Rachel Calvet

Alain Chamayou

B Hamdi

H Balard

L Boudriche

Alger Rp

Algeria Alger

Removal of lead(II) from aqueous solution using modified palygorskite, contribution of inverse gas chromatography

Keywords:

Removal of lead(II) from aqueous solution using modified palygorskite, contribution of inverse gas chromatography

L. Boudriche,

Introduction

Heavy metals, such as cadmium, lead, chromium, mercury, and copper, are released into the environment as a result of several industrial activities including manufacturing of microelectronics, electroplating, metal finishing, battery, tannery, processes in the metallurgical, and fertilizer industries. These metals lead to contamination of air, water and soil and consequently they can be absorbed by animals and plants. Due to their accumulation in the food chain and in the human body, they can present a risk for human health [START_REF] Potgieter | Heavy metals removal from solution by palygorskite clay[END_REF].

Conventional methods to treat contaminated effluents can be classified into several categories: adsorption (activated carbon, clays) [START_REF] Zhang | Roles of physical and chemical properties of activated carbon in the adsorption of lead ions[END_REF][START_REF] Bhattacharyya | Adsorption of a few heavy metals on natural and modified kaolinite and montmorillonite: a review[END_REF][START_REF] Souza | Selective adsorption of gold over copper cyanocomplexes on activated carbon[END_REF], precipitation [START_REF] Feng | Treatment of acid mine water by use of heavy metal precipitation and ion exchange[END_REF][START_REF] Haddou | Plasmacatalytic removal of lead acetate assisted by precipitation[END_REF], physico-chemical techniques (e.g. electrolysis, solvent extraction, membrane separation) [START_REF] Khider | Purification of water effluent from a milk factory by ultrafiltration using Algerian clay support[END_REF][START_REF] Wang | Separation of Zr and Hf from sulfuric acid solutions with amine-based extractants by solvent extraction[END_REF][START_REF] Zulhairun | The role of layered silicate loadings and their dispersion states on the gas separation performance of mixed matrix membrane[END_REF] and biological techniques (e.g. biosorption, phytoextraction) [START_REF] Farooq | Biosorption of heavy metal ions using wheat based biosorbents -a review of the recent literature[END_REF][START_REF] Tabaraki | Biosorption of lead(II) ions on Sargassum ilicifolium: application of response surface methodology[END_REF][START_REF] Yuan | Enhancement of Cd phytoextraction by two Amaranthus species with endophytic Rahnella sp[END_REF].

However, for economic and practical reasons, many laboratories show more and more interest in the use of new adsorbents based on natural materials [START_REF] Qaiser | Biosorption of lead from aqueous solution by Ficus religiosa leaves: batch and column study[END_REF][START_REF] Houari | Dynamic sorption of ionizable organic compounds (IOCs) and xylene from water using geomaterial-modified montmorillonite[END_REF]. Thus, materials such as natural or synthetic zeolites, tuffs, volcanic ash and especially clays are used in the treatment of liquid effluents loaded with pollutants.

In the current study, four modified palygorskite samples were used to remove lead metallic ions from aqueous solutions. Among them, three were obtained using different milling processes, and one by an acid treatment. These mechanical and chemical activations of palygorskite [START_REF] Boudriche | Effect of acid treatment on surface properties evolution of attapulgite clay: an application of inverse gas chromatography[END_REF][START_REF] Boudriche | Influence of different dry milling processes on the properties of an attapulgite clay, contribution of inverse gas chromatography[END_REF] induced changes in microstructure morphology and surface chemistry. All these modifications were expected to deeply change interaction capacities of the samples with the media, which was a lead(II) ion containing solution. These interactions could be assessed using inverse gas chromatographic analysis (IGC). Indeed, among the vapour adsorption techniques, inverse gas chromatography (IGC) is getting increasing attention as it offers several advantages such as the possibility of using a variety of probes and a broad range of temperatures [START_REF] Mohammadi-Jam | Inverse gas chromatography applications: a review[END_REF]. This technique is very helpful to determine interactions between specific probes and the solid under investigation packed into a column in order to predict behaviour of the solid with its environment. After determination, by IGC at infinite dilution, of classical parameters such as dispersive component of the free energy ( d s ) or specific free energy of adsorption (-G sp a ), this study focused, particularly, on the determination of irreversibility indexes of palygorskite, using IGC at finite concentration with the isopropanol probe. This parameter leads an assessment of amount of adsorption sites having a high energy of interaction on the palygorskite surface during the solid-gas adsorption process. This parameter will be correlated with another parameter characteristic of the surface clay, the cation exchange capacity, during solid-liquid adsorption process in the presence of a pollutant. Thus, the second part in this study covered the adsorption performance of this clay towards a pollutant in the static mode. The adsorption capacities of palygorskite towards Pb(II) ions were assessed using the plot of adsorption isotherms in equilibrium conditions.

