appli atio of "VM odel i o -li ea sepa a le p o le is gi e a t o-lass i sta e set of  

i i y x , , l i ,..., 1  he e N i R x  a d   0 , 1  i y , i y is lass la el. "VM sea hes fo a li ea lassifie     b x W x D T    i
highe di e sio al Hil e t spa e utilizi g a highe di e sio al appi g fu tio  

x  , he e the t o-lass sa ples a e li ea l sepa a le. As lo g as  

x D is o tai ed, fo a e i sta e X , the lass la el y is dete i ed the sig of  

X D :   0 1 0 0        y y X D
Te h i all , the highe di e sio al appi g fu tio    Li ea ke el fu tio :

  j T i j i x x x x K  , .  Pol o ial ke el fu tio :     . 0 , ,      d j T i j i r x x x x K  'BF ke el fu tio :     . 0 , exp , 2       j i j i x x x x K  "ig oid:     . 0 , tanh ,      r x x x x K j T i j i Afte defi i g a highe di e sio al fu tio   x  o a ke el fu tio   j i x x K ,
, "VM t ai i g p o le is t a sfo ed i to the follo i g opti izatio p o le to sea h fo the a i ua gi h pe pla e   4-2.3 Featu e sele tio ethod adopted i ou p o le I p a ti e, e applied the p i iple p oposed i [ ] fo uildi g up a "VM odel fo featu e sele tio of the e aluatio pa a ete s ased o the follo i g steps:

    l i b x W y i i T i ,..., 2 , 1 ; 1       , l i i ,..., 2 , 1 ; 0    I this
1. T a sfo the ta le of e pe i e ts i to to the fo at of a "VM p o le odel.

2. E pi i all sele t ke el fu tio . As the data a e o iousl o li ea sepa a le, e o side utilizatio of 'BF ke el.

3. Use oss-alidatio to fi d the est state of "VM a o di g to the a u a .

T ai i g the "VM

hole t ai i g set   e ha e to shape the data fo usi g it. The ge e al "VM fu tio a e depi ted as see i Figu e . -Usi g the o e SVM algo ith i o te t of GPC e t a tio

4-6 Usi g the o e "VM algo ith i o te t of GPC e t a tio

To fa ilitate the GPC e t a tio algo ith p oposed i Chapte , the ke p o le is ho to edu e the u e of a tio pa a ete s so as to de ease the ti e o ple it of GPC e t a tio algo ith . Tha ks to "VM algo ith , it p o ides us a ethod to eight the a tio pa a ete s, a d sele t those that ake a sig ifi a t o t i utio to satisf the e aluatio pa a ete s. I this se tio , e ill p opose I a ief su a of the p o ess i Figu e , the fi st fou steps a e i ega ds to the sele tio of the a tio pa a ete s a d thei alue "VM eights. The output is a edu ed set of a tio pa a ete s a d alues, hi h fa ilitate GPC e t a tio . As GPC e t a tio eeds full fa to ial e pe i e ts fo good o te t defi itio , the i puts e pe i e ts of p o ess o o l a ot o e full fa to ial e pe i e ts o a edu ed set of a tio pa a ete s fo the s ste . This leads to a ds pe fo i g a e g oup of e pe i e ts as sho i "tep . Fo the e e pe i e ts, e do ot k o hethe the ta geted GTC still a e e t a ted. Thus, e e t a t GTC fo the e e pe i e ts i o de to e aluate ou si ulatio odel he e a pa a ete s a e fi ed. Ou pu pose is to e if that at least the GTC e a ted to stud e ai s i the e pe i e ts. Alte atel , e a hoose a ta get GTC fo GPC e t a tio . We a also ake a o pa iso ith the o igi al GTC set to esti ate ou pa a ete sele tio . If ou ta get GTC is ot i ol ed i the e GTC set, hi h ea s e ake a ad sele tio ega di g pa a ete s a d o alues, e etu to sele t additio al pa a ete s a d alues out of the a ki g p o ided the "VM algo ith . Othe ise, he the ta geted GTC is p ese t, e e t a t the GPC to fo a ge e alized s ste of o t adi tio . I the follo i g, e illust ate ea h step a e a ple.  "ele t a a tio pa a ete depe di g o the pu pose of t i g to o e the d a d d effe ti e a tio pa a ete fo ea h e aluatio pa a ete . Fo e a ple, A is the d effe ti e a tio pa a ete fo Y a d Y .

 The u e of sele ted a tio pa a ete should e s all to suit the apa it of the GPC e t a tio algo ith .

I the e a ple, the sele tio set a e " = {A , A , A , A , A ,

A } = {A , A , A , A } U {A , A , A , A }, he e {A , A , A , A } is f o Y fo Co ept of o t adi tio , a d {A , A , A , A } is f o Y fo Co ept of the o t adi tio .
This e a ple ould e pe fo ed di e tl ith the GPC algo ith of Chapte .

Ho e e , e o l pe fo ed the alue sele tio fo a tio pa a ete set ".

The thi d step is the alue sele tio , as e plai ed i -. We e o ed {A , A , A , A } f o the e pe i e t i Appe di , odi g the alue of {A , A , A , A , A ,  "i ila to the a tio pa a ete sele tio , alue sele tio is also e ui ed to sele tio a alue set hi h t to o e all the ost effe ti e alue of ea h a tio pa a ete fo Y a d Y , as the positi e alue f o diffe e t a tio pa a ete s a e o i ed.

 Co p o ise the apa it of GPC e t a tio a d the u e of the sele ted alue. Too u h alue ill i ease the ti e o ple it of the GPC e t a tio algo ith .

Afte sele tio , the e ai i g a tio pa a ete s a d alues a e A ={ }, A ={ },A ={ , }, A ={ }, A ={ }, A ={ }.

Y2 = EP3 and EP4

-Usi g the o e SVM algo ith i o te t of GPC e t a tio 'ega di g the fi i g, e also ha e th ee situatio s:

 If the eights of o e a tio pa a ete a e o l positi e, e fi it at the la gest alue. As the de isio fu tio  

  b x W x D T   
, if W I is positi e, this ea s the a tio pa a ete Ai has a positi e effe t o satisf i g the e aluatio pa a ete .

Thus, e should fi it at the la gest alue to a i ize the positi e effe t. Fo e a ple, the eight of A is . fo Y a d . fo Y ; the efo e, e fi the i put le el of A to .

 If the eights of o e a tio pa a ete a e o l egati e, e fi it at the s allest alue. As the de isio fu tio  

  b x W x D T   
, if W I is egati e, it ea s the a tio pa a ete Ai has a egati e effe t o satisf i g the e aluatio pa a ete .

Thus, e should fi it s allest alue to i i ize the egati e effe t. Fo e a ple, the eight of A is -. fo Y a d -. fo Y ; the efo e, e fi the i put le el of A to .

 Whe o e a tio pa a ete has oth egati e a d positi e eights, the fi ed alue hoi e is ased o the follo i g p i iple: positi el satisf e aluatio pa a ete s, a d atte pt to ot se iousl dissatisf a e aluatio pa a ete s. The fi i g esult is {A = , A = , A = , A = }. The alue sele tio esults i "tep ake A = , A = , A = , A = a d A = , hi h ea s that e etai o l o e alue fo these a ia les. Thus, i this ase, the alue of these a ia les is also fi ed. "o o l a ia le A is ot fi ed a d has o e tha o e alue i.e., t o alues { , } . To su a ize, appl i g the "VM algo ith to the pa a ete s leads to fi i g the alue of A , A , A , a d A . Appl i g the "VM algo ith to the e ai i g set of APs leads us to fi the alues of A , A , A a d A . The e , the t o e ai i g e pe i e ts i step a e illust ated i Ta le : Ta le : Illust atio of t o e ai i g e pe i e ts

Fi ed A tio Pa a ete s AP Evaluatio Pa a ete s A A A A A A A A A A EP EP EP EP

As ou pu pose is to e t a t GPC fo ta get GTC, the a tio pa a ete a d e pe i e ts a e si ple e ough to pe fo the GPC e t a tio . We also ha e to e su e that ith the e edu ed set of a ia les a d e pe i e ts, e still get the GTC hose GPC a e supposed to e e t a ted. The efo e, the fifth step is GTC e t a tio . E pe ts looki g to these t o e pe i e ts a ot e a le to hoose a o g the . A o di g to the hose GTC, a o g the si o fli ts, a tio pa a ete s A , A , A , a d A a e oise a tio pa a ete s. These pa a ete s should ot elo g to the o ept of AP fo e plai i g the GTC. A deepe illust atio of this poi t e ui es o e i fo atio ega di g the p o le o te t a d studied s ste des iptio .

Ta le : 'a do l sele tio t o pe i e ts f o E a d E A A A A A A A A A A EP EP EP EP

----The e , ou ethod i deed helps i e o i g ot o l oise a tio pa a ete s, ut a also help i filte i g si ple ph si al o t adi tio s that ould ot e p o ided e pe ts.

4-6.2 EP ased e t a tio

4-6.3 Co pa i g the st ategies

No atte the GTC-ased e t a tio o EP-ased e t a tio , the oth a e ai i g at e t a ti g the GPC fo the ta get GTC. The ad a tage of the GTC-ased app oa h is the o e ta geted sele tio of the a tio pa a ete s, hi h ill li it the sele tio to the a tio pa a ete s that o l ha e effe ts o t o sides of the ta geted GTC. The disad a tage of GTC-ased app oa h is the li it of the u e of positi e i sta es i the "VM t ai i g. This is due to E o E ha i g a i suffi ie t u e of e pe i e ts that ould affe t the t ai i g esults of the "VM odel. The ad a tage of EP-ased e t a tio though, is the o side atio of all of the e aluatio pa a ete s du i g the stage of a tio pa a ete sele tio . We should fi d o e GTC ith the se o d app oa h; thus, e should ot eed to epeat the si plifi atio p o ess fo ea h GTC. Mo e p a ti al e pe i e ts a e e ui ed to he k this asse tio a d ake the o pa iso . Additio all , it ill ette shape the Pa eto set of the edu ed s ste . I a tualit , the se o d st ateg a e o side ed a st ateg fo sea hi g the ai a tio pa a ete s that i flue e the Pa eto set of the e aluatio pa a ete s o at least to e o e those that a e ot i flue i g.

4-7 Co lusi e e a ks

The p e ious o k has do u e ted the o igi of ge e alized te h i al o t adi tio a d ge e alized s ste of o t adi tio as ell as thei e t a tio algo ith ega di g the esults of e pe i e ts o si ulatio s. Ho e e , ea h algo ith is ased o e hausti e sea h, a d as su h, the a e ot usa le he the e a e too a pa a ete s. Espe iall , the p e ious GPC e t a tio algo ith that li its the i a a tio pa a ete s to t el e. I this hapte , e i t odu ed featu e sele tio algo ith fo o e of ost i po ta t algo ith s of "VM, hi h all the featu es a e 5-2 Case stud of dou le Ka a I this se tio , the stud ase is p ese ted to illust ate the use of the p oposed odel ha ge p o ess ith the tools i t odu ed i p e ious hapte s.

5-2.1 P o le fo ulatio a d si ulatio

This ase i ol es a si ple a ufa tu i g s ste a aged Ka a a ds si ulated ith the aid of the flo si ulatio soft a e Wit ess a d the si ulatio la out is sho i Figu e . Ho e e , fo the diffe e t K" a d the NK alues, the K" has a positi e effe t o "B a d "B . The easo is e iste e of the pa t ti e ha ge. The la ge the K" is, the less the pa t ti e ha ge. The la ge K" a lead to a la ge ua tit of ite i the uffe "to k_ , the e i easi g the i te al et ee ti es of p odu i g the ite . Not su p isi gl , the lo g i te al fo p odu i g the ite i di e tl de eased the total setup ti e, a d i eased the apa it of a hi e fo p odu i g ite . This e ha ed the se i e ualit ut i eased ite s fo a e age sto k. F o the eight at i , e a see that all the a tio pa a ete s a e i po ta t.

The efo e, e kept all the a tio pa a ete s {K" , K" , NK , NK }.

5-2.3.2.2 Weighti g a d sele ti g the alues of a tio pa a ete s I this se tio , the sa e ethod as pe fo ed as sele ti g the alue of a tio pa a ete the "VM-Weight. Fi st, odi g ea h alue of a tio pa a ete i a pa a ete s i this ase , the eati g the "VM-odel ith o e tha % oss alidatio -a u a . Fi all , p ese ti g the eight at i fo ea h a tio

5-2.3.2.4 GTC e t a tio a d GPC e t a tio

The GTC e t a tio algo ith as pe fo ed o the full fa to ial e pe i e ts.

T el e GTCs e e e t a ted a d the a e the sa e as the GTCs of o igi al s ste .

That ould i di ate oth of the a e a epta le odels i ega d to GTC e t a tio .

Based o the esults of the GTC e t a tio o the edu ed s ste , the GPC e t a tio as pe fo ed fo the ta get GTC i Figu e a. O e e had the GPC, the G"C odel as fo ulated as a i itial poi t of the T'I) a al sis. As the edu ed s ste had the sa e GTCs as the o igi al s ste , a d its e pe i e ts a e full fa to ial e pe i e ts; the GPC ould e e t a ted to a ds the ta get GTC. -Case stud of dou le Ka a

"e e al pa tial solutio s e e o tai ed, hi h a e su a ized elo :

 "olutio i di ated i e ti e sta da ds . Ke o ds: T'I), i e ti e desig , opti izatio , featu e sele tio .

  Guio, fo his o ti uous suppo t ithi PHD studies a d esea h, fo his oti atio , e thusias a d i e se k o ledge. Tha k ou fo ou ti e, ou patie e, fo the guida e i the a ea of the i e ti e p o le sol i g T'I) f o oth the theo eti al a d also f o the p a ti al poi t of ie . All suppo t ou p o ided e du i g these th ee ea s ade e g o a d o ti ue i a ade i life. It as a g eat pleasu e to lea f o ou i diffe e t do ai s, espe iall i the a o e e tio ed T'I). I a full o fide t that I ill e efit f o ou help i the est of a ee .

Figu e :

 e Figu e : Illust atio of ge e al ulti-o je ti e opti izatio p o le ....................... Figu e : F o opti izatio to i e tio th ough a o t adi tio .............................Figu e : OT"M-T'I) s ste of o t adi tio ..............................................................Figu e : TC a d PC i the o te t of opti izatio p o le spa e .............................Figu e : Ge e alized " ste of Co t adi tio ............................................................ Figu e : GTC a d GPC i the o te t of opti izatio p o le spa e ........................Figu e : Ge e al f a e o k fo i e ti e desig p o le sol i g ............................Figu e : App oa h fo odel ha ge ..........................................................................Figu e : Ge e i at i ) a a d a e a ple .......................................................Figu e : "u -p o le lo ks i at i ) ..................................................................

Figu e :

 e Figu e : Flo ha t of algo ith ...............................................................................Figu e : Co po e ts of ele t i al i uit eake a d the s he e .........................

Figu

  Figu e : E a ple of false lassi al TC a a d GTC ..............................................

Figu

  Figu e : E a ples of GTCs i the ase of ele t i al i uit eake ..........................

Figu

  Figu e : TC/ GTC u e e sus de sit fo ge e al at i es ................................Figu e : 'elatio et ee GTC/TC u e a d de sit of o es .............................Figu e : 'esidual alues a a d test of a ia e fo TC u e ........................ Figu e : P i ipal effe ts of fa to s a a d thei i te a tio s fo TC .................. Figu e : 'esidual alues a a d test of a ia e fo GTC ................................... Figu e : P i ipal effe ts of fa to s a a d thei i te a tio s fo GTC ............... Figu e : Opti izatio s i o atio ......................................................................... Figu e : " atte plots of lo k u e s ................................................................... Figu e : 'esidual alues a a d test of a ia e fo lo k u e ................... Figu e : P i ipal effe ts of fa to s a a d thei i te a tio s fo lo k u e Figu e : Ge e alized s ste of o t adi tio ..........................................................

Figu e :

 e Figu e : Ge e alized s ste of o t adi tio s fo the e a ple ..............................

Figu

  Figu e : "ea hi g p o ess of t o o epts ............................................................. Figu e : Illust atio of the lassi al ph si al o t adi tio ......................................

Figu e :

 e Figu e : Wit ess odel of the p o ess ....................................................................

Figu e :

 e Figu e : Pa eto f o tie of the i itial si ulatio ......................................................

Figu e :

 e Figu e : GPC a d its o te t elated to the i itial Ka a s ste ........................... Figu e : 'elatio et ee u e of states a d e pe i e ts APs ................. Figu e : 'elatio et ee u e of states a d e pe i e ts APs .................Figu e : 'elatio et ee u e of states a d e pe i e ts APs .................Figu e : Li k et ee u e of lassi al PC a d p odu t of "tates a d .......Figu e : 'elatio et ee PC a d u e of e pe i e ts i E a d E ..............Figu e : Bi a ta le a d o t adi tio odel ..................................................... Figu e : Featu e sele tio p o ess ith alidatio [ ] ......................................... Figu e : Co pa iso of o igi al a d appi g featu e spa e ................................. Figu e : Ge e al "VM odel ..................................................................................Figu e : A e a ple fo AP sele tio ..................................................................... Figu e : C oss-alidatio p o ess fo 'BF ke el "VM ...........................................

Figu

  Figu e : "VM t ai i g p o ess ................................................................................Figu e : Weight alues fo diffe e t o epts ith diffe e t sa ple size .............

Figu e :

 e Figu e : Weight alues fo diffe e t u e s of AP ..............................................

Figu e :

 e Figu e : Weight a iatio s fo diffe e t u e of i sta es ................................Figu e : Codi g alue of a tio pa a ete s i to i a .........................................Figu e : P o ess of GTC-ased e t a tio ..............................................................

Figu e :

 e Figu e : Ba ha t of eights fo a tio pa a ete s fo Y a d Y ........................

Figu e :

 e Figu e : Ba ha t of eights fo alues of AP ........................................................ Figu e : " ste of o t adi tio ith o te t .......................................................Figu e : P o ess of EP-ased e t a tio ................................................................. Figu e : Ge e al f a e o k fo i e ti e desig p o le sol i g ........................Figu e : P o ess of odel ha ge ..........................................................................Figu e : Dou le Ka a s ste ..............................................................................

  Figu e : a do e pe i e ts esults ............................................................

Figu e :

 e Figu e : GTCs i ol i g all the e aluatio pa a ete s ...........................................

  Figu e : full fa to ial e pe i e ts ...................................................................

Figu e :

 e Figu e : Ge e alized " ste of Co t adi tio ........................................................ Figu e : Ph si al o t adi tio ith o te t ..........................................................

Figu

  Figu e : T o sides of ta get GTC............................................................................. Figu e : Illust atio of suppl i g st ateg ...............................................................

Figu e :

 e Figu e : Co pa iso of pa tial Pa eto f o t of e ol ed a d o igi al odel .......... Figu e : Ka a _ p io it Pa eto s o igi al a do FIFO Pa eto ....................... Figu e : Ka a p io it Pa eto s e ol ed odel Pa eto ................................... Figu e : The Pa eto of A" a d A" fo th ee s ste s "B < . a d "B < . ......Figu e : Co t adi tio of the odel to e used fo i e ti e p o le s ...............Figu e : Bi a output fo ulti-o je ti e opti izatio ........................................

1- 2

 2 .1 I e ti e desig p o le sol i g P o le sol i g is a o o a ti it fo a u e of do ai s, a d its u ial ole i desig is pa ti ula l e og ized i [ ],[ ]. I ge e al, p o le sol i g a ot e disti guished f o p o le fo ulatio . A espe ta le fo ulatio of a p o le ea s app o i ati g a solutio . Ho e e , it is diffi ult to dete i e a ellfo ulated p o le . This o ept p esu es that so e p o le s a e ot ell fo ulated o a e ot eal p o le s. Thus, a uestio the a ises as to hat o stitutes a eal p o le . The diffe e t t pes of a s e s to this uestio a ise f o hete oge eous a s fo ta kli g the o ept of a p o le , its fo ulatio , a d thus, the a to a age its esolutio p o ess [ ]. The eati e o i e ti e desig p o le s e e ide tified as eithe ill-defi ed o ill-st u tu ed 'eit a i [ ]. This defi itio ea s the sta t state of p o le sol i g a ti ities a e ot o pletel spe ified, the goal state ould e ha ged o efo ulated i ti e, a d the t a sfo atio fu tio is also o pletel u spe ified. Mo eo e , Bo a del i [ ] o side s desig p o le s as ei g ope -e ded as the do ot ha e a si gle solutio ut a set of possi le solutio s. Thus, solutio s thesis is a esult of the hoi e of o e solutio f o se e al solutio s. Ofte e little i fo atio ega di g a desig p o le e ists that i di ates p o le sol i g e ui es a sig ifi a t st u tu i g of the p o le itself [ ]. P o le st u tu i g is a p o ess of d a i g upo e te al i fo atio to o pe sate fo issi g i fo atio a d usi g that i fo atio to o st u t the p o le spa e [ ]. The p o ess of p o le st u tu i g egi s ith a i te p etatio of the p o le situatio -defi itio of p o le pa a ete s a d fu tio s. The the ge e atio of desig e ui e e ts a d o st ai ts follo s. These e ui e e ts a d o st ai ts a e used to spe if the desig assig e t i.e., defi i g the p o le spa e as ell as to des i e a d e plo e aspe ts of the desi ed solutio i.e., e plo i g the solutio spa e . As p o le esolutio ai s at de elopi g a ellfo ulated p o le , it is e essa to e su e the e olutio of the fi st u de sta di g of the p o le as ell as the fi st odel of the p o le . Ou goal is the to p opose a ethod i hi h a i itial odel of the p o le ould e ha ged i o de to pu sue its esolutio . The o ept a d odel of p o le a e di e tl li ked to the atu e of the o side ed k o ledge. Thus, i the do ai of p o le sol i g fo te h i al s ste desig s, it is i po ta t to la if the t pe of k o ledge a d odel ele a t to the esolutio p o ess. The i e ti e p o le is a desig p o le that has o solutio ased o the k o o ditio s. I e ti e desig , hi h t ies to sol e the i e ti e p o le s, is a spe ifi a ti it that diffe s f o the t aditio al desig pe fo ed i esea h a d de elop e t depa t e ts [ ]. A i e tio supposes to i e t so ethi g, i.e., to p opose so ethi g e o so ethi g ot k o u til o . I e ti e p o le s a o e a k o field, te h i al o ot, a d spe ifi all so e p i iple, p odu t o fa t ele a t to that field. Desig i g a e te h i al s ste ea s pu si g the e olutio of a te h i al s ste [ ].

  a e used to sol e i e ti e p o le s: opti izatio ethods to opti ize the s ste pa a ete s a d i e ti e ethods to ha ge the p o le odel. The logi al su essio is that opti izatio te h i ues a e used fi st e ause of the atu e of the fo alized p o ess e ui ed fo p o le opti izatio . If o solutio is fou d, the desig e ill eso t to i e ti e sol i g te h i ues, hi h a e u h o e eati e ut ot ell fo alized et. I this thesis, these p o le s, hi h a ot e sol ed opti izatio ethods a d e ui e o e p ofou d ha ges of the odels, ill e o side ed p o le s of i e tio . 'ose a a d Ge o i [ ] p oposed a s ste of desig lassifi atio that de o poses i to th ee diffe e t su g oups ased o diffe e t p o le spa es i hi h p o le esolutio is esea hed a d sol i g ethods a e used to esol e the p o le :

  i o ati e a d eati e desig , i e ti e esolutio tools a e used. Based o the defi itio of eati e desig as a p o ess of sea hi g solutio s e o d the k o desig spa e, a autho s i lude the efo ulatio of desig p o le s i to the p o ess of eati e desig . Diffe e t theo ies ega di g the e pa sio of the p o le spa e a d the p i iples of dete i i g solutio s ehi d this spa e ha e ee p oposed i [ ],[ ],[ ],[ ]. O o e ha d, the theo ies ha e ought a out ha ges i dete i i g the p o le st u tu e as ell as its efo ulatio . Additio all , diffe e t theo ies ha e ought a out the e pa sio a d e olutio of the p o le spa e ased o used sol i g ethods.Bode i [ ] p oposes to e plo e a d t a sfo a o eptual spa e that u ifies a d st u tu es a do ai of thi ki g. E plo atio of this spa e ide tifies the li its a d poi ts he e possi le t a sfo atio s allo e pa di g the sea h spa e su h as e o i g o egati g a o st ai t. Mahe et al. i [ ] p oposed a odel fo desig e plo atio ased o a o putatio al oe olutio of the desig a d solutio spa e usi g a odified ge eti algo ith . The p o le spa e is defi ed as a fit ess fu tio i.e., ep ese tatio of fu tio al e ui e e ts a d the solutio spa e is defi ed as a set of desig ge es i.e., desig solutio s ha a te ized pa a ete s . T o s ste s ill e ol e i espo se to ea h othe , the featu es a d o st ai ts i the u e t solutio e o e e ite ia that edefi e the p o le spa e. This o ept is ased o a ge eti algo ith a d is pa t of e olutio a desig he e the u e t state of the theo is p ese ted i [ ]. Hat huel i [ ] p oposed a theo of e pa da le atio alit he e lea i g de i es ge e ate e p o le s a d o epts that lead to u e pe ted e pa sio s of i itial o epts. He p oposed a u ified desig theo he e the desig p o ess is odeled as a o-e pa sio of t o spa es: o epts a d k o ledge. A othe i te esti g theo as p oposed Do st i [ ]: he e the atu e of desig p o le s as studied ithi the f a e o k of "i o s theo of ill-st u tu ed p o le s a d thei sol i g as ell-st u tu ed p o le s. The desig is ased o the otio s of pa ado a d dis ou se. A pa ado is defi ed as a o ple state e t that o sists of t o o o e o fli ti g state e ts. The odel of pa ado a d dis ou se e ui es a edefi itio of a p o le ati situatio i o de to dete i e a solutio . Dis ou ses a e the ele e ta state e ts that o p ise a pa ado . This ethod des i es the o plete st u tu e of the te s a d elatio ships that lie at the asis of the thi ki g a d dis ussio s ithi a a ea of hu a a ti it .This is uite si ila to the o t adi tio s ithi the T'I) diale ti al app oa h. Altshulle [ ] p oposed the theo of i e ti e thi ki g T'I), hi h ta kles eati e te h i al p o le sol i g. Fo hi , eati it as to fi d a a he e o p o ise ould ot e e og ized as a solutio . The state e t of the p o le is a o plished goals i.e., hat ust e a hie ed a d ea s i.e., ho to a hie ed the goal a d hat ust e do e . The p o le esolutio p o ess ill lead to the a uisitio of e k o ledge, o at least ep ese t the k o ledge ased o a e u de sta di g, i o de to shift f o a p o le pe spe ti e to a ds a solutio fo us. The solutio is sea hed i the desig spa e he e possi le a ia ts of desig p o le s a d the solutio s e ist. The easo h e a ot sol e the p o le is that the e ui e e ts a e i o t adi tio s. Altshulle p oposed a ideal a hi e ith dete i ed pa a ete s as a p otot pe that i di ates the ost p o isi g di e tio to sea h fo a solutio . Te h i al o t adi tio s the i di ate the o sta les that ust e o e o e to a hie e the solutio . 1-2.2 Opti izatio e sus i e tio The goal of ou esea h o k is to fi d a solutio to desig p o le s o si g a desig p o le spa e a d to use oth opti izatio a d i e ti e sol i g p i iples. This p o le spa e is defi ed i [ ] i te s of states of p o le sol i g, he e ope ato s a d e aluatio fu tio s o e the p o le sol i g f o o e state to a othe . We a al ze the app oa hes used diffe e t sol i g ethods to e plo e the p o le spa e, hi h ope ato s a e used fo , a d he e a ade uate solutio to the desig p o le appea s i the p o le spa e. T o t pes of desig p o le s a e suggested. O e the p o le has ee odeled, the opti izatio desig p o le is sea hi g fo alues fo a fi ed set of a ia les. This app oa h p o pts the o je ti es to a i e at a opti al alue ithout ha gi g the odel o oeati e desig . The opti izatio ethods ha e ee p o e to e effe ti e i a situatio s, ut ot effe ti e fo i e ti e desig p o le s that e ui e i p o i g a s ste addi g e a ia les o e elatio ships et ee a ia les. Opti izatio algo ith s o se a spa e of pote tial solutio s, hi h is li ited the stated p o le spa e. If o solutio is fou d, the lassi al opti izatio algo ith s a e ot a le to o ti ue to e plo e the solutio spa e. Fo this ase, the i e ti e sol i g theo T'I) p oposes ethods to ha ge the stated p o le odel the e defi i g a e p o le spa e. Ou app oa h of odel ha ge is ased o the est esults de eloped f o the opti izatio ethods a d ep ese ted the Pa eto f o t [ ]. B o side i g a a it a opti izatio p o le ith k o je ti es, he e all o je ti es a e i i ized a d e uall i po ta t, i.e., o additio al k o ledge a out the p o le is a aila le.

Figu e :

 e Figu e : Illust atio of ge e al ulti-o je ti e opti izatio p o le Follo i g the ell-k o o ept of Pa eto do i a e, a o je ti e e to Y is said to do i ate othe o je ti e e to s if all o po e ts of the o side i g e to a e as good as the o po e ts of othe o je ti e e to s a d at least o e o po e t of Y is ette . A o di gl , e a sa that o e solutio is ette tha a othe solutio , i.e., do i ates , if f do i ates f . He e, opti al solutio s, as defi ed solutio s ot do i ated a othe solutio , a e apped to diffe e t o je ti e e to s. I othe o ds, the e a e ist se e al opti al o je ti e e to s ep ese ti g diffe e t t ade-offs et ee the o je ti es. Ou goal is to go e o d this li it ep ese ted the Pa eto f o t a d o tai esults f o the desi ed o je ti e spa e. Fo this pu pose, e use the est solutio s o tai ed the opti izatio ethods a d issued f o the Pa eto f o t ep ese ti g a o fli t of pe fo a e. As a e a ple Figu e , fo solutio , the e aluatio pa a ete PE is ette tha that fo solutio ; ho e e , the e aluatio pa a ete PE is o se a d i e e sa. This o fli t i the e aluatio o je ti e spa e is a li it e p essed te h i al o t adi tio . This o fli t also ep ese ts a e t poi t to use the diale ti al app oa h ith the ie of o t adi tio o espo di g to this o fli t as sho i Figu e . The su se ue t uestio is to dete i e ho to t a slate this o fli t th ough the sea h spa e s ste pa a ete s, hi h o espo d to the ph si al o t adi tio ithi the T'I) theo .

Figu

  Figu e : OT"M-T'I) s ste of o t adi tio Note that du i g the e olutio of T'I) ethodolog , te h i al o t adi tio s fi st appea ed i o ju tio ith suita le solutio tools. "u se ue tl afte a u e of ea s, the o eptio of ph si al o t adi tio a ose ith a e fa il of solutio tools. Fo Altshulle , the ph si al o t adi tio efle ted a deepe o t adi tio i the se se of diale ti s. The assu ptio is that ehi d e e te h i al o t adi tio as hidi g a o e fu da e tal ph si al o t adi tio .

Figu

  Figu e : TC a d PC i the o te t of opti izatio p o le spa e The Figu e illust ates the te h i al a d ph si al o t adi tio i the o te t of the opti izatio p o le spa e. The te h i al o t adi tio appea s i the o je ti e spa e as a o fli t et ee t o e aluatio pa a ete s hile the ph si al o t adi tio appea s i the de isio spa e a d e p esses the fa t that the a tio pa a ete X should ha e t o diffe e t alues a d at the sa e ti e to satisf Y a d Y f ,f .

  Figu e : Ge e alized " ste of Co t adi tio A othe ad a tage of the ge e alized te h i al o t adi tio is that it idges the ulti-opti izatio a d o t adi tio as sho i Figu e . Co t a to the lassi al T'I) o t adi tio s hi h a ou t fo just t o EPs, the ge e alized s ste of o t adi tio s o side s additio al e aluatio pa a ete s a d defi es the alidit of the o te t of o t adi tio s th ough the alues of the othe a tio pa a ete s.

(

  of satisfying (y1,y2) or y3 Experiment set satisfied (y1,y2) or y3 Action Parameter set of dissatisfying (y1,y2) or y3Experiment set dissatisfied (y1,y2) and y3

  Figu e : App oa h fo odel ha ge O e e pe i e ts ha e ee pe fo ed a d o satisf i g solutio as dete i ed opti izatio ethods, the e pe i e tal data se es as a i put i to the sea h of o t adi tio s. The o t adi tio s should e sol ed to o ti ue the p o le e olutio esulti g i ha ges to the s ste odel i o de to satisf the usto e s e ui e e ts. Fi st, the GTCs a e e t a ted usi g the p oposed e hausti e sea h algo ith . As the u e of GTC a e e la ge, the uestio of sele ti g the GTCs fo o side atio is u ial. We p opose to hoose the GTCs that a e uilt f o poi ts situated o the data Pa eto f o tie , i.e., the GTCs that a e ot do i ated a othe poi t. O e a GTC is sele ted, the elated ge e al ph si al o t adi tio s a e sea hed. A se o d algo ith fo GPC e t a tio should e used i o de to o plete the s ste of o t adi tio s. The the G"C is sol ed T'I) i e ti e sol i g ethods.

  Ta le : Classi al T'I) o t adi tioThese details i di ate the ge e i aspe t of the G"C, hi h e a les defi itio u de e tai o ditio s of e isti g T'I)-ased o t adi tio s. The lassi al T'I) odel of o t adi tio is st aightfo a d to sol e as it is easie fo a hu a e pe t to Y1 Y2 x1 … xg … xn ys yu yw … yh ei et. Ho e e , the G"C is o e diffi ult to i te p et a d sol e, the e p ese ti g a p o le ati situatio fo hi h o solutio is k o .

  The at i is di ided i to i e lo ks, a d i Ta le , e ha e fo ulated the featu es i to lo ks. I the lo ks he e E × Y a d E × Y ; all of the ele e ts a e e ual to . I the e ai i g lo ks asso iated ith Y a d Y , the e ust e at least o e ele e t e ual to ze o i ea h o .

Figu e :

 e Figu e : Ge e i at i ) a a d a e a ple The o s of the at i ep ese t the e pe i e ts hile the olu s o espo d to the e aluatio pa a ete s. The ge e i te zij of at i ) e uals he the e pe i e t ei eets the desig e ui e e ts fo the e aluatio pa a ete j othe ise zij e uals ze o. The desig goal is to satisf all of the e aluatio pa a ete s, i.e., to fi d a o of o es. Whe it is ot possi le to o tai su h a output usi g o l the a tio pa a ete s, i e ti e ethods ust the e



  At least o e e aluatio pa a ete f o the fi st set of pa a ete s Y that is ot satisfied i ea h e pe i e t of the se o d a d thi d set of e pe i e ts E a d E . Ta le : Ge e alized te h i al o t adi tio e p essed i e pe i e tal ta le Ta le sho s the at i of the e pe i e tal ta le de i ed g oupi g the olu s a d the o s. The at i has ee di ided i to lo ks, a d i the ta le, e ha e fo ulated the featu es i to lo ks. I the lo ks E ×Y a d E ×Y , all of the ele e ts a e e ual to . I the e ai i g lo ks asso iated ith Y a d Y , the e ust e at least o e ele e t e ual to i ea h o .

  othe as possi le thei pe utatio s. The the se iated ta le o i age e eals a st u tu e that de o st ates the elatio ship et ee the a ia les. The o ept of se iatio is uite si ple ut i its ge e al fo is diffi ult to i ple e t it o a o pute . I ou ase e a use the uasi-se iatio ethod of t o lasses he e the esiduals defi e Y a d the t o lasses defi e Y a d Y . This e ai s the lo k se iatio ethods [ ], hi h sea hes si ulta eous pa titio of o je ts o e pe i e ts a d att i utes o a ia les .The p i iple is ased o the pe utatio of the o s a d the olu s of a i a ta le i o de to ide tif the diago al disjoi t lo ks fo a i al de sit . We a also ite also the at i eo de i g p o le s, hi h seek to eo de o je ts i to a se ue e alo g a o e-di e sio al o ti uu [ ] e plo ato o i ato ial data a al sis te h i ues. The se iatio ethods a e elated to luste a al sis [ ]. Cluste a al sis is the o ga izatio of a olle tio of patte s -o se atio s usuall ep ese ted as a e to of easu e e ts, o a poi t i a ultidi e sio al spa e i to luste s g oups ased o si ila it . T pi al luste i g i ol es the patte ep ese tatio featu e e t a tio , defi itio of patte p o i it easu e, the p ope luste i g g oupi g a d e e tuall data a st a tio a d assess e t of output. Cluste i g is a su je ti e p o ess; the sa e set of data ite s ofte eeds to e pa titio ed diffe e tl fo diffe e t appli atio s. This su je ti it akes the p o ess of luste i g deli ate. Diffe e t t pes of luste i g ethods e ist su h as hie a hi al luste i g; K ea s luste i g; o t o ode luste i g [ ],[ ]. The k-ea s algo ith assig s ea h poi t to the luste hose e te is the ea est. Fo ou pu pose, t o-ode luste i g a e used he e the o je ts a d the featu es of the o je ts a e luste ed. This ethod p o ides a si ulta eous luste i g of the o s a d olu s of a e ta gula data at i ut a ot est i t othe pa ts of the at i Blo k odeli g [ ] deals ith the luste i g of a et o k. The goal is to edu e a la ge, pote tiall i ohe e t, et o k i to a s alle o p ehe si le st u tu e that a e o e eadil i te p eted. Blo k odeli g is ased o the idea that u its ithi a et o k a e g ouped ased o the e te t to hi h the a e e ui ale t,a o di g to so e ea i gful defi itio of e ui ale e. O e of the ai p o edu al goals of lo k odeli g is to ide tif luste s o lasses of u its that sha e si ila st u tu al ha a te isti s i te s of e ui ale e elatio . This ethod is ased o the g aph theo , a d spe ifi all o elatio s of do i a e et ee diffe e t u its. T o t pes of su h elatio s a e disti guished: st u tu al e ui ale e a d egula e ui ale e. I the fi st ase of st u tu al e ui ale e, the e ui ale t u its ha e the sa e o e tio patte to the sa e eigh o s. Fo the ase of egula e ui ale e, the e ui ale t u its ha e the sa e o si ila o e tio patte to diffe e t eigh o s. Fo ou ase, st u tu al e ui ale e ith o plete lo ks of o es should e sea hed. All a aila le ethods asso iated ith the a o e e tio ed app oa hes a e used to fi d o e o se e al u i ue solutio s to ou p o le . Ho e e , ot o e ethod a e used to fi d all the solutio s. I this pape , e use the i a i tege p og a i g odel to a al ze ou p o le . This esults i a spe ifi algo ith that p o ides all the solutio s fo ou p o le .

  goal is to fi d all of the -pa titio s of the olu set a d -pa titio s of the o set that eet the e ui e e ts i di ated i Ta le .Ta le : G"C ep ese tatio i e pe i

Fi..