Adsorbents elaboration and characterization

Adsorbent elaboration

The palygorskite used in this study, is a hydrated magnesium aluminium silicate, from the Ghoufi region, in the North-East of Algeria. According to Bradley [START_REF] Bradley | The structural scheme of attapulgite[END_REF], palygorskite is a fibrous clay mineral; its structure (Fig. 1) consists of ribbons of a 2:1 phyllosilicate, linked by periodical inversion of the apical oxygen of the continuous tetrahedral sheet and thus the octahedral sheet is discontinuous [START_REF] Mckeown | Vibrational analysis of palygorskite and sepiolite[END_REF].

A rock palygorskite was first coarsely crushed and sieved to obtain a size fraction less than 1 mm. This raw sample was then processed to obtain four modified palygorskite powders implemented in the lead adsorption experiments:

-A crushing in an agate mortar and sieving in order to select the fraction having a diameter below 350 m. -A milling in a pancake air jet mill AS 50 supplied by the Hosokawa Micron Company. The injection and grinding pressures were 4.0 × 10 5 and 3.5 × 10 5 Pa, respectively. -A milling for 60 h in a lab-scale vibratory ball mill called "Pulverisette0", provided by the Fritsch Company. This device consisted in an agate vibrating vessel equipped with a 5 cm ball.

The vibration amplitude of the vessel was fixed at 2 mm and 10 g samples were ground per experiment.

All the grinding processes were described in a previous study [START_REF] Boudriche | Influence of different dry milling processes on the properties of an attapulgite clay, contribution of inverse gas chromatography[END_REF].

-A chemical activation according to a protocol also described in a previous study [START_REF] Boudriche | Effect of acid treatment on surface properties evolution of attapulgite clay: an application of inverse gas chromatography[END_REF]. It consisted in an hydrochloric acid treatment carried out under reflux system at the boiling point of the HCl solution for 6 h. The experiment was done with an 0.5 M HCl concentration. After reflux, the solution was filtered and the residue washed with distilled water several times until elimination of all the chloride ions.

Characterization techniques

Particle size distribution measurements were performed using a Laser diffraction method on a Malvern Mastersizer 2000 device. The samples were analyzed using a dry-way feeder (Scirocco, Malvern) with a dispersion pressure of 3.5 × 10 5 Pa. Specific attention was paid to the Sauter mean diameter d 32 defined as follows:

d 32 = n i d 3 i n i d 2 i (1)
where n i is the number of particles with size d i .

The true density of samples was measured with a helium pycnometer (AccuPyc 1330-Micromeritics). The measurements were carried out with about 2-3 g of powder in a 5 mL cell. This technique is based on measuring a change in pressure of helium in a calibrated volume with and without a sample.

The Sauter mean diameter d 32 and true density allowed the calculation of the external specific surface area, a ext , according to the Eq. ( 2):

a ext = 6 • d 32 (2)
Particle morphology was investigated using a scanning electron microscope (Philips XL 30 model ESEM-FEG) operating at 3 kV.

The BET specific surface areas, meso-and micropore volumes were calculated using nitrogen adsorption at 77 K (ASAP 2010, Micromeritics). The same technique allowed the determination of the meso-and micropores volumes applying BJH and t-plot models, respectively. Size limits proposed by the International Union of Pure and Applied Chemistry are between 2 and 50 nm for mesopores and less than 2 nm for micropores. The samples were gassed out before analysis, at 378 K for 24 h at a pressure of 8 × 10 -1 Pa.

Meso-and macro-pores volumes, having a distribution between 3.2 nm and 1 m were determined by mercury porosimetry using a Micromeritics Autopore III WIN 9420 porosimeter.

Characterization results

The scanning electron microscope of the raw material exhibited a fibrous morphology with fibres having an average length less than 3 m (Fig. 2a). This fibrous structure was preserved within crushing in the mortar (Fig. 2b) or grinding in a pancake air jet mill (Fig. 2c) despite the fibres became shorter and more disorganized. On the contrary, fibre morphology was totally destructed after 60 h milling in Pulverisette0 (Fig. 2d). After acidic treatment, the fibrous structure was also maintained (Fig. 2e).