  If o e e to o po e t of C esp. C e uals , the o espo di g olu elo gs to the olu set Y esp. Y ; othe ise, it does ot elo g to Y esp. Y . "e o d, e use t o M-di e sio al i a e to s ' i= , to de ote the t If o e e to o po e t of ' esp. ' e uals , the o espo di g o elo gs to the o set E esp. E . The e to s a e as follo s:

2 YE

 2 to ze o a d egati e othe ise. It a e dete i ed f o a al sis, the a i u alue of this e uatio is ze o. The est i tio fo the lo k 1  sho o Ta le i di ates that the a di alit of 1 Y is g eate tha the su of the ele e ts i ea h o of the lo k 1 2 Y E  . Thus, e ha e the i e ualities fo ea h o of

  th ee additio al g oups of i e ualities. It should e oted that the e e ship of a o to 0 E is dete i ed the o ple e ta set

Figui

  Figu e : "u -p o le lo ks i at i )

  esults of the su -p o le s a e gathe ed, it is e essa to o i e the lo ks to sol e the o igi al p o le . The o i ato ial st ateg is to e a i e all o i atio s of the t o esults of the su -p o le s ased o the follo i g ule: If the i te se tio of thei o sets a d olu sets a p o le . The o e t ess of the st ateg is ased o the assu ptio that if the solutio sets of t o p o le s i lude ea h othe , the a e e ual. 2-2.3 P o le esolutio e hausti e sea h algo ith 2-2.3.1 "ea h algo ith fo the su -p o le We o des i e the ethod fo add essi g the su -p o le . The patte a e sea hed alo g the olu s a d o s. As ou p o le has a est i tio ega di g E , e sea h the lo ks o o .

3.

  Figu e : Flo ha t of algo ith

  le , e a e a a e that ith the o st ai of the E uatio , the x = r c . Ta le : T uth ta le fo , We a pe fo the sa e t a sfo atio fo r c . "u se ue tl , ou p o le has e o e a i a p og a i g p o le a d a e sol ed the use of a a ha d-ut algo ith [ ]. Ho e e , at e tai ti es the e a e e ui e e ts fo the u e of e aluatio pa a ete s i ol ed ithi the GTC. As dis ussed i [ ], a p oposed GTC sele tio p i iple i i ize the a di alit of Y . Thus a e uatio a e added i the o st ai ts to est i t the u e of e aluatio pa a ete s:

  Figu e : Co po e ts of ele t i al i uit eake a d the s he e The p o le has ee studied a d the ai s ste pa a ete s a d thei do ai s ha e ee defi ed as a tio pa a ete s:

  Figu e : E a ple of false lassi al TC a a d GTC The fi st set of e pe i e ts o e ed the sea h of ge e alized te h i al o t adi tio s i the ase of a ele t i al i uit eake Figu e . We ide tified ge e alized te h i al o t adi tio s ithi the possi le pai s of o epts. As a e a ple, e dis uss fou diffe e t GTCs, hi h a e i te p eted as follo s. GTC # ep ese ts the o t adi tio et ee the i uit eake eusa ilit a d oth the sp i g o e ou ti g a d o al ode elease . GTC # ep ese ts the o t adi tio et ee the follo i g pai s of pa a ete s: the i uit eake eusa ilit a d o al ode elease a d the ouple i uit eake dis epai a d sp i g o e ou ti g . GTC # ep ese ts the o t adi tio et ee the ouple i uit eake eusa ilit a d fi i g pi i itial positio etu a d the ouple sp i g o e ou ti g a d o al ode elease . Fi all , GTC # ep ese ts the o t adi tio et ee the ouple i uit eake eusa ilit a d fi i g pi i itial positio etu a d the est of the e aluatio pa a ete s.

Figu

  Figu e : E a ples of GTCs i the ase of ele t i al i uit eake

  Figu e : TC/ GTC u e e sus de sit fo ge e al at i es

  Figu e : P i ipal effe ts of fa to s a a d thei i te a tio s fo TC

  Figu e : P i ipal effe ts of fa to s a a d thei i te a tio s fo GTC

  Figu e : " atte plots of lo k u e s

  Figu e : P i ipal effe ts of fa to s a a d thei i te a tio s fo lo k u e

I

  Figu e : Ge e alized s ste of o t adi tio

  Figu e : Ge e alized s ste of o t adi tio s fo the e a ple Looki g fo a ge e alized ph si al o t adi tio fo the G"C, as ep ese ted i Figu e , ea s sea hi g fo t o Co epts su h as: Co ept A ,A ,A ,A ,A  = . = .[ = + = + = ]= Co ept A ,A ,A ,A ,A  [ = + = ]. = . = . = = Whe t i g to fo ulate the o t adi tio , o e a easil e og ize that o lassi al T'I) ph si al o t adi tio e ists. E e if A al a s e uals i e pe i e ts of E , a d e uals i these of E , it does ot fit the o ditio . We ha e the o ditio A =  [ = + = ]. = . = . = = ; ho e e , it does ot fit the o ditio A =  = . = .[ = + = + = ]= as fo e pe i e t e , A = he eas = . = = . A si ple a to fo ulate the t o o epts is to o side the odels fo ed the o side atio of all the a aila le k o ledge of e pe i e ts of E o E . The , he

  hi h is the sa e fo Co ept , i.e., a o ept uilt ith the fi e e pe i e ts e , e , e , e , a d e . Ho e e , su h a ep ese tatio , e e if it is e a t, is ot e essa il the o e app op iate to path leadi g to esolutio . A e e o e si plified e p essio ould o side ed fo the t o o epts: Co ept A ,A ,A ,A ,A = A = . A = a d Co ept A ,A ,A ,A ,A = A = . A = . This o t adi tio is a e o e ea i gful fo the e pe ts a d a p o ide guida e to a ds a o ept solutio o side i g the diffe e e fo Co ept , he e o l A = . With ega d to Ta le , it is ele a t as the p e ious fo ulatio ; ho e e , ith ega d of the o side ed de isio esea h spa e, the fi st fo ulatio as o e o st ai ed. The efo e, this poi ted to a ds a o e a o ed esea h spa e. A u e of GPC a e fo ulated fo o e o side ed GTC; the efo e, the uestio ises of hi h o e is o e ele a t to o side fo esolutio of the p o le s. To e a le to a s e this uestio , the fi st p o le to sol e, hi h is p ese ted i this hapte , is to list all the possi le GPCs o to ha e a s theti o e ie of the . 3-2 Fo ulatio of the BIP p o le a d the e hausti e sea h algo ith As see p e iousl , the e a e a o ept a didates fo elo gi g to a GPC. To seek a possi le GPC, e eed to e a le to ep ese t a ge e al shape of the o ept that allo s sea hi g fo a o ept elo gi g to a GPC. I this se tio , e p opose a pa a et i fo of o ept pa a ete s, hi h a e e ui ed to e if a set of i a e uatio s to defi e a ad issi le o ept of the GPCs. This set of i a e uatio s ill defi e the set of ad issi le o epts. Ho e e , as this set a e e la ge, it a ot e si ple to list all o ept solutio s o e e fi d all of the . To add ess this p o le , spe ifi p ope ties a e used fo the sea h p o le . It a e sho that o e spe ifi GPC a su a ize all possi le GPCs. The sea h p o le fo this spe ifi GPC a the e o tai ed addi g a o je ti e fu tio to the p e ious set of e uatio s; thus, this sea h esults i sol i g a t a ta le i a i tege opti izatio p o le .

Fo;

  Figu e : "ea hi g p o ess of t o o epts The o putatio o ple it of o ept sea hi g The ti e o su ptio fo a full fa to ial e pe i e t o espo ds to t o pa ts. The fi st pa t is to e o e the states i E +E a d E +E . Thus, the o putatio ti e is × | + | + | + | . The se o d pa t i ol es o pa i g the states f o t o o epts. It a ot e k o the e a t u e of states fo the t o o epts. Ho e e , the e is a uppe ou d s a d lo e ou d . Thus, the o pa i g ti e is a ges f o to s . Based o t o pa t ti e o su ptio , s has a de isi e ole i the ti e o ple it as follo s: s i fa t is the u e of states: = [∏ + =

  Figu e : Illust atio of the lassi al ph si al o t adi tio The o te t of o t adi tio des i es a a kg ou d of the o t adi tio . It is o e like supe s ste of the o fli t pa a ete , hi h is the e i o e t of o fli t ele e t. As the ph si al o t adi tio i Figu e , the e i o e t is A = A = , the o fli t is A = s A = . If e ha ge the e i o e t, the o t adi tio o o l ha ges.

Figu e :

 e Figu e : Wit ess odel of the p o ess The i e to is o t olled a Ka a s ste , ased o a t pe of eo de poi t s ste . The alue of the eo de poi t is itte o the Ka a a d. The o de ua tit is also itte o the Ka a a d. Whe the i e to le el is lo e tha the eo de poi t, the Ka a a d is se t to the supplie . Goods a e deli e ed ith

Figu e :

 e Figu e : Pa eto f o tie of the i itial si ulatio

  -fou states e e e t a ted fo Co ept , states fo Co ept . Thus, the e a e , GPCs ith o te t, of the o l i ol e o e a tio pa a ete o fli t. I o de to fo ulate the s ste of o t adi tio s, a o g all these o t adi tio s, o l t o states ha e ee o side ed fo fo i g the ph si al o t adi tio . These t o states o espo d to the t o e t e e poi ts of the Pa eto f o tie , i.e., the o es taki g sepa atel the est alues of ea h e aluatio pa a ete s. The a e the state e uatio s of 'eo de Poi t = Lot size = s ap ate = s 'eo de Poi t = Lot size = s ap ate = . The s ste of o t adi tio s that has ee e t a ted out of the e pe i e ts is p ese ted i Figu e .

Figu

  Figu e : GPC a d its o te t elated to the i itial Ka a s ste This o t adi tio stated that a lassi al T'I) ph si al o t adi tio e ists if the a tio pa a ete s eo de poi t a d the supplie s ap ate a e espe ti el fi ed at u its a d %. As a esult, the lot size has to e to a hie e a a e age sto k of u its, ut it has to e i o de to satisf a se i e eakdo of %.

g

  eat pote tial to e i p o ed. The GTC e t a tio p o ides the i fo atio a out the u e of e pe i e ts i the sets E a d E . The uestio is if this has a effe t o the GPC e t a tio ? I o de to a s e this uestio a d i estigate the elatio et ee the u e of the ph si al o t adi tio s a d o espo di g GTC, e p oposed t o g oups of full fa to ial e pe i e ts. The fi st g oup is to stud the elatio et ee the u e of states a d the u e of e pe i e ts i E a d E . The se o d g oup is to stud the elatio ship et ee the u e of states a d the u e of ph si al o t adi tio s. The se o d g oup is also eo ga ized i the last se tio to p ese t the elatio et ee u e e pe i e ts a d the u e of lassi al ph si al o t adi tio ith o te t.

  Figu e : 'elatio et ee u e of states a d e pe i e ts APs The follo i g e pe i e ts a e si ila to p e ious e pe i e ts. Additio all a d Bi a a tio pa a ete s e e pulled. The e a do l sele ted the sa e pe e tages of u e of e pe i e ts i o de to stud the a iatio of the u e of states. F o Figu e a d Figu e , the fitted li e e ealed that the u e of states a d pe e tage of e pe i e ts i ol ed i the o ept has a u i pol o ial elatio .

  Figu e : 'elatio et ee u e of states a d e pe i e ts APs O e all, e a o lude that ith a i ease of the pe e tage of e pe i e ts, hi h is o p ised i the o ept, the u e of states e pe ie es a u i g o th.It suggests that he e hoose GTC, if e a t to hoose a GTC i hi h o epts has a o e states, e eed to hoose the o e t o i atio of E a d E ased o a la ge u e of e pe i e ts.

  Figu e : Li k et ee u e of lassi al PC a d p odu t of "tates a d The elatio of the u e of lassi al ph si al o t adi tio is a li ea p opo tio of "tate * "tate . Additio all , ea h "tate is a u i p opo tio to the u e of e pe i e ts o pe e tage asso iated ith the o ept. He e, e a p o ide a esti atio that the u e of lassi al ph si al o t adi tio s is ased o a u i p opo tio of the u e of e pe i e ts i E a d E .

  Let us o p o ide so e highlights a out the ed li e that leads us to use featu e sele tio odel fo add essi g the p o le stated a o e. Let us o side a e a ple he e the e a e th ee a tio pa a ete s A , A , A a d t o e aluatio pa a ete s de oted EP a d EP . A set of eight e pe i e ts de oted e , …,e , the esults of hi h a e p o ided i the i a ta le i Figu e , is pe fo ed o the s ste . I this ta le, positi e o e alues of the EP a d EP olu s ea that the alues of EP o EP satisf the e ui e e t fo the gi e e pe i e t. 'e e sel ze o alues of the EP a d EP olu s ea that the alues of EP o EP do ot satisf the e ui e e t fo the gi e e pe i e t. I ou ase, e pe i e ts f o E = {e , e , e } satisf EP ut ot EP ; those f o E = {e , e e } satisf EP ut ot EP ; a d those f o E = {e , e } do ot satisf a e ui e e t. The sets E a d E defi e the do ai of e pe i e ts he e the te h i al o t adi tio TC a d TC eside.

Figu

  Figu e : Bi a ta le a d o t adi tio odel Let us o o side the a tio pa a ete s. The o es a d ze o alues i the ta le of Figu e efe to t o diffe e t le els of the a tio s pa a ete s du i g the e pe i e ts. O e a e a k that Co ept is a fu tio that dis i i ates e pe i e ts f o E f o the e ai i g set E +E . Like ise, Co ept is a fu tio that dis i i ates e pe i e ts f o E f o the e ai i g set of e pe i e ts E +E . The ide tifi atio of the pa a ete s that allo s lassif i g ele e ts i to t o disjoi t sets is k o as the featu e sele tio p o le i se e al esea h a eas. The p oposed sea h p i iple of the pa a ete s i ol ed i te h i al o t adi tio s is ased o featu e sele tio fo the lassifie . The e isti g featu e sele tio algo ith s a e good sta ti g poi ts fo add essi g ou a tio pa a ete sele tio p o le . The e t se tio p o ides a ui k o e ie of the featu e sele tio algo ith s.

-

  Algo ith s of featu e sele tio : o e ie a d hoi e a al sis a d ge e a al sis. As the a e suggests, the featu e sele tio task o sists of sele ti g a opti al su set of featu es a o di g to a e tai ite io i o de to i p o e the a u a of the lassifi atio p o le . The tasks also a e e su i g the data i i g algo ith s o k faste o lage size data, the e p o idi g a ette u de sta di g of the i ed esults [ ],[ ]. The hole p o ess of featu e sele tio depi ted i Figu e ai l i ludes th ee steps: ge e atio p o edu e, e aluatio fu tio a d stoppi g ite io . Ge e atio p o edu e is to ge e ate a su set of featu es fo e aluatio . E aluatio fu tio is a fu tio to e aluate the ade ua of a featu e su set p odu ed ge e atio p o edu e. The stop ite io de ides he to stop the esult f o the e aluatio fu tio a d a oids e hausti el sea hi g the e ti e su set spa e. The last step alidatio i Figu e is ot a pa t of the featu e sele tio p o ess itself, its o je ti e is to test the alidit of the su set sele ted the featu e sele tio algo ith .

  Figu e : Co pa iso of o igi al a d appi g featu e spa e I [ ], "VM as lassifie fi st ti e o t i uted to featu e sele tio p o le i a e lassifi atio p o le , its a hie e e ts e phasize o the esti atio of ea h ge e, a d adopted e u si e eli i atio to a k featu es "VM 'e u si e Featu e Eli i atio , "VM-'FE . To e spe ifi , the esti atio of "VM is ased o the eight oeffi ie t of li ea lassifie i t a sfo ed spa e. Fo i te p eti g the eight oeffi ie t, e assu e that the li ea lassifie has the ge e al fo of   b x w i i

-

  Algo ith s of featu e sele tio : o e ie a d hoi e "u je t to

  opti izatio p o le , W is the eight e to of fi al de isio fu tio egati e sla k a ia les fo o -sepa a le situatio . C is the pe alt pa a ete fo p ese ti g the eight of a outlie i o -sepa a le situatio . Ea h o st ai t is uilt f o the gi e i sta e. The eight e to W is the e aluated alue of the featu es. 'ega di g the opti izatio p o le sol i g, it a e t a sfo ed to a o e uad ati p og a i g p o le a d e sol ed [ ].

  Output the eight W as the e aluatio of ea h featu e. I ega d to the "VM e u si e featu es a d eli i atio algo ith i [ ], the eight alue of W is used fo a easu e of a ki g. It e o es the s allest te s of a solute alue afte ea h t ai i g "VM, the the i e ted o de ould sho o the o de of e o i g. I te p etatio of W as a e aluatio of featu e: th oughout li ea de isio fu tio  of ea h o po e t of x pla s a sig ifi a t ole i de isio aki g, if a solute alue of eight is la ge, the o espo d featu e ix ha e a la ge o t i utio i the sig of   X D , hi h de otes the fi al de isio . I the e t se tio , e ill p ese t ho to i te p et the eight fo a ki g the a tio pa a ete a d u de sta d the ea i g of positi e a d egati e eight ased o the De isio fu tio  theo eti al odel e did de elop tools fo a ki g the APs e plai i g the pe fo a e of ea h EP sepa ati g the pe fo a e i t o lasses: good a d othe s. This allo s uildi g a st ateg of sele ti g APs ased o the EPs. This odel also allo s usi g the t o sets of t o lasses defi ed a gi e GTC, a d uildi g a se o d st ateg of sele tio of the APs. Ne t it allo s fo p o idi g a o e algo ith that is p ese ted fo a ki g the AP elated to ea h EP. The p a ti al ules fo usi g the outputs of this algo ith a e the dis ussed. The sa e algo ith ill e used fu the i this hapte fo a ki g the APs elated to a gi e GTC. Mo eo e , this algo ith ill e applied fo sele ti g a d a ki g the alues of ea h AP. Fi all e ill sho t o st ategies fo usi g this algo ith ithi the GTC e t a tio o te t. 4-3 P oposed o e "VM algo ith fo a ki g the APs elated to ea h EP This se tio sho s ho the "VM featu e sele tio ethodolog as applied to p o ide a luste i g a d a a ki g of the a tio pa a ete s. This ill allo the use to sele t the APs that a ea h the desi ed alue fo ea h EP sepa atel . The luste i g sepa ates the AP i t o g oups of AP: the APs that positi el i flue e EP to a ds the desi ed esult, a d se o d, the APs that egati el i flue e EP to a ds the desi ed esult. If e a e o l o e ed ega di g the i flue e ithout positi e d egati e, the set of APs a e a ked usi g the o e i flue i g pa a ete to the less i flue i g pa a ete e ause of eights p o ided the algo ith . The a to use the output fo ou p o le is dis ussed i se tio -.We p oposed to sele t 'BF ke el a d use a e isti g C++ li a fo this ke el [ ],

Figu e :

 e Figu e : Ge e al "VM odel To su a ize, the alues of Xi a d Yi a e p o ided as i puts a d the C a d a e defi ed The "VM ill p o ide the eights that a e useful fo ou pu pose. It also p o ides othe outputs a d  that a e i p a ti al fo ou pu pose. The e ai i g se tio e plai s a d illust ates ho to appl the ge e i p o ess fo ou ase i fi e steps as depi ted i se tio -. fo ou ase. We shall illust ate the ge e al p o edu e ith the e a ple of Figu e . I this ase the e a e fou a tio pa a ete s A ,A ,A ,A , fou e aluatio pa a ete s EP , EP , EP , EP , a d te e pe i e ts e ,e ,…,e .

Figu.

  Figu e : A e a ple fo AP sele tio I this se tio e fo us o a p o edu e p o idi g the APs elated to o e EP. Thus, e use a e a ple EP . We ould like to dete i e the APs e ui ed to e ai tai ed fo e plai i g the alues of EP a d a k the . Both luste i g a d a ki g ill e p o ided the eights p o ided the "VM featu e sele tio p o edu e. I deed

Figu

  Figu e : "VM t ai i g p o ess Whe pe fo i g the a o e p o ess fo EP o the e a ple of Figu e , the i sta es fo EP a e A ,A ,A ,A ,EP of e pe i e ts e ,e ,e ,e ,e ,e ,e ,e ,e ,e . The th ee-fold oss-alidatio as pe fo ed, a d he C= a d = . , the oss-alidatio a u a is %. The eight e to e aluati g the AP fo EP is p o ided i the EP o of Ta le . Whe epeati g the

  Figu e : Weight alues fo diffe e t o epts ith diffe e t sa ple size F o Figu e , e ould also o tai a othe esult ith the i easi g of the sa ple size he e the eight diffe e e et ee diffe e t dis i i ati e-le el of pa a ete s as isi g. Fo i sta e, i Figu e , e a see that the gap of eights et ee A a d A fo the sa e sa ple size e e e pe di g ith a i easi g of sa ple size. This esult suggests to us the sa ple size has a positi e effe t o i te sif i g the dis i i ati e a ilit of the positi e i flue t pa a ete s. Ho e e , a othe p o le a ose a out ho a e pe i e ts e eeded to pe fo to e su e that the eight diffe e e is la ge e ough to e e og ized. This p o le esulted i a se o d g oup of e pe i e ts he e the APs, APs, APs a d APs ith i a alue e e defi ed. That ea t the e pe i e tal spa e as

Figu e :

 e Figu e : Codi g alue of a tio pa a ete s i to i a

  t o st ategies to edu e the u e of a tio pa a ete s a d thei u e of diffe e t alues ased o "VM algo ith fo GPC e t a tio . The fi st st ateg is ased o the i fo atio p o ided the GTC, he e e eight the a tio pa a ete s fo the t o sets of e aluatio pa a ete Y a d Y ot Y as defi ed the GTC. The se o d is ased o the i fo atio p o ided ea h e aluatio pa a ete , he e e eight the a tio pa a ete s fo ea h e aluatio pa a ete . 4-6.1 GTC ased e t a tio As Chapte des i ed, GTC has t o set of e aluatio pa a ete s, Y a d Y , su h as i Ta le , Y = { , }, Y = { , , }. As des i ed i Ta le , GTC di ides the e pe i e ts i to E , E a d E . Y is satisfied E , a d eje ted E ∪ . Y is satisfied E , a d eje ted E ∪ . Ou pu pose is to sele t the ost positi e eighted a tio pa a ete s a d thei alues. These ill ha e the ost positi e effe t o satisf i g the e aluatio pa a ete s of Y o Y , a d the e t a t the GPC f o the sele ted a tio pa a ete s a d its alues. Ta le : E pe i e t esult of ele t i al i uit eake The lass la el is ot o e e aluatio pa a ete ut the e aluatio pa a ete set Y a d Y , as Y is satisfied the e pe i e ts of E , a d eje ted e pe i e ts of E ∪ . The e , fo lass la el el the e pe i e ts i E as , a d e pe i e ts i E ∪ as . The "VM should p o ide the a tio pa a ete s i ol ed i o ept . The sa e thi g is fo Y he e fo the lass la el is la el the e pe i e ts i E as ith the e pe i e ts i E ∪ as . The , "VM should p o ide us the a tio pa a ete s i ol ed i Co ept of the s ste of o t adi tio s. Afte defi i g the e pe i e ts a d lass la el as ell as, i sta es of e ould sta t ou p o ess, hi h is p ese ted i Figu e .

Figu-

  Figu e : P o ess of GTC-ased e t a tio The fi st step is the eighti g a tio pa a ete fo Y a d Y . We de elop a e a ple i Appe di of e pe i e ts that e e a do l ge e ated; te i a a tio pa a ete s a d fou e aluatio pa a ete s. I o de to e plai the p o ess, e took a e a ple he e the a tio pa a ete s a d alues a e k o . The o epts fo e aluatio pa a ete a e p ese ted elo : EP = A = A = A = EP = A = A = A = EP = A = A = A = EP = A = A = A = EP = A = A = A = ea s that he A = a d A = a d A = , the e aluatio pa a ete is satisfied, a d de oted .The ta get GTC is p ese ted the shaded ells he e Y is {EP ,EP } s Y is {EP , EP } i Appe di . We pe fo the fi st step of eighti g the a tio pa a ete to Y a d Y , ith the eights p ese ted i Ta le .Ta le : Weights fo a tio pa a ete s

  A = ,….,A = ,A = }, fou e aluatio pa a ete s {EP , EP , EP , EP }. The eights a e sho i Ta le . Ta le : Weight at i of alues of a tio pa a ete s fo the e a ple As eights of a tio pa a ete s, the a ha t fo Y a d Y a e sho i Figu e . 'ega di g the alue sele tio , e also follo ed se e al p i iples:  O l o side the alue ith positi e eight fo Y a d Y . Fo e a ple i Ta le , the alue set " fo Y is {A = , A = , A = , A = }. The alue set " fo Y is {A = , A = , A = , A = }.

( a )

 a Figu e : Ba ha t of eights fo alues of AP The fo th step is to pe fo full fa to ial e pe i e ts fo the edu ed s ste . The pa a ete s e e e t a ted f o o e set of e pe i e ts. We ade su e that the si plified eal o si ulated s ste s still p o ide the GTC a d the GPC fo hi h e eed. I o de to pe fo the e pe i e ts, it is e ui ed to p o ide a fi ed alue to {A , A , A , A }. The uestio is the hat alue should e gi e to the .

  Fo e a ple, A has a eight of . fo Y , hi h e ui es A = . O the othe ha d, A has a eight -of . fo Y , hi h e ui e A = . Afte ala i g the satisfa to a d dissatisfa to to Y a d Y , as . is o e tha . , e fi A = .

"e e

 e Figu e : " ste of o t adi tio ith o te t What is the o t i utio of ou ethod i o t adi tio fo ulatio i this ase? The e a e o l t o e pe i e ts i the fo ulatio of o t adi tio . Ca e just sele t t o e pe i e ts espe ti el f o E a d E i Appe di to fo the sa e o t adi tio ? The a s e to this uestio is o. We ha e he ked E a d E , a d the o l o e o e of the t o e pe i e ts. Thus this o t adi tio ould ot e o tai ed f o the i itial set of e pe i e ts. If e had a othe a do set of e pe i e ts, it a e e happe that o e of these t o e pe i e ts elo g to the sa ple of e pe i e ts set. Ho e e ith the p oposed "VM ethodolog e ould ha e fou d it. The se o d o t i utio of this app oa h o e s the oise p o ided the a ia les a d alues that e e e o ed this ethodolog . Thus, the ethodolog filte s p o ides u usa le ph si al o t adi tio s. Let us e plai . If e a do l sele t

Figu

  Figu e : P o ess of EP-ased e t a tio

  eighted o t i utio . Based o the eight p o ided the "VM app oa h, e p oposed to ake a sele tio of a tio pa a ete s a d thei alues as to si plif the s ste that edu es the o putatio al o ple it of the GPC e hausti e sea hi g algo ith . Based o this tool, hi h a ha dle se e al thousa ds of APs, t o st ategies e e p oposed i this hapte : GTC-ased GPC-e t a tio a d e aluatio pa a ete s ased GPC-e t a tio . Fo GTC-ased e t a tio , the sele tio of a tio pa a ete s a d alues e e o ie tated to a ds the t o-side of ge e alized te h i al o t adi tio Y a d Y ; he eas the e aluatio pa a ete ased e t a tio o ie tated to a d ea h e aluatio pa a ete . I o de to ette i te p et ou ethodolog , a dou le Ka a ase stud ill e illust ated i the e t hapte , the e ti e p o ess ill e i t odu ed ased o the GTC e t a tio , GPC e t a tio a d a tio pa a ete s sele tio . Fo this ase, solutio f o T'I) ill e p oposed, a d o pa ed ith e pe ts solutio a d o igi al s ste . We a see the Pa eto of the e ol ed s ste f o T'I) solutio o e the Pa eto of the o igi al s ste a d e pe ts p oposed s ste i the e t hapte . The pa a ete sele tio ethod p oposed i this hapte has a o t i utio to a s e Q , ho a e e t a t the ele a t o t adi tio s ithout e hausti e esea h, e ause the sele tio p o ess filte s a u i po ta t a tio pa a ete s so that a states f o these a tio pa a ete s ha e ee e o ed, like thee a ple i -. , e fi ed a tio pa a ete {A = ,A = ,A = ,A = }, that ea s e a tuall e o e the states i hi h { A = ,A = ,A = ,A = }. Chapter 5 P o ess of i e ti e p o le sol i g This hapte fi st p ese ts a ge e al f a e o k of the i e ti e desig p o le sol i g p o ess, hi h i teg ates si ulatio , opti izatio , a d T'I) ased ethods. "e o d, a ase stud dis ussi g a dou le Ka a s ste illust ates ho the algo ith s p ese ted i hapte s , a d a e used ithi the p e ious ge e al f a e o k. 5-1 E ti e p o ess As e tio ed i the p e ious hapte , e used the diale ti al app oa h f o the T'I) theo to sol e i e ti e desig p o le s that a ot e sol ed solel opti izatio ethods. P a ti al e ide e has sho that so eti es it a e less e pe si e to use a i e ti e p o le sol i g ethod e e if the p o le a e sol ed opti izatio . Ho e e , i a situatio s, oth app oa hes a e e ui ed to p o ide satisfa to solutio s a d a e used i se ue e. A theo eti al o ge e al f a e o k fo desig p o le sol i g p o ess ased o the si ulatio -opti izatioi e tio loops he si ulatio o e pe i e tal ea s a e a aila le is p oposed a d sho o Figu e . The sol i g p o ess i ol es se e fu tio s as ep ese ted o es i Figu e . The fu tio s a e pe fo ed i depe de tl usi g diffe e t ethods a d tools su h as desig of p o le odels ualit fu tio deplo e t, desig of e pe ie e … ; si ulato odels CAD, Wit ess ; si ulatio algo ith s sto hasti opti izatio , ge eti algo ith s ; ulti-ite ia de isio a al sis; a d ha gi g odel ethods su h as T'I), et . The fi st fu tio ep ese ts the p o le fo ulatio a d defi itio th ough the e ui e e ts a d the dissatisfa tio of the usto e . The e aluatio pa a ete s EPi a e used to des i e the o je ti es a d a e easu ed to he k hethe the usto e s e ui e e ts a e satisfied. The a tio pa a ete s APi ith thei possi le alues ep ese t the s ste a ia les o hi h o e a a t. "o e elatio s 'i et ee s ste a ia les a d pa a ete s a e des i ed th ough the s ste o st ai ts.

  Figu e : Ge e al f a e o k fo i e ti e desig p o le sol i g

Figu e :

 e Figu e : Dou le Ka a s ste The s ste is o posed of o e a ufa tu i g a hi e p odu i g t o diffe e t ite s sto ed i t o i depe de t i e to ies a d deli e ed to t o ki ds of usto e s, usto e _ a d usto e _ . The i te al ti e of usto e s a i al ti e follo s a u ifo a do dist i utio i.e. i te al of usto e _ s a i al ti e follo s a u ifo dist i utio . , . , a d i te al of usto e _ s a i al ti e follo s a u ifo dist i utio . ; . . It is a si ple pull s ste he e Ka a a ds a e se t a k to the a ufa tu e a hi e he the o tai e is e pt . The Ka a a d p o ides the ua tit to e put i to a o tai e . The a ufa tu e a hi e has a t o diffe e t set up ti es fo ea h ite i.e., ti e u it fo the fi st ite a d ti e u its fo the se o d ite , the ope atio ti e is . ti e u it fo oth ite s a d the t a spo tatio ti es f o a ufa tu i g a hi e to the i e to ies is egle ted. The t a spo tatio Ka a "ize f o the a hi e to the usto e s i e to ies is o e Ka a . The s heduli g ule fo the a hi e is FIFO fi st i fi st out a o di g to the a i i g Ka a a ds. Thus a setup is pe fo ed a ti e the t pe of ite Ka a ha ges i the Ka a aiti g li e. The total u i g ti e of o e si ulatio is ti e u its ti e u it o espo ds to hou , ith ti e u its e ui ed fo a up ti e. Du i g the a up ti e, all the Ka a a ds o e i to the odel a d go to the a ufa tu e a hi e, thus the i itial sto k of t o i e to ies is f o the a ufa tu e of a up ti e. This stud is odeled as follo s: the Ka a size ua tit of ite s o espo di g to o e Ka a a d a d the u e of Ka a a ds a e the a tio pa a ete s of the

5- 2 . 2

 22 Opti izatio a d solutio filteO e the a tio pa a ete s NK , NK , K" , K" a d e aluatio pa a ete s A" , "B , A" , "B a e dete i ed, the e pe i e ts a e pe fo ed. The Wit ess p o ides tools fo a do e pe i e ts. We used a a do e pe i e t as a opti izatio a d e pe i e ts e e pe fo ed. Fo a o e ie t ie , e used A" +A" a d "B +"B as t o a es ith the esults sho i Figu e . I ou p o le , the goal is to ha e a situatio ith o late ess a d o sto k, hi h ea s that the alue of ea h e aluatio pa a ete is ideall ta geted to e ze o. Ho e e , this goal is i possi le to e a hie ed the s ste des i ed a o e. The est alues that e did o tai sepa atel opti izatio ea s fo ea h e aluatio pa a ete s of this s ste as "B = , A" = , "B = , a d A" = . No e pe i e ts p o ided a solutio he e all the e aluatio pa a ete s e e si ulta eousl ithi the i te al [ ; . ]. This solutio ould ot e ea hed the a o e des i ed s ste . Thus, ou o je ti e as the to odif the odel of the e isti g s ste as little as possi le su h that a solutio he e ea h e aluatio pa a ete sta ds ithi the a ge [ , . ] e isted. "u h a solutio should outpe fo a solutio of the a tual s ste .

-

  Figu e :a do e pe i e ts esults

  Figu e : full fa to ial e pe i e ts I te s of the su of the fou e aluatio pa a ete s, it as dis o e ed the solutio as lose to the ideal poi t tha a do solutio as ell. I Ta le , ette solutio s , e e dis o e ed i te of the su of the fou e aluatio pa a ete s tha the a do solutio of o igi al s ste , . Ta le : Best alues f o edu ed s ste AP EP K" K" NK NK "B A" "B A" "u of EP . . . . . . . . . . . . . . . . . . . .

  Figu e : Ph si al o t adi tio ith o te t



  Figu e : Illust atio of suppl i g st ateg To ealize the solutio a d keep the o te t, e ade ite s fo sto k_ du i g the a i g up ti e, a d defi ed Ka a _ = . I o de to keep the supple e ta h th , hi h is to se d Ka a to a hi e afte deli e i g eight ite s, e let the Ka a go to the a hi e afte deli e i g ea h eight ite s, a d keep t o ite s ithe sto k du i g the supple e ta ti e of p odu i g fo Ka a _ . Thus, the e ha is is to ake Ka a "ize_ = , a d the e is se u it sto k = , he the Ka a _ ith ite s etu to sto k_ . Ka a _ ust supple e t the se u it sto k if its ite s less tha . B this app oa h, the si ulatio esult as "Q = , "Q = , A" = . , a d A" = . , he eas the est si ulatio solutio of o igi al odel that ade "Q = a d "Q = had a esult of A" = . a d A" = . .

Figu

  Figu e : Ka a p io it Pa eto s e ol ed odel Pa eto I o de to de o st ate the supe io of e ol ed FIFO, e sele ted the e pe i e ts esults "B < . a d "B< . fo e ol ed FIFO, Ka a p io it a d o igi al FIFO full e pe i e ts . We o l o side ed the est t o e aluatio pa a ete A" a d A" , a d the Pa eto of th ee g oups of esults a e p ese ted i Figu e . F o this figu e, e a easil see that he "B a d "B is satisfied < . , the e ol ed FIFO a p o ide the est esolutio s a o g th ee s ste s.

Fo i estigati

  Figu e : Bi a output fo ulti-o je ti e opti izatio With ega d to Q , the EP-ased GPC e t a tio st ateg sho ed that it i te sifies the e t e e poi ts fo a o i atio of those e aluatio pa a ete s ot o tai ed the opti izatio p o ess. Thus, e suppose that the GTC-ased GPC e t a tio st ateg i Chapte a also help us e eal the e t e e poi t fo Y a d Y the t o sides of GTC as ell as Y +Y a didate solutio . The efo e, this st ateg ould assist the ulti-o je ti e opti izatio to sea h fo o je ti e Y +Y . This ea s that afte opti izatio , e ould use the a tio pa a ete ith alues f o the EP-ased GPC e t a tio to o e o e the Pa eto of opti izatio .

  positio e les a ti it s de solutio de p o l e i l es da s la oite « odel ha ge » du p o essus de o eptio su i-dessous. La figu e i-dessous su e la d a he p opos e à pa ti de do es o te ues pa l e p i e tatio ph si ue ou pa la si ulatio . Puis ous a o s illust le p o essus de la solutio des p o l es i e tifs su u e e ple de s st e logisti ue à dou le Ka a . Ce p o essus i t g e l e t a tio des o t adi tio s te h i ues g alis es hapit e , l e t a tio des o t adi tio s ph si ues g alis es hapit e , l ide tifi atio des pa a t es pa ti ipa ts au o t adi tio s ph si ues et fi ale e t la solutio as e su les p i ipes de T'I) de la o t adi tio hoisie. L e e ple o siste d u e a hi e fa i ua t deu t pes de p oduits et app o isio a t deu sto ks diff e ts. A t a e s l e p i e tatio su e as d tude ous a o s illust l utilisatio des diff e ts algo ith es p opos s da s la th se pou pou oi po d e au uestio s pos es da s la p o l ati ue de ot e t a ail de e he he et au uelles ous a o s po du da s le hapit e . 6. Dis ussio o lusive et pe spe tives Not e d a he de e he he ous a e e à p og essi e e t ett e e pla e des outils/algo ith es/e p i e tatio s pou pou oi po d e au uestio s lass es à diff e ts i eau de ot e p o l ati ue de solutio de p o l e da s la o eptio i e ti e. Afi de po d e au p e ie i eau de uestio s o e a t le o ept de la o t adi tio da s la T'I) ous a o s p opos des algo ith es e haustifs d e t

  Mots l s : T'I), Co eptio i e ti e, Opti isatio , Featu e sele tio . A st a t The thesis deals ith p o le s of i e tio he e solutio s opti izatio ethods do ot eet the o je ti es of p o le s to sol e. The p o le s p e iousl defi ed e ploit fo thei esolutio , a p o le e te di g the odel of lassi al T'I) i a a o i al fo alled "ge e alized s ste of o t adi tio s." This esea h d a s up a esolutio p o ess ased o the loop si ulatio -opti izatio -i e tio usi g oth sol i g ethods of opti izatio a d i e tio . Mo e p e isel , it odels the e t a tio of ge e alized o t a tio s f o si ulatio data as o i ato ial opti izatio p o le s a d offe s algo ith s that offe all the solutio s to these p o le s. I additio , it p o ides heu isti s to sele t a ia les a d its ele a t alues i ol ed i ge e alized o t adi tio s a d/o useful fo opti izatio . The o t i utio s o e theo a d p a ti e of the i e ti e desig . The thesis also e plo es oss-fe tilizatio et ee opti izatio a d T'I).