Other characterizations (IR spectrum, PXRD pattern, adsorption isotherm, etc.) of the raw material and the processed ones were presented in previous works [START_REF] Boudriche | Effect of acid treatment on surface properties evolution of attapulgite clay: an application of inverse gas chromatography[END_REF][START_REF] Boudriche | Influence of different dry milling processes on the properties of an attapulgite clay, contribution of inverse gas chromatography[END_REF][START_REF] Boudriche | An assessment of the surface properties of milled attapulgite using inverse gas chromatography[END_REF].

Different characteristic parameters such as the equivalent diameters (d 50 , d 32 ), external specific surface area (a ext ), density ( ), specific surface area measured by nitrogen adsorption (a BET ), porous volumes (V micro , V meso , V porous ) were determined. The main results of characterization of the processed materials are presented in Table 1.

The highest specific surface area was obtained for the sample treated with the acid solution. Indeed, acid treatment leads to the remove of carbonates that generates porosity and to the increase of specific surface area.

The mesoporous volume, V meso , determined by nitrogen adsorption and according to the BJH model characterizes the mesopores with diameters between 2 and 50 nm. The porous volume, V porous , obtained by mercury porosimetry includes larger pores diameters, from 3 to 1000 nm, i.e. meso-and macropores. It can be observed that V porous is slightly lower than V meso , except for the sample ground with Pulverisette0. A possible explanation is that measurement made by mercury porosimetry was performed on a tablet and the compression could modify the porous network. Nevertheless, V porous and V meso are similar; they indicate low macroporosity.

Comparing the different samples, whatever the porous volume considered (V micro , V meso or V porous ), the highest one was observed for the sample treated with hydrochloric acid. It is also the result of the removal of carbonates that generates porosity. 3. Characterization of adsorbent surface properties by inverse gas chromatography (IGC)

Theoretical part

Inverse gas chromatography (IGC) can be carried out according to two different implementations at: infinite dilution (IGC-ID) and finite concentration (IGC-FC).

IGC-ID analysis

This technique reflects the interaction developed between a probe and high energy sites on the solid. It consists on the injection of negligible quantities of probes molecules (vapour) with known properties (polarities, ramification). Experimentally, the infinite dilution domain was defined by the fact that the retention time or volume remained constant in function of the injection probe volume, this linear chromatography correspond to the Henry's region. Then, depending on the chemical nature of the probe molecule, the IGC-ID provides different parameters:

-The dispersive component of the surface energy ( d s ), obtained by injection of linear alkanes. This parameter indicates the ability of the solid surface to have non-specific interactions with probe molecules [START_REF] Dorris | Adsorption spreading pressure and London force interactions of hydrocarbons on cellulose and wood fiber surfaces[END_REF].

-The nanomorphological index I M ( t ), established by injection of branched or cyclic alkanes, delivers information about the roughness of the solid surface at the molecular scale [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations[END_REF]. -The specific component of the surface energy (-G sp a ), determined by injections of polar probes, gives access to polar interactions, mainly the acid-base interactions [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations[END_REF].

More details regarding the calculations of various parameters obtained from IGC-ID experiments were given in a previous paper [START_REF] Boudriche | Influence of different dry milling processes on the properties of an attapulgite clay, contribution of inverse gas chromatography[END_REF].

IGC-FC analysis

This technique includes injecting some microlitres of liquid probe (1-20 L) into the column in order to cover the surface of the solid with a probe mono-layer. A strong asymmetric chromatographic peak is obtained (Fig. 3). The more rapid method is "the elution characteristic point method" (ECP) that allows the acquisition of part of the desorption isotherm from a unique chromatographic peak. According to this method, the first derivative of the isotherm is related to the retention time for each point of the rear diffuse profile of the chromatogram by the Conder's equation (3):

∂N ∂P L,tr = JD mRT (t r -t 0 ) ( 3
)
where N is the number of desorbed molecules, P the partial pressure of the probe at the output of the column, L the column length, t r the retention time of a characteristic point on the rear diffuse profile of the chromatogram, t 0 the retention time of CH 4 , D the flow rate at the output of the column, J the James-Martin correction factor, m the mass of adsorbent, R the Perfect gas law constant, and T the oven temperature. After the integration of Eq. ( 3), the desorption isotherm can be obtained, and so the specific surface area of the solid and the BET constant of the organic probe can be calculated using a special software from the ADSCIENTIS society (Wittelsheim, France).

At the end of the chromatogram, the temperature of the chromatograph oven is increased up to the conditioning temperature, leading to a secondary small peak corresponding to the amount of probe adsorbed irreversibly on the solid surface at the analysis temperature.

3.1.2.1. Irreversibility index. An irreversibility index (I irr ) [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF] can be calculated from the ratio of the area of the thermodesorption peak to the total area of the chromatogram, as expressed in Eq. ( 4):

I irr = S th S rv + S th (4)
where S rv is the area of the main chromatographic peak and S th the area corresponding to the thermodesorption peak.

The irreversibility index provides an assessment of the proportion of high energy sites depending on the nature of the probe. For example, with an isopropanol probe, the I irr estimates the sites able to develop hydrogen bonds.

3.1.2.2. Distribution function of the energies of adsorption. Estimation of the surface heterogeneity of a solid using the adsorption energy distribution function (DF) is generally based on a physical adsorption model, which admits that the global isotherm may be considered as a sum of local isotherms of adsorption on isoenergetic domains (patchwork model) [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF][START_REF] Balard | Estimation of the surface energetic heterogeneity of a solid by inverse gas chromatography[END_REF][START_REF] Rudzinski | Physical adsorption of gases on heterogeneous solid surface: evaluation of the adsorption energy distribution from adsorption isotherms and heats of adsorption[END_REF].

Thus, the distribution function of the relative abundance of each type of domain, having the same characteristic energy of interaction (ε), is given by the following integral (Eq. ( 5)): where N(T, P) is the number of molecules adsorbed at pressure P and temperature T, N 0 is the number of the molecules which can form a monolayer, Â(ε, T, P) is the local isotherm corresponding to adsorption sites having the same characteristic adsorption energy ε, (ε) is the so-called distribution function of the adsorption energies (DFAE) describing the energies which exist at the gas-solid interface, ˝is the physical domain of the adsorption energy, and ε is the characteristic energy.

N(T, P) = N 0 ˝Â(ε, T, P) (ε) dε (5)
3.1.2.3. Heterogeneity index. The index of surface heterogeneity, I hete , defined in Eq. ( 6) can be determined by comparing the computed DF with the DF describing a homogeneous surface that fits the left descending branch of the experimental DF towards the lowest interaction energies [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF]:

I hete = A -A H A ( 6
)
where A is the area under the experimental DF and A H is that under the homogeneous DF. The distribution functions were computed using a special software from the ADSCIENTIS society (Wittelsheim, France).

Experimental conditions

The IGC measurements were performed with two GC devices (Agilent 7890A and 6890) equipped with sensitive flame ionization detectors (FID). Helium was used as carrier gas with a flow rate of 30 mL.min -1 . The injector and detector temperatures were 403 K and 473 K, respectively. The columns were filled with a mixture of palygorskite powder and glass beads. The amount of powder in the column was chosen according to the pressure drop, which had to be lower than 10 5 Pa in order to avoid leaks at the septum and fittings. A reproducibility study was made on the raw material, namely three columns were prepared with the raw palygorskite, and analyzed to obtain a standard deviation. That gave the quantities after the (±) sign appearing in the results of Tables 2-4.

IGC-ID experiments

The IGC-ID study was done with an oven temperature of 403 K, using stainless steel columns of 20 cm in length, with 6.35 mm in diameter. The columns were conditioned overnight at 423 K. The oven temperature for the analysis was chosen equal to 403 K to allow for a good separation between the peak of methane and the peak of the probe.

The probes used were linear alkanes (n-hexane C6, nheptane C7 and n-octane C8), two branched alkanes, the 2,3,4-trimethylpentane (2,3,4-TMP) and the 2,5-dimethylhexane (2,5-DMH), a cyclic alkane, the cycloctane (Cyclo8) and polar probes (chloroform CHCl 3 and dichloromethane CH 2 Cl 2 ). These probes had chromatographic grade (>99%) purity.