  The o t adi tio s ust e lea a d u de sta da le i the ea l stage of the esolutio p o ess so as to hoose o e o t adi tio to esol e. The p a ti e has sho that a ad hoi e of a o t adi tio a lead to a de ease i the effe ti e ess of the p o le sol i g p o ess. He e, the e t a tio a d the i te p etatio of o t adi tio s pla a esse tial ole i the diale ti al app oa h.The idea of o t adi tio has ee ei fo ed ithi the ou da ies of the ge e al theo of ad a ed thi ki g OT"M-T'I) ased o diale ti al thi ki g, hi h is t pi all ell adapted to sol i g te h i al desig p o le s [ ]. The p o le is stated i the shape of the o t adi tio s used fo fi di g a o t adi tio -f ee odel

	ithi the f a e o k of the gi e o je ti es [ ]. The ad i ist ati e o t adi tio is
	T'I) does ot esol e the uestio of the app op iate hoi e of o t adi tio . Ou ot kept ithi the o de of OT"M-T'I), as this o t adi tio defi itio o l efe s
	h pothesis e plai i g this pa ti ula p a ti al p o le of o t adi tio hoi e, he e to the o je ti e he e o o espo di g sol i g tool e ists. T o t pes of
	the o t adi tio o ept ithi T'I), should e e o ked a d la ified. o t adi tio a e p oposed i OT"M-T'I): the o t adi tio of a s ste a d the
	As e tio ed efo e, T'I) is a theo i itiated o t adi tio of the pa a ete , hi h espe ti el ge e alize the T'I) te h i al a d Altshulle [ ],[ ], hi h is ph si al o t adi tio s. Mo eo e , a s ste of o t adi tio is p oposed ithi the
	I Figu e , t o alues of a tio pa a ete fo	a ph si al o t adi tio . Fo
	e a ple he AP= VALUE , EP i p o es; ho e e , the EP o ditio	ill o se .

dedi ated to the s thesis of ethods fo the esolutio of i e ti e p o le s, i.e., fo p o le s fo hi h the sol e does ot k o of a solutio . The e e ist th ee ai a io s: the o side atio of ge e i te de ies to des i e the te h i al s ste s e olutio , the o te tual aspe t of a p o le , a d the o t adi to aspe t of a p o le . The fi st t o a io s p o ide la ifi atio of the o e p o le a d i put i to e aluatio of a pote tial solutio , he eas the thi d a io is di e tl li ked to the ep ese tatio of the p o le . The last a io ide tifies the o t adi tio s i he e t to a p o le ati situatio i side a s ste . I its o igi al defi itio , o t adi tio s ithi T'I) a e defi ed at th ee diffe e t le els. These th ee le els o espo d to a p og essi e u de sta di g of the p o le o igi : -Ad i ist ative o t adi tio is a situatio he e a o je ti e is gi e , ut ot satisfied. This le el o espo ds to the ide tifi atio of p o le e iste e he e so ethi g has to e ha ged. Ho e e , the sol e is ot a a e of the e ui ed p o ess. -Te h i al o t adi tio TC e p esses the oppositio et ee t o pa a ete s he e o e fa to i p o es hile a othe o e dete io ates. The te h i al o t adi tio is di e tl li ked ith the i possi ilit to satisf t o spe ifi atio pa a ete s si ulta eousl . -Ph si al o t adi tio PC efle ts the p o le of a s ste pa a ete that ust e ist i t o diffe e t states si ulta eousl . This o t adi tio ide tifies the o e p o le he e o e s ste pa a ete ust e i diffe e t states to satisf diffe e t spe ifi atio pa a ete s. f a e o k of OT"M-T'I) to uild ohe e e et ee the le els of o t adi tio of the s ste a d o t adi tio of pa a ete . OT"M-T'I) stated a ele e t-a e of p ope talue ENV odel to des i e the o t adi tio . Fo u if i g the otatio , e p opose a desig odel, hi h i ludes th ee t pes of o po e ts: -Ele e ts [ ]: Ele e ts a e o stitue ts of a s ste . Fo e a ple, the ha e d i es the ail, i.e., a ele e t = a ha e . -Pa a ete [ ]: Pa a ete des i es ele e ts assig i g the a spe ifi it that hi h efle ts a e pli it k o ledge of the a ea o se ed. The e a e t o atego ies of pa a ete s: o A tio pa a ete AP : a AP is also alled a o t ol pa a ete , a d its states a e odified desig e . o E aluatio pa a ete EP : a EP as o se ed to e aluate positi e o egati e s ste pe fo a e ased o the desig e s e ui ed ite ia.

-Value [ ]: Values a e p i a il adje ti es used to des i e a pa a ete su h as the eight of the a il should e hea . I this ase, Value=hea . This te h i al pa a ete is k o as te h i al o t adi tio . Ho e e , he AP= VALUE , the EP i p o es hile EP o se s, hi h is k o as te h i al o t adi tio . TC a d TC a e utuall o ple e ta .

  tio s e ist as it as e tio ed efo e. The GTC odel i Figu e epla es t o e aluatio pa a ete s defi ed i a lassi al te h i al o t adi tio ith t o o epts of e aluatio pa a ete s. A o ept o sists of a e aluatio pa a ete o a logi al disju tio of se e al e aluatio pa a ete s. O e pa a ete a o l pa ti ipate i o e of the t o o epts i ol ed i a GTC. The desi ed esult is the si ulta eous satisfa tio of the t o o epts. I ea h o ept, the e is at least o e

	A sig ifi a t u e of a tio a d e aluatio pa a ete s elated	u e ous li ks
	a ose ith the e olutio of o e o ple desig p o le s. As a esult, it is diffi ult
	to o se the desig spa e e ause of desig	o st ai ts, hi h a o the
	oppo tu ities fo o tai i g the desi ed solutio [ ]. I o de to fill the gap et ee
	o t adi tio gathe i g a d ep ese tatio , the o ept of ep ese ti g a desig
	p o le as a et o k of o t adi tio s hile usi g se a ti ules to d i e a desig
	usi g a et o k as i t odu ed i [ ]. Additio all , the et o k p o le	as
	p oposed i [ ],[ ], hi h a e t a sfe ed i to a et o k of o t adi tio s. A
	fo al defi itio of a o t adi tio a d its pote tial a iatio s as p oposed i [ ].
	The o ept of a o t adi tio loud as a th ee-alue g aphi al ep ese tatio of a
		Technical
	Physical	Contradiction
	contradiction

set of ele e ta o t adi tio s as p ese ted i [ ]. A sig ifi a t u e of these p oposals a e ased o te h i al o t adi tio s a d o t i ute to t a sfe i g a o ple p o le i to a lassi al T'I) o t adi tio , hi h a e sol ed T'I) i e ti e p i iples. As fa as lassi al T'I) o t adi tio s a e o e ed, the e a e se e al li itatio s a d gaps i thei defi itio a d utilizatio . We ote i e tai situatio s the p o e a se e of o t adi tio s, appea i g f o the a aila le elatio s et ee the a ia les of the s ste , hi h o espo ds to the o t adi tio defi itio p o ided the lassi al T'I) app oa h [ ]. The o se ed ge e al t e d a e su a ized as follo s: the o e e pe i e ts a d k o ledge ega di g a s ste that e ists, the lo e the ha e of fi di g a te h i al o t adi tio i.e., a i put fo i e ti e p o le -sol i g ethods . A othe i o e ie e is that the lassi al te h i al o t adi tio o side s o l t o e aluatio pa a ete s. "upposi g that the e e ists a te h i al o t adi tio that a e sol ed, othi g a e said a out the satisfa tio of the othe e aluatio pa a ete s. Mo eo e , the e is a la k of the e pli it defi itio of the o te t e ui ed to alidate the o t adi tio s fo the sol i g ethod. I o de to add ess these li itatio s, the o ept of a ge e alized s ste of o t adi tio s G"C i ol i g ge e alized te h i al o t adi tio s GTC a d ge e alized ph si al o t adi tio s GPC as p oposed i the p e ious o k [ ] as a e ha ed e ui ale t to the lassi al T'I) o t adi tio s. These ge e alized o epts a oid situatio s he e o lassi al T'I) te h i al a d ph si al o t adi

  ed pe utatio s of the o s a d olu s of the e ta gula at i . Diffe e t ethods of data a al sis a e used to ide tif the lo ks i the at i . The p ope ties of the Ge e alized " ste of Co t adi tio s a e ha a te ized the set of defi itio s that e a les the e t a tio of the G"C f o the e pe i e tatio ta le. A e pe i e tatio ta le a e ha a te ized : u h a defi itio p o ides a path fo eo ga izi g the e pe i e tatio ta le pe utatio s of the o s a d of the olu s i o de to g oup the p e iousl defi ed Ei a d Yi [ ] Ta le .

	Ta le : G"C ep ese tatio i e pe i e tatio output
	 A set of a tio pa a ete s X= , , …, , X Y	Y	Y
	 A set of do ai s D= D , D , …, D alues fo i, E E ×Y :	he e Di defi es the possi le a ge of
	 A set of e aluatio pa a ete s Y= , , …, p ha a te ized	i a
	Mo eo e ;
	 E is a set of e pe i e ts fo hi h all the e aluatio pa a ete s of Y a e
	satisfied.

The pu pose is to o tai t o sets of e aluatio pa a ete s that a e i o t adi tio . This o t adi tio is t a slated as t o o thogo al lo ks of o es o tai alues, eithe if i is satisfied, o if i is ot satisfied, a d  A set of e pe i e ts E= e , e , …, e . A e pe i e t ei is a pa ti ula i sta tiatio of the a tio pa a ete s: ai , ai , …, ai , su h that aij  Dj o i ed ith the i du ed alues of e aluatio pa a ete s zi , zi , …, zip esulti g i the i a alues of zij = if j is satisfied e pe i e t ei, o zij = if j is ot satisfied e pe i e t ei.

The goal is to satisf all the e aluatio pa a ete s. Ho e e , the situatio should e o side ed he e su h a solutio does ot e ist i the o side ed ta le a o e, i.e.,

that o e pe i e t e a les the satisfa tio of all the e aluatio pa a ete s.

A Ge e alized " ste of Co t adi tio s seeks to ide tif the follo i g ta le of e pe i e ts:



Th ee sets of e aluatio pa a ete s Y , Y a d Y , su h that Y ∩Y =, Y ∩Y =, Y ∩Y =, Y Y Y =Y, Y ≠Ø a d Y ≠Ø.  Th ee sets of e pe i e ts E , E a d E su h that E ∩E =, E ∩E =, E ∩E =, E E E =E, E ≠Ø a d E ≠Ø.  E is a set of e pe i e ts fo hi h all the e aluatio pa a ete s of Y a e satisfied. "

  the ai fa to affe ti g the algo ith s speed. Thus, to i p o e the algo ith , e o ked to fi d so e est i tio fo dis a di g lo ks efo e the at hi g phase. This p o le a also e lassified as a data i i g p o le a d is of TCs de eases ith de sit a d is ge e all e ual to ze o afte %.Ne e theless, the u e of olu s a ts as a shape fa to . Fo i sta e, the a i u alue of GTCs, hi h is o tai ed fo de sit e ual to %, i eases e po e tiall ith the u e of olu s. The ai fa to s affe ti g the u e of te h i al o t adi tio s a d ge e alized te h i al o t adi tio s as ide tified ith the aid of the p i iples of the desig of e pe i e ts a d statisti al a al sis tests.

	he the a i u dis ussio , e o lude this hapte a d dis uss hat uestio s this hapte u e of e aluatio pa a ete s is less tha . The at hi g Chapter 3 E t a tio of ge e alized ph si al o t adi tio e a led to a s e . 3-1 I t odu tio a d state of the a t ti e is si ila to se iatio a d at i eo de i g p o le s; su h as the t o-ode luste i g I Chapte , the i e ti e p o le as li ited o l to the o je ti e o e aluatio
	p o le . Ho e e , these ethods do ot p opose to fi d all possi le solutio s. The I this hapte , e i t odu e a theo eti al p o le fo the e t a tio of ge e alized p o le , a d so as p ese ted th ough the ge e alized te h i al o t adi tio as a
	e hausti e algo ith a s e s Q a d Q a out the u e of TC a d GTC a d ho These esults ill ha e a i pa t o ou st ateg fo sol i g i e ti e desig ph si al o t adi tio s a d p a ti al sol i g p i iples to o tai the e hausti e ge e alizatio of the lassi al te h i al o t adi tio . As the te h i al o t adi tio s Num of Columns Matching time(s) Num of Blocks Searching time(s) Data1 5 0.007 31 0.190 Data2 8 0.240 255 0.197 to e t a t the , a d it p o ides a po e ful tool fo e t a ti g GTCs he a p o le s a d fo sele ti g the ost app op iate te h i al o ge e alized te h i al sea h algo ith . I the se o d pa t of this hapte , the GPC e t a tio p o le is a e o e ed ith the e aluatio pa a ete s, the i e ti e p o le as
	Data3 Data4 Data5 e aluatio pa a ete is less tha 10 12 15 o t adi tio s to sol e su h p o le s. Additio all , the elatio 3.632 1023 0.234 50.159 4095 0.401 3666.167 32767 . Mo eo e , a li ea i a p og a fo ulated i to a i a i tege p og a fo ulated o l at the e aluatio pa a ete s le el, hi h is e ual to the et o k of i g odel et ee the i g odel. The ge e alized te h i al 2.283 is p oposed, hi h p o ides a oppo tu it to sea h a ha a te ized GTC ased o u e of o t adi tio s a d the e pe i e tal ta le ould p o ide the a s e to o t adi tio di ides the hole set of e pe i e ts E i to th ee su sets: a su set o t adi tio s [ ] i OT"M-T'I). To o tai a deepe o p ehe sio a d
	a d sol ed	o afte the e u e atio a d e o al of diffe e t states. The %. The alues of TCs e illust ate
	a d GTCs of the i uit eake e a ple a e o siste t ith the esults of this ge e al the p o le fo ulatio a d the sea h algo ith fo the ase of a si ple i e to
	populatio of at i es. I o de to ge e alize p e ious esults, e e aluated the Ka a situatio . The e pe i e ts a e pe fo ed a d a dis ussio is p o ided
	i pa t of the u e of olu s, de sit a d o s o the u e of GTCs a d TCs. ega di g ho the u e of e pe i e ts i ol ed i the ge e alized te h i al

Thus, a hu a e pe t is ot a le to ide tif a d o side all of the o i atio s, hi h is h e atte pted to auto ate the sea h fo ge e alized te h i al o t adi tio s. The ethod is elia le the sea hi g st ateg i o st ai t. This odel positi el a s e s the Q i te s of GTC ide tifi atio usi g opti izatio ethods, a d p o ides a fou datio fo a s e i g Q sea hi g ele a t o t adi tio s ithout e hausti e sea h if e k o a d a t a sfo the p i iple of GTC sele tio i to BIP o st ai ts. I additio , se tio -. dis usses the GTC i the i a Pa eto is the sa e as the o igi al e pe i e tal ta le. This p ope t a help us effe ti el edu e the o putatio o ple it i sol i g li ea i a p og a i g p o le . Be ause of the algo ith , it e o es possi le to ua titati el e aluate the olu e of o t adi tio s a d he k the h pothesis a out a it of TC e iste e. I the e pe i e tal se tio of this pape , the esults of ou algo ith fo the ase of a ele t i al i uit eake e e p o ided. These esults o fi the la ge u e of GTCs. "e o dl a a al sis of the u e of GTCs a d TCs e sus the de sit of o es fo the populatio of i a at i es as pe fo ed ith the sa e u e of o s a d olu s tha the i uit eake . The esults sho that the a e age u e of GTCs i eases ith de sit u til % a d the de eases, hile the u e of TCs de eases ith de sit a d is ge e all e ual to ze The a al sis of the esults sho s that, fo a gi e u e of o s a d olu s, the a e age alue of GTCs a d TCs e ol e i the sa e a as fo the i uit eake . The a e age u e of GTCs i eases ith de sit u til % a d the de eases, hile the u e Q , su h as he the de sit of o es is o e tha %; the e is o TC; a d u e of GTC is sig ifi a tl g eate tha u e of TCs. O e all ge e alized te h i al o t adi tio s a e ide tified, se e al eli i atio st ategies a e su se ue tl eeded to hoose o l the GTCs leadi g to esolutio of the desig p o le . T o diffe e t ite ia e e p oposed i [ ] to sele t the ost ea i gful ge e alized te h i al o t adi tio s. Ne e theless, ge e alized te h i al o t adi tio s p o ide o l a pa tial solutio i T'I) p o le sol i g. To esol e the o t adi tio s, o e details a e eeded ega di g the s ste pa a ete s a d the elatio ships the eof. The e t hapte dis usses the ide tifi atio of ph si al o t adi tio s a o di g to the ide tified GTCs. satisf i g the fi st set of e aluatio pa a ete s E ; the se o d su set satisf i g the set of e aluatio pa a ete s E ; a d the thi d su set o plete the p e ious t o e aluatio pa a ete s, E . The sea h of ea h o ept of ge e alized ph si al o t adi tio is fi st defi ed as the sea h fo dis i i ati g o epts fo the sets of e pe i e ts as defi ed ge e alized te h i al o t adi tio . To sea h fo CONCEPT ea s to sea h a fu tio that e og izes the ele e ts f o E a d eli i ates the ele e ts f o E U E . To sea h fo o ept efe s to sea hi g fo a fu tio that e og izes the ele e ts f o E a d eli i ates the ele e ts f o E U E . The esea h i a i tege p og a is defi ed a d the p op ieties a e used to sol e the fu tio . These o t adi tio s a e u e ous a d i possi le to list. He e, e i di ate that o e spe ifi ge e alized ph si al o t adi tio ould o ti ue all possi le ge e alized ph si al o t adi tio s. The sea h of this spe ifi o t adi tio ould e pe fo ed addi g the o je ti e fu tio to the set of e uatio s i the i a p og a ; the efo e, e ill sol e fo the i a i tege opti izatio p o le . The e hausti e sea h algo ith is p ese ted i the thi d pa t o t adi tio s affe ts the u e of lassi al ph si al o t adi tio s. I the -I t odu tio a d state of the a t i te p etatio of the i e ti e p o le , the ph si al o t adi tio should e fo ulated a d ide tified as a i itial poi t fo the i e ti e sol i g p o ess.

  o states: the supplie s ap ate is e ual to % a d the 'eo de Poi t is e ual to hile lot size is . Whe the e a e less tha p odu ts i the i e to , the supplie se ds p odu ts to the sto k e ause of the lead ti e. This poi t lies o

	Pa eto f o tie he e Lot size =	a hie es the ost ideal lo est a e age sto k
	hile "e i e B eakdo	e uals to se i e ate is	% . O the othe side, if lot
	size = , it ea s he the e is less tha	p odu ts i the i e to . The supplie
	ill the se d o l p odu t to the sto k, hi h a i es afte eight ti e u its of lead
	ti e. Ho e e , du i g this ti e, o e tha	p odu t should e deli e ed, hi h
	leads to the a e age sto k =	ut a se i e eakdo	of	% se i e ate of	%
	o l . This is a othe poi t o the Pa eto f o tie i i izi g the a e age sto k ut
	a i ize the se i e eakdo .
	To i te p et this GPC fo this si ple Ka a	odel, the e a e t o APs des i i g the

apa it of p odu tio : a lot size a d a eo de Poi t. The 'eo de Poi t des i es the f e ue of suppl i g, a d the Lot size des i es the ua tit to suppl . The e a e t

  E p% de otes the pe e tage of e pe i e ts. We a the see that the u e of states e pe ie es u i g o th ith the pe e tage of e pe i e ts.

	e pe i e tal ta le a d e a do l hoose	% ,	% ,	% ,	% ,
		% ,	% ,	% o s a d the epeated th ee ti es fo ea h. I Figu e
	number of states	60,00% Fitted Line Plot 50,00% 40,00% Concept set = -38,10 + 619,6 Exp% 30,00% a a d , 70,00% 20,00% 10,00% 600 500 400 300 200 100 0 -1244 ( Exp%)**2 + 2102 Exp%**3	S R-Sq R-Sq(adj) Regression 12,5051 99,5% 99,4% 95% CI 95% PI
			Exp%
			a Fitted li e plot

he e AP has t o optio s. "o the e a e e pe i e ts i full fa to ial

  The eight e to of "VM a e see as a des iptio of dista e et ee sa ples a d a h pe pla e [ ]. The thi d o e is o elatioased easu e. Fo e a ple, the

	4-2.2 "VM Featu e "ele tio P i iple
	The "uppo t Ve to Ma hi e "VM as p oposed i [ ]; "VM esse tiall pe fo s
	Pea so o elatio oeffi ie t is a easu e of li ea o elatio li ea lassifi atio a o -li ea appi g of the o igi al spa e to a high-di e sio et ee t o
	a ia les [ ]; thus, it is also a good a to e aluate the o t i utio f o featu es spa e, hi h is alled ke el t i k. This o -li ea appi g te h i ue helps us look to lasses. The othe e a ple is o elatio ased a featu e sele tio algo ith CF" fo a lassifi atio u e i apped featu e spa e i hi h the lassifi atio u e is
	[ ], CF" ai s at sele ti g a su set of featu es, hi h a e highl o elated ith the a li ea lassifi atio pla e. Fo e a ple i Figu e a , the e a e t o g oups of
	lass, et u o elated ith ea h othe . sa ples p ese ted i les a d t ia gles. The lassifi atio u e is o iousl a
	Ho e e , the featu e sele tio algo ith s p oposed p e iousl a e ot suita le to i le, + = . Ho e e , li ea te h i ue is a atu e te h olog ith a
	ou sele tio p o le . Th ough i estigati g the o je ti e of ph si al o t adi tio ad a tages, su h as good o putatio pe fo a e. The p o le is ho to use
	e t a tio , featu e sele tio fo e aluatio pa a ete ai s at sele ti g the a tio li ea te h i ue to deal ith a o -li ea lassifi atio . If e de elop a appi g
	pa a ete s that a e a le to ake e aluatio pa a ete s at satisfied i te als as
	de oted	o es i Figu e	. The e , ou pu pose is esse tiall to sea h a
		Original
		Feature	Generation	subset	Evaluation
		set
					Goodness of the subset
			No		Stop criterion	Yes	Validation
		Figu e : Featu e sele tio p o ess ith alidatio [ ]
	O iousl , the hoi e of the e aluatio	easu es fo dete i i g the est featu e o
	est featu e su set pla s a i po ta t ole i the hole p o ess of featu e sele tio .
	'e e tl , a u e t fo us i the e aluatio fu tio	o e s th ee t pes of
	easu es. The fi st o e is the i fo atio theo -ased e aluatio . This e aluatio is The e , the Pea so o elatio oeffi ie t p ese ts the easu e e t of a gle
	to de ease the u e tai t et ee featu es a d lasses. Fo e a ple, i fo atio et ee t o a do e to s. Apa t f o that, "VM eight is a othe featu e
	gai eighti g algo ith p oposed as used to e aluate a d a k the featu e i the te t atego izatio [ ]. Gu o i [ ]. The eighti g is o the asis of the
	Additio all , utual i fo atio as used i the algo ith M'M' fo ge e sele tio "VM lassifie , i hi h the li ea eight e to of the featu es p ese ts the dista e
	[ ]. The se o d s e a io is a dista e-ased e aluatio . This e aluatio o t i utio et ee the sa ple a d the lassifi atio h pe pla e. Thus, the eight easu es
	the sepa a ilit of t o lasses i te s of dista e. Fo e a ple, 'ELIEF as a of the featu es i the "VM lassifie a di e tl e ade uate fo e aluatio . The sig

featu e-eighti g algo ith p oposed i [ ], hi h e aluates featu es th ough i estigati g the dista t diffe e e et ee t o lass sa ples. Fu the o e, "VM-'FE as p oposed as a ge e sele tio algo ith i the ase of a e ge e sele tio . positi e-effe t su set of the a tio pa a ete s that is si ple e ough fo GPC e t a tio . Ho e e , ost featu e sele tio algo ith s ai tai oth positi e a d egati e featu es. Fo i sta e he sea hi g fo o ept , ost featu e sele tio algo ith s ould p o ide a set of pa a ete s that allo s fo lassif i g the e pe i e ts i E i.e., positi e featu es defi i g o ept a d i E ᴜ E i.e., egati e featu es defi i g a e pt o ept i ou p o le ; ho e e , e o l eed the pa a ete s defi i g o ept . "u se ue tl , fi di g a featu e sele tio algo ith that a e used i ou si plifi atio p o ess e o es the ke p o le of solutio . Assig ed featu e eighti g ethods a e ou solutio . The ost t pi al a d u ial ethod is the Pea so o elatio oeffi ie t. Its atu e is the osi e alue of t o e to s of sa ples, hi h is fitti g f o the t o a do a ia les. of eight displa s the positi e o egati e effe t. A eighti g algo ith ased o "VM as i ple e ted, usto ized a d e aluated i the follo i g se tio .

  s ste o hi h e a a t. To e aluate the pe fo a e of this s ste , the a e age sto k i the i e to ies a d the a e age aiti g ti e fo usto e s fo oth ite s

	a e defi ed as the e aluatio pa a ete s. I su	a , fou a tio pa a ete s a e
	defi ed: u e of Ka a fo ite		NK , u e of Ka a fo ite	NK ,
	Ka a size fo ite	K" , a d Ka a size fo ite	K" . I additio , the fou
	e aluatio pa a ete s a e a e age sto k i sto k	A" , a e age sto k i sto k
	A" , se i e eakdo	fo ite	"B	o espo di g to the a e age late ess of
	the deli e to usto e a d se i e eakdo	fo ite	"B . The defi itio of
	the a ge of a tio pa a ete s fo opti izatio should e defi ed	e gi ee fi st,
	the dedu ed if the e is a good solutio out of the defi ed a ge th ough a statisti al
	a al sis of ge e ated solutio s. Fo ou ase, the a ge is defi ed f o	to	fo
	ea h a tio pa a ete .

  . , Fo atio of i o pols ste s : I di ated to use t o a hi es to p odu e ite s. Although this solutio

	a te h i all sol e ou p o le , i gi g a othe	a hi e is a la ge ha ge
	that does ot follo s the p i iple of i i al ha ge i T'I) o that ould e
	o side ed as too e pe si e. Thus it ould o l e a alte ati e solutio i ase
	of o satisf i g solutio .
	 Pa tial solutio f o ideal fi al esult	IF' : Ka a fo ite	, ithout
	o pli atio of s ste a d ithout ha ful side effe ts, eli i ates <a e age
	sto k> du i g the < ti e he p odu i g the ite s fo Ka a	o he Ka a
	is i the Ka a sto k > i side the < a hi e a d sto k> a d keeps the a ilit to
	p o ide <ite s to usto e e ui e e ts i ti e>. O the a al sis of this pa tial
	solutio , if e a t to e o e the a e age sto k	Ka a du i g <ti e he
	p odu i g the ite s fo Ka a	a d he Ka a	is i the Ka a sto k>, e
	should de ease the Ka a size he p odu i g ite s fo Ka a	o edu i g
	the ite s he Ka a is at usto e sto k.

  Co lusio I this hapte , fi st e e ie ed the ge e al f a e o k of i e ti e desig p o ess as p oposed i Chapte . I this p o ess, the i e ti e desig is pe fo ed i the solutio the e pe ts p oposed. The esults i di ated that the e ol ed s ste had ette pe fo a e tha the e pe ts p oposed s ste . U fo tu atel , ou e ol ed s ste still did ot a hie e the ideal fi al esults as the fou e aluatio pa a ete lo ated i [ , . ].Ho e e , i the ase stud , the e a e t o te h i al o t adi tio s a d t el e ge e alized te h i al o t adi tio s. This suppo ts the a s e to Q , that GTC is o e u e ous tha TC. It also p oposed to a s e to Q , he e hoosi g the GTCChapteThe se o d le el of uestio s ega di g the ethodolog o e s the p a ti al o se ue es of the e defi itio of o t adi tio s fo the i e ti e p o le Ho e e , to the est of ou k o ledge, the e is o po e ful tool that a effe ti el sol e the i a i tege p og a i g p o le fo the se o d st ateg . The data p o le does ot a ise i the e a t esolutio algo ith p oposed i the thesis, ut it ill a ise fo the heu isti algo ith desig ed to sol e the sa e p o le fo s ste s that o tai a la ge u e of a ia les. Chapte : E t a tio of ge e alized ph si al o t adi tio I Chapte , e p oposed a GPC ide tifi atio a d e t a tio algo ith , th ough the e t a tio of t o GPC o epts, ea h of hi h i ol es a s ste states. The possi le use fo this algo ith , hi h as ot e pe ted at the egi i g of the stud , is the possi ilit of ide tif i g the lassi al o ge e alized ph si al o t adi tio s i the o te t of setti g a tio pa a ete s. This allo s us to o side o e appli atio s as pa t of the i e ti e desig a d assista e i u de sta di g the o t adi tio s. I deed, i the lassi al app oa h, the o t adi tio s p o ided Chapte Chapte . U de this p o ess, e o e ted the t o algo ith s of ge e al o t adi tio e t a tio a d i e ti e solutio . I the illust atio pa t, a ase stud fo dou le Ka a as i t odu ed a d i p o ed u de this i e ti e p o ess, hi h is a p o isi g esult fo the p oposed i e ti e p o ess. I the pa a ete sele tio "C is o e diffi ult to i te p et, a d thus to sol e, ut it e ists i a p o le ati situatio fo hi h o solutio is k o . This o t adi tio is illust ated i Figu e . As e tio ed i -. a d -. , e a s e ed Q the GTC a d GPC e t a tio algo ith he the u e of e aluatio pa a ete s is fe e tha fiftee a d the i a a tio pa a ete s a e fe e tha t el e. Fo othe situatio s, e ause of o putatio al li itatio , e ould ot sea h the o t adi tio s e hausti el , utp oposed st ategies to o tai at least so e ge e alized o t adi tio s. The efo e, the othe fa to e eed to o side is the size of the G"C e aluatio pa a ete . We p opose hoosi g the G"C ith the la gest size. Chapte f o A'I) C as to ha ge si gle Ka a to se e al Ka a u i g i the odel; su se ue tl , Pa eto goes e o d the o igi al Pa eto of si ple Ka a . Ho e e , this p oposed solutio o l ei e ted the e isti g si ple Ka a s ste .

	-Co t i utio s -Co t i utio s	hapte s hapte s		Chapte
	5-4 fifth step-odel ha ge. Fo this step, e p oposed a s ste ati i e ti e p o ess, hi h i teg ated GTC e t a tio Chapte , GPC e t a tio Chapte , EP/GTC-ased GPC e t a tio Chapte a d i e ti e p o le sol i g T'I) . To illust ate this odel ha ge p o ess, e ade a e a ple of a dou le Ka a , o e a hi e suppl i g t o t pes of ite s fo t o diffe e t sto ks. Afte a al sis, this odel e ol ed a e supple e ta st ateg . I the e d, e also ade a o pa iso e pe i e ts i E a d E . The sol i g p o ess of ph si al o t adi tio e t a t the ge e alized o t adi tio s i t i si all the sa e a as opti izatio p o ess? fou d ite ia that defi e the ele a t o t adi tio . The p oposed sele tio ethod i e ti e p o le sol i g p o ess. the e a sig ifi a t u e of those o t adi tio s? Ca e al a s Questio : Alte atel , if this li k e ists, ould it e e ploited to fa ilitate the ele a t o t adi tio s f o u e ous o t adi tio s, ut thus fa , e ha e ot T'I), a d the o te t should e see as supe io s ste pa a ete s du i g the ge e alized te h i al a d/o ph si al o t adi tio s e ist a d a e o t adi tio s? of the dou le Ka a i di ated to us that the ph si al o t adi tio should e sol ed Questio : Whe o lassi al te h i al o ph si al o t adi tio e ists, do the Questio : If this li k e ists, ould it e used to ide tif ge e alized ith o te t Chapter 6 Co lusio a d futu e p ospe ti es The i t odu tio hapte i t odu ed the p o le ati of ou o k ia te uestio s. The pu poses of this hapte a e to su a ize the o t i utio s a d li itatio s of ou o k that leads us to dis uss the a s e s to these uestio s a d to p opose a p ospe ti e fo futu e esea h. sol i g: Questio : O e the o t adi tio s ha e ee ide tified a d e t a ted, ho a e use the i the i e ti e p o le sol i g p o ess? Questio : Ho a e e t a t the ele a t o t adi tio s ithout e hausti e esea h, hi h is ofte too e pe si e a d ti e o su i g despite a poste io i filte i g? Questio : Ca e use the o ept of a ge e alized o t adi tio to e p ess the fiftee . The e hausti e algo ith fo GTC e t a tio p ese ted i this hapte akes it possi le to a s e Q he the u e of a ia les is fe e tha fiftee . With this algo ith , e a also o side a s e i g Q fo te h i al o t adi tio pe fo i g app op iate e pe i e ts. F o these e pe i e ts, e ade the follo i g o lusio s:  The o e a aila le solutio s the e a e that eet ultiple e aluatio o je ti es, the s alle is the possi ilit of o tai i g a lassi al te h i al o t adi tio . Whe o t adi tio . The situatio of the o t adi tio as a al zed e pe ts, a d thus the s ste of o t adi tio o ga ized the k o ledge of e pe ts fo the s ste a d positi el a s e ed Q . 6-2.2 lassi al ph si al o t adi tio ith o te t as p oposed i this hapte o pa i g the t o states i ea h o ept. The o ept e t a tio Ne e theless, the solutio ight e heape , e ause it takes f o the e isti g 6-2.3 Chapte : Ide tifi atio of ke pa a ete s step of dou le Ka a , e adopted EP-ased GPC e t a tio . We sele ted a tio solutio s o l that hi h is e ui ed fo the spe ifi situatio . I o de to ad a e as i itiall t a sfo ed i to a i a i tege p og a i g p o le , a d the The ai of Chapte as to p opose heu isti s fo sele ti g ele a t pa a ete s a d pa a ete s a d alues o ie ted to satisf i g ea h e aluatio pa a ete . The full I o de to a s e Q , e eed to defi e the ele a t o t adi tio . The o ept of a d test the p a ti al p o le of Q , o e ase studies ha e to e pe fo ed. At the e ause its thei alues fo sea hi g ele a t ge e alized o t adi tio s. Fo doi g this, the fa to ial e pe i e ts o the sele tio esults i di ated that this sele tio esult ele a t a diffe ith the spe ifi p o le . I o de to e o e a a e of the sa e ti e, fo a s e i g Q , e eed to i ui e the e pe ts, a d dete i e o st ai t is a logi al e uatio , e p oposed a filte ethod fo filte i g all possi le ide tifi atio of pa a ete s, hi h is to lassif dis i i ati e pa a ete s fo t o ould help us o tai a solutio e o d the o igi al Pa eto e pe i e ts i o de to diffe e t situatio s a d i te esti g sele ti g ite ia, se e al p a ti al e pe i e ts hethe the a alidate the o tai ed o t adi tio s o lea a out the s ste s o ept states. sepa ate sets, as add essed i te s of a hi e lea i g ethods i a tifi ial i p o e the opti izatio esults. should e pe fo ed. Wo ki g ith the a tual soft a e ould allo this e eha io . 6-1 'e i de of the i itial uestio s I Chapte , e i t odu ed the a kg ou d fo ou thesis a d ou oti atio s to e te d the o ept of T'I) o t adi tio i i e ti e p o le sol i g i o de to ette fo ulate a d a al ze the i e ti e desig p o le . I o de to o ga ize ou uestio s that lo ate ou p o le ati i th ee diffe e t le els. Let us e all the te uestio s. The fi st le el of uestio s ega di g the desig theo is o e ed ith the o ept of o t adi tio , hi h is o e of the fou datio s of T'I): i pli it k o ledge f o a s ste e pe t? Fi all , the thi d le el of uestio s dis usses the e plo atio of the elatio ship et ee opti izatio ethods a d T'I) i o de to de elop oss-fe tilizatio f o a Questio : Ca e use ethods a d o epts f o the opti izatio i o de to fa ilitate the ide tifi atio of ge e alized o t adi tio s? Questio : Is the e a elatio ship et ee the Pa eto o epts a d the ge e alized o t adi tio s? o e % of the ta gets i the e pe i e t ta le is satisfied, the e is i tuall o possi ilit of o tai i g a lassi al te h i al o t adi tio . This poi t e plai s the diffi ulties e ou te ed hu a e pe ts to fo ulate o t adi tio s ased o the lassi al odel of T'I) o t adi tio i so e situatio s. i tellige e. We fi st sho ed that the ide tifi atio of pa a ete s a d alues used i the o ept of ge e alized ph si al o t adi tio is si ila to a se ies of p o le s k o as the featu e sele tio p o le i so e a eas of esea h. A o g the ethods of featu e sele tio , those sig ed featu e sele tio see to est suit I the ase stud , e p ese ted ho to use A'I) C to sol e the ge e al ph si al o t adi tio ith o te t, a d fi all o tai the i p o ed solutio . This p o ess u dou tedl suggests the a aila ilit of the T'I) solutio o the ge e al o t adi tio o tai ed ith o te t; a d this is pa tiall hat e a t to a s e fo 6-3 Dis ussio uestio s a d p ospe ti e k o ledge i the futu e. As a sta ti g poi t, e p opose the follo i g optio s fo a al zi g the set of o t adi tio s: Fo Q , Chapte p oposed a i a p og a i g odel fo si gle GTC e t a tio , if e e e to t a sfo ou e ui e e ts i to a o st ai t fo the i a p og a odel, e ould ha ge ou ele a t GTC e t a tio p o le to a i a p og a i g p o le , hi h ould p o ide us ith the oppo tu it of sol i g su h agai st the ased o the u e of asso iated e aluatio pa a ete s a d the u e of p o le s a d p ese t ou o t i utio s, Chapte also p oposed te ge e al theo eti al a d/o a p a ti al poi t of ie . ou ase. T o ethods e e i ple e ted a d tested: Pea so o elatio Q . p o le the i a p og a i g algo ith , si ila to a h a d ut ethod. I
	Pa eto, fo e a ple, f o the eha io al ep ese tatio a d the o je ti es of the s ste ? If so, the hat a e the o se ue es? Questio : Ho a the ge e alized o t adi tio s e e hausti el ide tified a d e t a ted? Questio : O e all ge e alized o t adi tio s a e k o , ho a the ele a t o t adi tio s e hose o defi ed? Alte atel , ho a a ele a t o t adi tio e defi ed i a st aightfo a d a e ? 6-2 Co t i utio s hapte s 6-2.1 Chapte : E t a tio of ge e alized te h i al o t adi tio I Chapte , e p oposed a GTC ide tifi atio a d e t a tio odel i the fo of opti izatio p og a s a d t o solutio st ategies. The fi st solutio st ateg is a e hausti e sea hi g algo ith that a ide tif a d e t a t all GTC f o a e pe i e tal ta le he the u e of e aluatio pa a ete is fe e tha fiftee . The appli atio of the esults of this hapte also p o ides pa tial a s e s to Q a d Q . As des i ed i Chapte , the ase stud fo the ele t i al i uit eake as p o essed GTC e t a tio , a d the esults e e alidated e pe ts. A o g GTCs, fou e e fou d a d i te p eted e pe ts, su h i te p etatio esse tiall but then it is not easily interpreted by human experts helps e pe ts e p ess i pli it k o ledge of the s ste , a d e defi e GTC as ou helps us ake data p ep o essi g fo filte i g a la ge a ou t of i ele a t solutio fo the o igi al p o le , ut this pa t eeds o e statisti al studies; e do o t adi tio s a d edu e o t adi tio size, hi h i di e tl o t i utes to the ot fu the dis uss this situatio . I this hapte , Q is add essed ele a t o t adi tio e t a tio . the GPC e t a tio algo ith . The ase stud fo the ele t i al i uit eake has o TC, ut GTC; e pe fo ed GPC e t a tio to a 6-2.4 Chapte : P o ess of odel ha ge usi g th ee diffe e t  "ele ti g a GPC ith o te t a d o e o se e al a ia les; the otio of o te t is then it does not exist in any inventive problem to be Classical TRIZ contradiction p oposed i Chapte . gi e GTC, t o o epts e e o tai ed that ould eate u e ous ph si al algo ith s Contradiction model to be easily interpreted by human experts DESIRED RESULT With ti e, if so e spe ifi outputs appea ed to e i te esti g, heu isti s ould e o t adi tio s ith o te t, a d thus the esult of the ase stud pa tiall a s e s Q . Fo the ase stud of a si ple Ka a , e e t a ted GPC fo t o o fli t I Chapte , e fi st e alled the ge e al f a e o k fo i e ti e desig p o le has to be GSC to exist in any inventive problem uilt fo o ki g o o e a ia les o p o idi g the sele ted set di e tl ithout
	The se o d e t a ts o e GTC o je ti e fo futu e i estigatio .	a e isti g i a p og a	i g algo ith as a
	supple e ta st ateg he the u e of e aluatio pa a ete s is g eate tha

 The u e of ge e alized te h i al o t adi tio s see s to i ease u til the disappea a e of the lassi al te h i al o t adi tio s; ho e e , it also g aduall de eases as e i ease the u e of satisfied ta gets. The e is al a s at least o e ge e alized o t adi tio i the data, u less the p o le is o pletel sol ed i.e. all ta gets a e satisfied; the e is o Pa eto .