IGC-FC experiments

For IGC-FC, the chromatographic columns were 10 cm in length and 6.35 mm or 3.18 mm in internal diameter. The conditioning temperature was 423 K. According to the Conder criterion [START_REF] Conder | Physicochemical Measurement by Gas Chromatography[END_REF], analysis temperature was fixed at 326 K with the n-octane (C8) and at 316 K with the probe isopropanol (IP) (Aldrich, purity >99%) used to study the surface chemistry. This criterion states that vapour contribution of the probe to the flow of carrier gas should not exceed 5% of the initial flow at the maximum of the chromatographic peak.

Results and discussion

IGC-ID

Table 2 displays the values of the dispersive components of surface energy, d s , the morphological indexes, I M ( t ), and the specific components of surface energy with acidic probes, -G sp a , of modified palygorskite samples, used as adsorbents in this study.

The d s initial value of 164 mJ.m -2 is typical of a phyllosilicate, this high value is attributed to the insertion of the alkanes probes into the fibrous channels of the palygorskite or into structure defects between fibres [START_REF] Boudriche | An assessment of the surface properties of milled attapulgite using inverse gas chromatography[END_REF]. Chemical and mechanical treatments to elaborate adsorbents, affected the values of the d s of the raw material, a decrease was observed whatever the process, especially after 60 h of grinding in the Pulverisette0 from 164 mJ.m -2 to 116 mJ.m -2 . This change reflects the disappearance of structural defects under mechanical stresses, reducing the ability of alkane probes to adsorb on the solid surface.

The nanomorphology index I M ( t ) parameters did not change significantly with grinding and chemical activation, except for the sample milled in Pulverisette0. The I M ( t ) parameters obtained by injecting the cyclooctane and the 2,3,4-trimethylpentane probes, had a high value in comparison to the other samples, reflecting the reduction of surface roughness during 60 h of milling in Pul-verisette0.

The basic character of the adsorbents was assessed by injecting acidic probes (chloroform and dichloromethane). The specific interaction parameters, -G sp a , obtained by injecting the two probes, remains constant, meaning that no chemical change occurs at adsorbents surface after chemical and mechanical treatments. Basic probes (ether, acetone, DMSO, DMF, methanol, toluene and 1,4-dioxane) were also injected but not eluted at the analysis temperature. The acidic character of the palygorskite surface can explain the retention of the basic probes. Therefore, the Guttman's acidic and basic numbers usually used to characterize the acid-base interactions could not be calculated.

In summary, the IGC-ID parameters obtained in this study indicates that the sample milled in Pulverisette0 during 60 h, is the most strongly affected by the mechanical treatment. But IGC-ID parameters are clearly related to the adsorption sites having the greatest energy of interaction [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations[END_REF]. Other experiments were carried out using the IGC-FC mode.

IGC-FC

3.3.2.1. Specific surface area. The specific surface areas and irreversible indexes were measured by IGC-FC (Table 3) using noctane and isopropanol probes.

The specific surface areas obtained with nitrogen and n-octane were similar except for the sample treated with the acid solution. This gap could be due to the uncertainty on the molecular areas of the organic probes, which were computed from the adsorption isotherm data measured on non-porous solids. The higher the specific surface area and the porosity, the higher the uncertainly on the molecular areas of organic probes and higher the discrepancy between the nitrogen specific surface area and the organic probes as observed for palygorskite treated with HCl.

The specific surface areas obtained with isopropanol were lower whatever the sample. It could be explained not only by the uncertainty in the molecular area of the probe but also by the more irreversible character of isopropanol adsorption compared to that of n-octane, as testified by their respective irreversible indexes (I irr ) (Table 3). Of course, this irreversible adsorption contributed to the decrease in the measured specific surface areas, computed from the reversible part of the adsorption phenomenon.

The specific surface areas varied in the same way regardless of the three probes used. Indeed, the specific surface area values of the sample treated with HCl were higher with the three probes, than those of raw palygorskite, in contrast to the values obtained for the sample milled in Pulverisette0, which were the lowest. The increasing of specific surface area was attributed to the elimination of carbonates with the acid treatment effect, and consequently to the creation of new porosity accessible to probes. On the other side, the decrease in the specific surface area after milling can be explained by the alteration of the internal structure of particles (physical alteration, such as the disappearance of porosity) [START_REF] Boudriche | Influence of different dry milling processes on the properties of an attapulgite clay, contribution of inverse gas chromatography[END_REF].

Surface energetic heterogeneity.