The o t adi tio s f o the eal ase data did ot fu da e tall diffe f o those of the a do data o si ila ha a te isti s. Thus, it see s that e a use a do l ge e ated data to o st u t a d alidate the heu isti ide tifi atio of te h i al o t adi tio s. A e pe ts e e p o ide e pli itl the o te t of alidit of o t adi tio the alues of those a ia les ot i ol ed i the o t adi tio . Fo e a ple, the o t adi tio s fou d e pe ts ould e u de stood o o pleted defi i g the li its of thei alidit , o i e e sa, the si ple GTC o t adi tio s lose to the T'I) lassi al o t adi tio s ould e p oposed to the e pe t addi g the li its of thei alidit . "o eti es, sea hi g fo a sa ple of o t adi tio s helps ide tif the solutio s of the opti izatio p o le . I deed, it is possi le that i the set of e pe i e ts, sea hi g Co epts a d is sepa ate, a d t o uo fli ti g states ould appea i ea h o ept. I this ase, the o i atio of the t o o epts ould e a pote tial e aluatio pa a ete s "e i e B eakdo a d A e age "to k . The e a e . ph si al o t adi tio s ith o te t, e sele ted o e a d fo ulated the s ste of oeffi ie t a d "uppo t Ve to Ma hi e "VM ; the est esults e e o tai ed the "VM that e adopted. We de eloped a "VM-ased ethodolog usto ized to ou p o le s. I additio , the featu e sele tioased a tio pa a ete sele tio p o ided a pa tial solutio fo Q e ause the sele tio p o ess e o ed a i ele a t pa a ete s that did ot pa ti ipate i the o t adi tio fo ulatio . I Q e a t to sele t the sol i g, a d the a p o ess fo o tai i g a i e ti e solutio f o the e pe i e ts esults as p oposed, that o i es the GTC e t a tio algo ith f o Chapte , GPC e t a tio algo ith f o Chapte a d pa a ete sele tio st ateg f o I this pa t, e su a ize the e te t to hi h e a s e ed the te uestio s, a d dis uss hat e should do to atte pt to o pletel a s e all te uestio s i the futu e. Q is pa tiall a s e ed the e pe i e ts o du ted i Chapte s a d . I the futu e, e ould like to de elop a ulti-opti izatio algo ith that a app oa h Pa eto, hile fa ilitati g GTC e t a tio . The lassi al T'I) odel of o t adi tio is easie to sol e e ause it is easie to i te p et fo a hu a e pe t of the do ai : it is o e sig ifi a t. O the othe ha d, GFigu e : Co t adi tio of odel to e used fo i e ti e p o le s  Filte i g a ia les i ol ed i GTC o GPC , hi h is the goal of Chapte . "o e a tio pa a ete s do ot al a s ha e a effe t o the e aluatio pa a ete i ol ed i GTC. Afte e o i g these a tio pa a ete s, e a e o e se e al ph si al o t adi tio s.  "ele ti g o t adi tio s ith spe ifi ha a te isti s EP set a d e pe i e t sizes . The e a e t o ke ha a te isti s that a e i po ta t fo des i i g o t adi tio s: e pe i e t a d e aluatio pa a ete sizes fo G"C, i.e. the size of E +E a d that of Y +Y . G"C e pe i e t size i di ates the a ou t of k o ledge a out the p o le ati situatio , a d thus e p opose hoosi g the G"C asso iated ith the la gest e pe i e t size. O the othe ha d, sol i g a o t adi tio also ea s satisf i g all the e aluatio pa a ete s i plied i the o t adi tio . e pli itatio of all ge e alized o t adi tio . Fo Q , e o du ted t o t ials o the esolutio of si ple Ka a i Chapte a d dou le Ka a i Chapte . Fo si ple Ka a , the esolutio e o tai ed additio , e a t to de elop a heu isti algo ith that di e tl sea hes fo GTC i the e pe i e t esults. Fo GPC filte i g, e ill p og essi el de elop a utilizatio of the featu e sele tio algo ith i GTC-ased GPC e t a tio ; the ideal situatio is to di e tl use the esults to fo ulate a ge e alized ph si al o t adi tio ithout pe fo i g e e pe i e ts. Fo Q , the a s e is o ious: GTC o GPC e t a tio is a sea hi g p o le ; e p oposed usi g the opti izatio odel to fi d, GTC a d GPC i Chapte a d , a d p oposed a "VM odel he e the lea i g p o ess is a opti izatio p o ess fo a tio pa a ete sele tio , hi h is to fa ilitate GPC e t a tio .

opti isatio pou la o eptio i ve tive

  Ke ji, K. et al. The Featu e "ele tio P o le : T adi tio al Methods a d a Ne Algo ith . I : P o eedi gs of the th Natio al Co fe e e o A tifi ial I tellige e. "a Jose, CA, ou elle fa ille de thodes. Pou Altshulle la o t adi tio ph si ue t aduisait u e o t adi tio plus p ofo de au se s de la diale ti ue . L h poth se tait ue de i e toute o t adi tio te h i ue se a hait u e o t adi tio plus fo da e tale, la o t adi tio ph si ue. Figu e : s st e de o t adi tio s lassi ue de la T'I) Nos oti atio s p i ipales de l utilisatio des app o hes as es su la diale ti ue so t dou les : d u e pa t, ide tifie les o t adi tio s afi de ieu o p e d e,

	, pp. Hall, M.A. Co elatio -Based Featu e "ele tio fo Dis ete a d Nu e i lass -. Ma hi e Lea i g. I : ICML P o eedi gs of the Se e tee th I te atio al Co fe e e o Ma hi e lea i g. , pp. -. Vladi i N, V. The Natu e of Statisti al Lea i g Theo . "p i ge Ne Yo k, . Tai a U i e sit , . Les t a au p se t s da s le de la o t adi tio g alis e ous o t o fo t s da s l id e u il a u lie e t e la o t adi tio s a e t de l appa e te i possi ilit à satisfai e les esoi s oi e s i s i e t da s les e he hes e es Hsu, C. et al. A P a ti al Guide to Suppo t Ve to Classifi atio . Natio al e ide tifie pou l hu ai ; e e a he elle est suffisa e t p ise pou t e t ait e thodes d opti isatio et ui essite t des t a sfo atio s plus p ofo des des Résumé en français e pa u o di ateu d s lo s u o dispose de do es su le o po te e t d u od les se o t o sid s o e des p o l es d i e tio . e e e e s st e. L o jet p e ie ette th se est de p opose des o e s d ide tifie es o t adi tio s à pa ti de do es e p i e tales ou de si ulatio de s st es e La o eptio i e ti e se ase su des p i ipes sp ifi ues de solutio de p o l es afi de p opose de ou elles solutio s ati es po da t au ahie des M thodes d'Ce te te su e e f a çais le o te te et les sultats des t a au de Lei Li da s le ue de leu utilisatio pou la o p he sio des p o l es et leu solutio . Da s ha ges. Pa i es thodes, la T'I) a o e usse pou Th o ie de ' solutio e e ad e de ses t a au de th se. u se o d te ps, es ou eau outils peu e t t e utilis s pou te te d a al se et des P o l es d I e tio epose su l app o he diale ti ue des p o l es e e 1. I t odu tio l ide tifi atio des o t adi tio s. E fi , les e he hes e es pou la o st u tio te h i ues passe pa l ide tifi atio puis la solutio de o t adi tio s. Ces 1.1. Co texte de la th se d e pli ue e tai es diffi ult s p ati ues e o t es pa l hu ai lo s de Altshulle Paramètre d'Action . L u des a io es de la T'I) stipule ue l olutio des s st es (d'
	depuis u e ui zai e d a th o ie de l opti isatio et la T'I) au t a e s du o ept de o t adi tio . Les outils e au LGECO da s le ad e des appli atio s de la th o ie d olutio da s u o te te sp ifi ue ; elles se a ifeste t pa des o flits de C istia i i, N. et al. a i t odu tio to suppo t e to a hi es a d othe ke el-ased lea i g ethods. Ne Yo k, NY: a idge u i e sit p ess Ne Yo k, NY, U"A, de solutio des p o l es d i e tio T'I) et de so e te sio da s di e s d elopp s da s ette th se ise t gale e t à e plo e le lie e t e la th o ie de aleu s e t e les pa a t es des s st es te h i ues. La T'I) p opose diff e ts . do ai es. La T'I) est u e se le de thodes o ga is es e s st e, la o es l opti isatio et elle de la solutio des p o l es d i e tio ia les o epts de i eau de fo ulatio des o t adi tio s do t seuls deu so t utiles à la solutio
	Ca e o , G. ARI) E plo ed: A step--step guide to ARI) the Algo ith fo Sol i g I e ti e P o le s,C eatespa e, August o t adi tio g alis e et d e se le de Pa eto. Afi de o t e la po t e du p o l e : la o t adi tio te h i ue et la o t adi tio ph si ue. OT"M-T'I) , p. Kho e ko et al.
		t e	su	le
	o ept de o t adi tio , l e se le des uestio s au uelles eut po d e la deu i eau p de ts de o t adi tio . La o t adi tio te h i ue e p i e
	d a hes e ista tes. Co th se, l o ga isatio de la e he he pou a i e et l o ga isatio de la estitutio e e tai s fo de e ts de la T'I) tels ue la fle io l oppositio e t e deu pa a t es d u s st e, et le fait ue l a lio atio de l u
	diale ti ue so t t s g des t a au da s le des pa a t es e t ai e la d g adatio du se o d. La o t adi tio ph si ue d fi it i ues, uel ues t a au o t te t u e d a he a alogue oi e.
	à elle d Altshulle pou d aut es do ai es d appli atio tels ue le a age e t, la 1.2. Ba kg ou d deu tats o t adi toi es e uis pou u seul et e pa a t e. Le s st e de
	pu li it , la logisti ue et . "i tous es t a au o aisse t u e tai su s, des diffi ult s o t adi tio s elie u e o t adi tio ph si ue à deu o t adi tio s te h i ues ui La solutio de p o l es o upe u e pla e p po d a te da s les a ti it s de u e tes appa aisse t da s la ise e oeu e de la fo ulatio des p o l es pa leu o t adi tio sous-ja e te ; e fut gale e t le as lo s ue le la o atoi e s est e gag da s u e e he he su l e ploitatio des od les u i ues de o po te e t de s st es pou ide tifie pa u al ulateu les o t adi tio s sous-ja e tes au li ites du s st e. Ce faisa t, il est lai e e t appa u ue la d fi itio du o ept de o t adi tio tel ue d fi i pa la T'I) tait t op ague pou t e utilis o e tel pa des outils i fo ati ues, oi e u elle pou ait e t e à l o igi e des diffi ult s e o t es pa les g oupes o eptio Bo a del . Diff e tes thodes et outils so t p opos s pou fo ule et soud e les p o l es de o eptio . Pa i les diff e tes app o hes, u e lassifi atio possi le est de disti gue les thodes d opti isatio de elles d i e tio . U e fois le p o l e od lis , l opti isatio o siste à e he he des aleu s pou u e se le fi e de a ia les, sa s e ise e ause de e od le. Les thodes d opti isatio o t p ou leu effi a it da s de o euses situatio s ais e so t pas o çues pou soud e les p o l es essita t de t a sfo e le s st e à opti ise e ajouta t de ou elles a ia les et de ou elles elatio s e p i e t pou uoi les deu tats o t adi toi es so t e uis. Les deu Not e h poth se e pli ua t e p o l e p ati ue tait ota e t ue le o ept o t adi tio s te h i ues so t o pl e tai es et o espo de t à l a lio atio d u p e ie pa a t e ui e t ai e la d g adatio du se o d, et de o t adi tio de la T'I) doit t e et a aill et p is . ip o ue e t, à Les t a au pass s o t pe is de soulig e u e la u e da s la d fi itio et l a lio atio du se o d pa a t e ui e t ai e la d g adatio du p e ie . Da s Eltze a d De Guio l utilisatio des o t adi tio s dites « lassi ues ». Pa i les li ites o ote a les deu pa a t es i pli u es da s les o t adi tio s te h i ues o t t o l i e iste e a e da s e tai es situatio s de o t adi tio s o espo da t à la s pa a t es d aluatio , a ils pa ti ipe t à la d fi itio do e pa la T'I) lassi ue da s les elatio s dispo i les e t e les d fi itio de l o je tif du p o l e à soud e, ta dis ue le pa a t e a a t isa t la o t adi tio ph si ue d fi it u a ia les d u s st e, et l a se e de d fi itio e pli ite du o te te de alidit des o e d agi su la situatio , il est o o t adi tio s da s les thodes de solutio . Pou o le es li ites la
	e t e les a ia les. Da s la th se, les p o l es ui e peu e t t e solus pa les o t adi tio g alis e a t p opos e. La st u tu e de la o t adi tio g alis e
	est a alogue à elle de la T'I) lassi ue Figu e	e e plaça t les pa a t es pa

pa G. Altshulle da s le ut de fa ilite l i e tio d o jets ph si ues. La th o ie sous-ja e te à es o i aiso s de thodes epose su u e se le d h poth ses fo da e tales issues de la diale ti ue et de l a al se de l olutio des s st es te h i ues. La ajo it des t a au «d i o atio » e s da s e do ai e so t d o d e i e tal; ils o t pou ut d a lio e les di e ses o posa tes des d utilisateu s hu ai s pou d fi i les o t adi tio s. Ces aiso s p ati ues et th o i ues ous o t a e à e oi la d fi itio de la o t adi tio et à p opose la o t adi tio g alis e. Cette ou elle o t adi tio est e o e plus diffi ile à g ale de l app o he, les e e ples d illust atio p is da s la th se so t ti s aussi ie de la o eptio d o jets ue elle des p o essus de logisti ue i te e. Les pa ag aphes sui a ts de ette i t odu tio p ise t p og essi e e , ui a t d elopp da s le ut d appli ue les a io es de la T'I) pou âti des thodes de solutio de p o l es d i e tio appli a les au s st es o te h i ues, p opose e out e u s st e de o t adi tio s ui lie les pa a t e d a tio . Noto s ue da s l olutio de la T'I) la o t adi tio te h i ue est appa ue e p e ie a e des thodes de solutio adapt es, puis plus d u e dizai e d a e ap s est appa u le o ept de o t adi tio ph si ue a o pag d u e e p i e les p o l es de la o eptio i e ti e, et, d aut e pa t, d a o de la solutio de es p o l es a e des app o hes de solutio des o t adi tio s. Les o t adi tio s doi e t t e lai e e t d fi ies et o p he si les au d ut du p o essus de solutio afi de pou oi hoisi elle s pe etta t de soud e le p o l e. E effet, la p ati ue a o t u u au ais hoi de la o t adi tio peut o dui e à di i ue l effi a it du p o essus de solutio de p o l e. D où le ôle esse tiel de l e t a tio et l i te p tatio des o t adi tio s da s l app o he diale ti ue. La T'I) e sout pas la uestio du hoi pe ti e t de la o t adi tio .

un élément) doit être dans l'ETAT 1 mais cela dégrade le PARAMETRE d'EVALUATION 2 pour améliorer le PARAMETRE d'EVALUATION 1 doit être dans l'ETAT 2 pour améliorer le PARAMETRE d'EVALUATION 2 mais cela dégrade le PARAMETRE d'EVALUATION 1

  Figu e . Les o epts so t des o i aiso s logi ues de a ia le et de aleu s. Le pa a t e d a tio et ses deu tats de la T'I) lassi ue est e pla pa deu e se les de pa a t es d a tio et leu s tats asso i s ot s Co ept et Co ept da s la Figu e . Les pa a t es d aluatio et de la Figu e so t e pla s pa des e se les de pa a t es d aluatio Y et Y espe ti e e t da s la Figu e . Ai si, lo s ue les pa a t es d a tio po de t au Co ept , l e se le des aleu s p ises pa les pa a t es d aluatio Y est satisfaisa t alo s ue l e se le des aleu s p ises pa les pa a t es d aluatio Y est i satisfaisa t et i e e sa. Noto s ue la o t adi tio de T'I) lassi ue est u as pa ti ulie de o t adi tio g alis e.

	des o epts
		CONTRADICTION TECHNIQUE 1
		RESULTAT
		DESIRE
	CONTRADICTION PHYSIQUE	CONTRADICTION TECHNIQUE 2

Figu e : " st e de o t adi tio s g alis es 1.

3. P o l ati ue Da

  des as où au u e o t adi tio de la T'I) lassi ue e iste et pou ta t les p o l es e peu e t pas t e solus pa l opti isatio . De e fait, le o ept des o t adi tio s g alis es a t i t oduit. Ces o t adi tio s g alis es e so t p ati ue e t pas e he h es a leu e p essio est diffi ile à p o e oi pou l esp it hu ai . E effet, u e pe t hu ai peut assez fa ile e t alide u e o t adi tio g alis e, ais il est eau oup plus diffi ile pou lui de la d fi i . De plus, e lo s u o e he he des o t adi tio s ph si ues ou te h i ues si ples selo od le de la T'I) lassi ue , le p ati ie hu ai peut t e o f o t à ses p op es li ites d e pe tise lo s ue le s st e est t op o ple e ou s il a pas d e pe tise su le s st e o sid .Cette th se o t i ue à po d e à u e p o l ati ue se situa t à plusieu s i eau .Les pa ag aphes sui a ts p ise t es i eau et les uestio s asso i es.Le p e ie i eau de uestio s de l o d e de la th o ie de la o eptio o e e le o ept de o t adi tio l u des fo de e ts de la T'I) : Qua d au u e o t adi tio te h i ue ou ph si ue lassi ue est dispo i le les o t adi tio s te h i ues g alis es et les o t adi tio s ph si ues g alis es e iste t elles et so t-elles o euses ? Peut-o toujou s à pa ti de la ep se tatio o po te e tale d u s st e et d o je tifs d te i e ses o t adi tio s g alis es de a i e i t i s ue au e tit e u u Pa eto pa e e ple . Quelles so t les o s ue es ? Da s e as, o e t les ide tifie et les e t ai e de a i e e hausti e ? U e fois o ues, o e t hoisi d fi i elles ui so t pe ti e tes ? Ou e o e, o e t d fi i u e o t adi tio pe ti e te ? Le se o d i eau d o d e thodologi ue o e e les o s ue es p ati ues d u e ou elle d fi itio des o t adi tio s pou la solutio des p o l es i e tifs : U e fois les o t adi tio s ide tifi es et e t aites, o e t pou o s-ous les utilise da s la solutio des p o l es i e tifs ? Co e t e t ai e des o euses o t adi tio s elles ui so t pe ti e tes de a i e effi a e et effi ie te sa s e he he e hausti e sou e t t op outeuse e te ps de e he he et de filt age a post io i ? Pou o s-ous utilise le o ept de la o t adi tio g alis e pou e p i e la o aissa e i pli ite d e pe ts d u s st e ? E fi , le t oisi e i eau des uestio s o e e l e plo atio du lie e t e les thodes d opti isatio et la T'I) pou fai e u e fe tilisatio ois e d u poi t de ue th o i ue et/ou p ati ue a t a o d . Pou o s-ous utilise les thodes et les o epts d opti isatio afi de fa ilite l ide tifi atio des o t adi tio s g alis es ? Y-a-t-il u lie e t e le o ept de Pa eto et la o t adi tio g alis e ? "i e lie e iste, peut-il t e is à p ofit pou ide tifie les o t adi tio s g alis es I e se e t si e lie e iste, sa o aissa e peut-elle t e ise à p ofit pou fa ilite les p o essus d opti isatio ? Le ut de ette th se est po d e pa tielle e t ou e ti e e t au uestio s p de tes. La st at gie de e he he adopt e pou po d e est d ite da s la se tio sui a te. Pou po d e à es uestio s il a t d id de o st ui e da s u p e ie te ps u outil d e t a tio e hausti e des o t adi tio s g alis es te h i ues puis ph si ues à pa ti de do es. Pou e fai e, les p o l es d ide tifi atio des o t adi tio s te h i ue et ph si ues g alis es o t t od lis s pa des p o l es d opti isatio o i atoi e, puis u algo ith e de solutio a t p opos pou ha ue as. U e fois es algo ith es s, ils o t pu t e utilis s pou t aite les uestio s Q et Q de ot e p o l ati ue pa des tudes e pi i ues i l es. Ils o t gale e t pe is de fai e des h poth ses su les po ses au uestio s Q et Q . De fait, ous a o s po du positi e e t à la uestio Q . Les thodes e hausti es o t leu s li ites : d u e pa t, elles e peu e t t e ises e oeu e ue pou des s st es au o e de a ia les li it s te ps de al ul h o ophage , et d aut e pa t, o e le o t e les po ses au uestio s Q et Q es o t adi tio s so t e t e e t o euses. Cette li ite se fait su tout esse ti au i eau des pa a t es d a tio . Pou e ule la li ite li e au o e de a ia les, ot e st at gie a o sist à a al se les do es de so te à ide tifie les a ia les d a tio et leu aleu s i pli u es da s les o epts des o t adi tio s ph si ues g alis es sa s a oi à d te i e les o epts eues, puis d utilise l algo ith e e haustif su le s st e duit au a ia les ide tifi es. La d a he pe etta t le p t aite e t et la du tio des a ia les d a tio e ue de l ide tifi atio des o t adi tio s a t alis e e te ta t d appo te des po ses au uestio s Q et Q . U e alte ati e à ette s ue e, ui est pas d elopp da s ette th se, se a la o eptio d heu isti ue de e he he di e te de o t adi tio s pe ti e tes à pa ti de do es sa s e he he e hausti e de ellesi. La ise au poi t de es algo ith es suppose l ide tifi atio de p op i t s p op es au o t adi tio s « pe ti e tes ». La e he he de es p op i t s peut se fai e pa la alisatio de as a e des e pe ts de o eptio i e ti e oupl e à l a al se des sultats des do es e hausti es i i ous p e d o s u as d ole a ad i ue du do ai e de la logisti ue . Nous esp o s ai si po d e à la uestio Q . Da s le ad e de th se ous e pe so s pas pou oi do e u e po se o pl te à la uestio Q ais ous pe so s pou oi o t i ue e e p i e ta t les heu isti ues p de tes su des as a ad i ues et els lo s ue le o e de a ia les s p te. La uestio Q est dis ut e au u de la s th se des sultats Afi de estitue es t a au et les po ses à la p o l ati ue i-dessus, les hapit es sui a t l i t odu tio du oi e so t o ga is s de la a i e sui a te. Les hapit es et t aite t espe ti e e t de l ide tifi atio des o t adi tio s te h i ues et ph si ues. Ils fo ule t le p o l e d opti isatio , p opose t u algo ith e de solutio ui est e suite utilis pou po d e au uestio s idessus. Le hapit e a o de le p o l e de l ide tifi atio des a ia les pa ti ipa t au o t adi tio s ph si ue, p opose u e heu isti ue de ase ui est alu e, p opose u e des d a hes d ide tifi atio à pa ti de ette heu isti ue puis dis ute les o t i utio s au uestio s de la p o l ati ue. Le hapit e p opose u e a i e de o i e les outils d elopp s da s les hapit es p de ts au sei d u e thodologie de solutio de p o l es d i e tio . Cette p opositio est illust e à l aide d u p o l e su u s st e de Ka a . Le hapit e p opose u e dis ussio de s th se su les o t i utio s et les li ites des sultats des hapit es p de ts p is da s leu e se le. Il p opose gale e t des pe spe ti es à la Che et al., do t la solutio est o ga is e e sous p o l es. Ce p o l e o i atoi e se le NP-diffi ile. Les solutio s à e p o l e so t les o t adi tio s g alis es. U algo ith e do t l o je tif est l ide tifi atio des toutes les solutio s à e p o l e d ide tifi atio et d e t a tio des o t adi tio s te h i ues g alis es est p opos . Il utilise o e do es d e t e les do es issues de pla d e p ie es su des s st es ph si ues ou su des si ulateu s. "a o ple it et ses li ites so t p se t es et alu es su l e e ple d u disjo teu le t i ue. L espa e de e he he des o t adi tio s te h i ues g alis es est d fi i pa le o e des pa a t es du s st e et pa le o e d e p ie es i pli u es. L algo ith e p se t da s e hapit e pe et do de po d e à la uestio Q lo s ue le o e de a ia les est li it à . Disposa t de et algo ith e ous pou o s e isage de po d e gale e t à la uestio Q pou les o t adi tio s te h i ues e alisa t des e p ie es adapt es. De es e p ie es, il esso t les l e ts sui a ts : Plus o dispose de solutio s po da t à des o je tifs d aluatio ultiples, oi s il a de ha e de pou oi fo ule u e o t adi tio te h i ue lassi ue. Lo s u o po d à plus de % des o je tifs il a p ati ue e t plus de ha e de t ou e u e o t adi tio te h i ue lassi ue. Ce poi t e pli ue les diffi ult s e o t es pa les e pe ts hu ai s pou fo ule des o t adi tio s selo le od le de la T'I) lassi ue da s e tai es situatio s. Le o e de o t adi tio s te h i ues g alis es se le oit e jus u à la dispa itio des o t adi tio s lassi ues, il di i ue epe da t gale e t e suite au fu et à esu e u o aug e te le o e d o je tifs attei ts. Il e iste toujou s au oi s u e o t adi tio g alis e da s les do es sauf si le p o l e est totale e t solu i.e. tous les o je tifs so t attei ts, il a pas de Pa eto . ui e et alide des heu isti ues d ide tifi atio des o t adi tio s te h i ues. Le p o l e des do es e se pose pas pou l algo ith e de solutio e a te p opos da s le oi e, ais il se pose a pou des heu isti ues ui ise t à soud e le e p o l e pou des s st es o te a t u g a d o e de a ia les. L appli atio des sultats de e hapit e pe et gale e t de do e des po ses pa tielles au uestio s Q à Q . Pou la e he he e hausti e a e l algo ith e p opos ous so es li it s pa pa a t es d aluatio . Ce hapit e t aite de la e he he de toutes les o t adi tio s ph si ues asso i es à u e o t adi tio te h i ue g alis e, p opose u algo ith e, dis ute ses li ites, ses o t i utio s à la p o l ati ue de th se et ses appli atio s pote tielles. La e he he de ha ue o ept d u e o t adi tio ph si ue g alis e est d a o d d fi ie o e la e he he de o epts dis i i a ts su des e se les d fi is pa la o t adi tio te h i ue g alis e. E effet, u e o t adi tio te h i ue g alis e pa titio e l e se le l espa e des a tio s E e t ois e se les : l e se le de l espa e d a tio ui satisfait les pa a t es d aluatio Y ue ous oto s E , elui ui satisfait les pa a t es Y ue ous d o o s E et le t oisi e ui o pl te E et E pou fo e E ue ous oto s E . 'e he he u o ept e ie t à e he he u e fo tio ui dis i i e ui e o ait des l e ts de E et les dis i i e de E UE . I e se e t, e he he u o ept e ie t à e he he u e fo tio ui e o ait des l e ts de E et les dis i i e de E UE . Le p o l e de e he he est d fi it sous la fo e d u p o l e de p og a atio i ai e e o es e tie s do t o utilise les p op i t s pou le soud e. Ces o t adi tio s peu e t t e t s o euses et i possi les à liste da s u te ps aiso a le. Pou pallie e p o l e ous o t o s u u e o t adi tio ph si ue g alis e sp ifi ue peut su e toutes les o t adi tio s ph si ues g alis es possi les. La e he he de ette o t adi tio sp ifi ue peut t e faite e ajouta t u e fo tio o je ti e à l e se le des uatio s à satisfai e da s le p og a e i ai e, e ui e ie t à soud e le p o l e d opti isatio e tie i ai e. Da s e hapit e, l algo ith e est illust à l aide d e e ples o ets ota e t le as du disjo teu le t i ue ui o t e le o e t s i po ta t des s st es de o t adi tio s g alis es ui peut t e t ou . La o ple it de l algo ith e est d fi ie et les li ites p ati ues d utilisatio s de l algo ith e so t do es : pa e e ple le o e des pa a t es d a tio du s st e à t aite est li it les as d tude e s o t e t ue l e t a tio e hausti e fo tio e si oi s de pa a t es d a tio du s st e a e au a i u deu i eau de aleu s à t aite su les o di ateu s à ot e dispositio . L utilisatio de l algo ith e a gale e t pe is d appo te u e po se pa tielle à la uestio Q e o pa a t les o t adi tio s fo ul es pa des e pe ts i d pe da ts et elles d fi ies pa les algo ith es p de ts. U e e ploitatio possi le de l algo ith e et i atte due au d pa t de l tude est la possi ilit d ide tifie des o t adi tio s ph si ues lassi ues ou g alis es da s u o te te de glage des pa a t es d a tio . Ce i pe et d e isage de ultiples appli atio s da s le ad e de la o eptio i e ti e et de l aide à la o p he sio des o t adi tio s. Ai si pa e e ple, o peut o p e d e ou o pl te des o t adi tio s ises pa des e pe ts e d fi issa t leu li ite de alidit , ou i e se e t p opose au o epteu s des o t adi tio s si ples se app o ha t de elles de la T'I) lassi ue e ajouta t les li ites de alidit . La e he he des o t adi tio s su u ha tillo pe et pa fois d ide tifie des solutio s au p o l e d opti isatio . E effet, il se peut ue su l e se le d e p ie es, les o epts et t ou s s pa e t e soie t pas o t adi toi es. Da s e as, la o i aiso de es o epts est u e solutio pote tielle au p o l e i itial ui est peut-t e pas u p o l e d i e tio .

	1.4. D a he de e he he au uestio s p de tes. 1.5. O ga isatio du oi e e he he p se t e da s le oi e. 2. E t a tio des o t adi tio s te h i ues g Le p o l e d ide tifi atio est d a o d d it et efo ul sous la fo e d u alis es p og a e d opti isatio e o e e tie i ai e Les o t adi tio s issues de do es de as els e se disti gue t pas fo da e tale e t de elles des do es al atoi es a a t des a a t isti ues se la les. Il se le do u o puisse utilise des do es g es al atoi e e t alis es Pou fo e u s st e de o t adi tio s g alis es o e elui de la Figu e , o peut asso ie plusieu s o t adi tio s ph si ues g alis es à u e o t adi tio pou o st 3. Ide tifi atio des o t adi tio s ph si ues g te h i ue g alis e.

s la p ati ue a tuelle le s st e de o t adi tio s est e he h pa i te ie d e pe ts. Da s os t a au de e he he p de ts, ous a o s d o t u il e iste 4.

Ide tifi atio des pa a t es pa ti ipa t au o t adi tio s ph si ues

  Co e p is au hapit e , l utilisatio des algo ith es de e he he e hausti e des o t adi tio s g alis es a ses li ites ua t au o e de pa a t es pou a t t e t ait s a e u o di ateu . Pou l algo ith e de e he he des o t adi tio s te h i ues g alis es ous e pou o s t aite ue pa a t es d aluatio et da s le as de l algo ith e de e he he des o t adi tio s ph si ues g alis es ous e pou o s t aite ue pa a t es d a tio a e aleu s ha u . E e a he, le t aite e t des sultats o te us a e es algo ith es da s les as els, ous a e e s l h poth se ue da s la plupa t des as, seule e t uel ues pa a t es d a tio s so t i pli u s da s les o t adi tio s ph si ues g alis es. U e solutio se ait do de e pas o sid e tous les pa a t es d a tio et toutes leu s aleu s pou d fi i et ide tifie les o t adi tio s. L o je tif de e hapit e est de p opose des heu isti ues pe etta t de s le tio e des pa a t es pe ti e ts et leu s aleu s pe ti e tes pou la e he he des o t adi tio s g alis es. Pou ela l ide tifi atio des pa a t es pe etta t de lasse les l e ts da s deu e se les disti ts est a o d e sous l a gle des thodes d app e tissages e i tellige e a tifi ielle. Nous o e ço s pa o t e ue l ide tifi atio des pa a t es et de ses aleu s e t a t da s les o epts des o t adi tio s ph si ues g alis es s appa e te à u e s ie de p o l es o us sous le o a le de « featu e sele tio p o le » da s e tai s do ai es de e he he Liu & Motoda, . Il s agit de t ou e l e se le opti al des a a t isti ues d u e se le de do es afi d a lio e la p isio d u lassifieu , d a l e les algo ith es d e plo atio des do es et de fou i u e eilleu e o p he sio de ses sultats. Da s la p e i e pa tie de e hapit e, l tat de l a t et le hoi d algo ith es de featu e sele tio adapt à ot e o je tif so t p se t s ; ot e o je tif ta t de he he l e se le des pa a t es d a tio ui o t u effet positif sig ifi atif su les pa a t es d aluatio . Pa i les thodes de « featu e sele tio » elles de « sig ed featu e sele tio » se le t les plus adapt es à ot e as. Deu thodes o t t i pl e t es et test es : Pea so Co elatio Coeffi ie t et "uppo t Ve to Ma hi e "VM ; les eilleu s sultats so t o te us a e la "VM ue ous a o s adopt e et do t ous p se to s l appli atio à ot e situatio da s e hapit e. La thode "VM t a sfo e u p o l e oli ai e e u p o l e li ai e est-à-di e fou it u e lassifi atio li ai e da s l espa e de e he he des a a t isti ues o -li ai e e fo tio des poids de es a a t isti ues. Plus la a a t isti ue le pa a t e d a tio a du poids da s la thode "VM plus il a de l i flue e su l e se le tudi le pa a t e d aluatio et sa aleu o je ti e . U aut e a a tage de la thode "VM est ue ous pou o s o sid e ha ue pa a t e d aluatio o e sulta t des o i aiso s des pa a t es d a tio . Deu d a hes à ase de l utilisatio p t e d algo ith es de t pe "VM so t p opos es. La p e i e s appuie su les fa illes d e p ie es d fi ies pa u e o t adi tio te h i ue g alis e ; la se o de s appuie su les fa illes d fi ies pa les pe fo a es attei tes ou o de ha ue a ia le d aluatio . Pou alue l algo ith e e t al o çu à ase de "VM, u e se le de as do t o o ait la po se le o ept à ide tifie est o st uit. Les sultats de l appli atio de l algo ith e à ette ase de as so t fou is et dis ut s. L e ploitatio des sultats o te us ous a e gale e t à fl hi à l e plo atio du lie e t e la d a he d ide tifi atio des pa a t es et les thodes d opti isatio , ota e t su la e he he des a ia les l s pou t ou e le Pa eto.

  a tio des o t adi tio s g alis es as s su les p o l es d opti isatio o i atoi e o e t e t ai e les o t adi tio s g alis es de a i e e hausti e Q et ous a o s e des tudes e pi i ues. Les sultats o t e t ue si le as où au u e o t adi tio te h i ue ou ph si ue lassi ue est dispo i le est assez o u et oit a e le o e des solutio s dispo i les, au oi s u e o t adi tio g alis e e iste toujou s, et, da s la ajo it des as, elles-i so t e t e e t o euses po se à la uestio Q . Da s e as, la uestio o e t hoisi /d fi i les o t adi tio s pe ti e tes se pose Q . Nous essa o s d po d e e e ploita t et utilisa t les lie s e t e les thodes et les o epts d opti isatio et la T'I), tel ue le o ept de Pa eto. E e te ps le fait de g e eau oup de sultats li ite les thodes e hausti es d e t a tio des o t adi tio s e te es de o e de pa a t es pou a t t e p is e o pte da s les algo ith es. Pou fai e fa e au li ites des thodes e hausti es, ot e st at gie a o sist à ett e e pla e des heu isti ues ui ise t à soud e le e p o l e pou des s st es o te a t u g a d o e de a ia les. U e e ploitatio possi le de l algo ith e est la possi ilit d ide tifie des o t adi tio s ph si ues lassi ues ou g alis es da s u o te te de glage des pa a t es d a tio . Ce i pe et d e isage de ultiples appli atio s da s le ad e de la o eptio i e ti e et de l aide à la o p he sio des o t adi tio s. Ai si pa e e ple, o peut o p e d e ou o pl te des o t adi tio s ises pa des e pe ts e d fi issa t leu li ite de alidit , ou i e se e t, p opose au o epteu s des o t adi tio s si ples se app o ha t de elles de la T'I) lassi ue e ajouta t les li ites de alidit . "uite à la ise e pla e su essi e des algo ith es et des heu isti ues ous a o s t e e s à t aite les uestio s o e a t les o s ue es p ati ues des ou elles o t adi tio s pou la solutio des p o l es i e tifs Q . L utilisatio de l algo ith e a gale e t pe is d appo te u e po se pa tielle à la uestio Q e o pa a t les o t adi tio s fo ul es pa des e pe ts i d pe da ts et elles d fi ies pa les algo ith es p de ts. Au fu et à esu e de os t a au de e he he ous so es de plus e plus a e s à fl hi su la a i e de o i e les algo ith es et les heu isti ues p de ts da s u e d a he g ale d e t a tio des o t adi tio s g alis es pe ti e tes de a i e effi a e et effi ie te sa s e he he e hausti e Q . Il s agit d a al se les do es de so te à ide tifie les a ia les d a tio et leu aleu s i pli u es da s les o epts des o t adi tio s ph si ues g alis es sa s a oi à d te i e les o epts eues, puis d utilise l algo ith e e haustif su le s st e duit au a ia les ide tifi es. La d a he pe etta t le p t aite e t et la du tio des a ia les d a tio e ue de l ide tifi atio des o t adi tio s pe ti e tes est alis e e e plo a t le lie e t e les thodes d opti isatio et la T'I) e ui pe et d appo te des po ses au uestio s Q , Q et Q . L ide tifi atio des a ia les et aleu s i pli u es da s les o t adi tio s pe et d appo te u e eilleu e o p he sio oi e l ide tifi atio des l e ts a ia les l s pou he he le Pa eto Q . Le hapit e se te i e pa u e dis ussio p ospe ti e. La th se t aite des p o l es d i e tio où les solutio s des thodes d opti isatio e satisfo t pas au o je tifs des p o l es à soud e. Les p o l es ai si d fi is e ploite t, pou leu solutio , u od le de p o l e te da t le od le de la T'I) lassi ue sous u e fo e a o i ue appel e «s st e de o t adi tio s g alis es ». Cette e he he i st u e te u p o essus de solutio as su la ou le si ulatio -opti isatio -i e tio pe etta t d utilise à la fois des thodes d opti isatio et d i e tio . Plus p is e t, elle od lise l e t a tio des o t a tio s g alis es à pa ti de do es de si ulatio sous fo e de p o l es d opti isatio o i atoi e et p opose des algo ith es do a t toutes les solutio s à es p o l es. De plus, elle p opose des heu isti ues pou s le tio e les a ia les et les aleu s pe ti e tes i te e a t da s les o t adi tio s g alis es et/ou utiles pou l opti isatio . Les o t i utio s o e e t la th o ie et la p ati ue de la o eptio i e ti e. La th se e plo e gale e t la fe tilisatio ois e e t e l opti isatio et la T'I).

	Lei LIN
	Optimization methods for inventive design
	' su

http:// .la e . o /f / it ess/

Acknowledgements

List of Tables

Fo the GTC i Ta le

, the e pe i e ts a e ot full fa to ial; thus, the GPC e t a tio des i ed i Figu e as pe fo ed. The e a e states i ol ed i

Co ept , a d states i Co ept . The a e p ese ted i Ta le .

Ta le : T o o epts of GTC fo ele t i al i uit eake -.