The heterogeneous character of the solids was studied by determining the distribution functions (DF) of the adsorption energies of both n-octane and isopropanol probes (Fig. 4). The first one, an apolar probe, is mainly sensitive to the surface morphology, and the second one, a polar probe, is more sensitive to the surface functionality, especially the presence of silanol groups.

The distribution functions (DF) of the adsorption energies obtained with n-octane, which exchanges only dispersive interactions with the solid surface, are essentially monomodal. Comparing the heterogeneity indexes obtained with this same probe (Table 4), the sample treated with the acid solution leads to a value higher (20.7%) than those obtained with the other samples (around 13%). The high specific surface area and porosity of the sample treated with acid can explain the high I hete observed with n-octane, which is sensitive to the solid morphology. The results obtained with noctane demonstrate that the mechanical treatment did not cause significant changes in surface morphology of palygorskite fibres on the contrary of the acid treatment.

With isopropanol, which is sensitive to the surface functionality, the DF exhibits a monomodal shape with a tail extending towards the high energies. However differences can be noted:

-The sample treated with HCl shows a weak shoulder at 26 kJ.mol -1 , probably related to the dissolution of carbonate impurities which liberates high energetic sites. -The sample milled in Pulverisette0 during 60 h, reveals two shoulders at high energies at 27 kJ.mol -1 and 35 kJ.mol -1 , traducing the appearance of polar sites under mechanical effect that could strongly interact with the isopropanol probe.

The highest isopropanol hetegeneity index was obtained for the sample milled with the Pulverisette0 (46.5%) testifying the appearance of high energy sites, which are able to develop hydrogen bond.

In conclusion regarding surface energetic heterogeneity, the acid treatment leads to significant modifications of the surface morphology, which is related to the removal of carbonates and the appearance of porosity. The mechanical treatment, especially the Pulverisette0 seems to release high energy sites, able to develop hydrogen bonds probably silanol groups.

Lead adsorption studies

Pb(II) adsorption experiments

The solutions of Pb(II) were prepared by dissolving lead nitrate (Pb(NO 3 ) 2 , Aldrich, ≥99%) in deionized water. Lead solutions and palygorskite powder were placed in a 500 mL reactor equipped with a four blade stirring propeller. Adsorption capacity of the treated samples was studied with 5 g of powder in 500 mL of waste solution. Different lead concentrations, ranging from 100 to 7000 mg.L -1 , were prepared, with an initial pH of 5.3. The contact time for which the adsorption reached equilibrium was set at 5 h despite a previous study showed that the pH was stabilized after half an hour of stirring. The mixtures were agitated at a speed of 400 rpm. Then, the samples were collected and filtered with polypropylen filter cartridges (0.45 m-pore diameter) and analyzed by inductively coupled plasma (ICP) thereafter. The ICP spectrometer used was an Ultima2 model from Horiba JobinYvon company. Lead was analyzed at 220.3 nm wavelength.

The adsorption capacity of Pb(II) ions could be calculated using Eq. [START_REF] Khider | Purification of water effluent from a milk factory by ultrafiltration using Algerian clay support[END_REF]:

Q e = C 0 -C e m • V (7)
where Q e (mg.g -1 ), the adsorption capacity, is the amount of metal ions adsorbed at equilibrium per unit mass of adsorbent, C 0 (mg.L -1 ) and C e (mg.L -1 ) are the Pb(II) ion concentrations before adsorption and at equilibrium, respectively, V (L) is the initial volume of the Pb(II) ion solution, and m (g) is the weight of the adsorbent. The data from isotherm measurements were fitted using the Langmuir [START_REF] Langmuir | The adsorption of gases on plane surfaces of glass, mica and platinum[END_REF] and Freundlich [START_REF] Freundlich | Uber die adsorption in lasungen[END_REF] models. The first one assumes monolayer adsorption on a surface containing a finite number of homogeneous adsorption sites, with no lateral interaction between the adsorbed molecules. While, the Freundlich model suggests a multilayer adsorption on adsorbent. The Langmuir equation is expressed as follows:

Q e = b • Q m • C e 1 + b • C e ( 8
)
where Q m (mg.g -1 ) and b (L.mg -1 ) are the maximum adsorption capacity and the Langmuir constant, respectively. The linearized Langmuir equation is written as follows:

C e Q e = C e Q m + 1 b • Q m (9)
The constants Q m and b are obtained from slope and intercept of the linear plot of C e /Q e versus C e , respectively.

The Freundlich equation is expressed as follows:

Q e = K f • C 1/n e (10)
The Freundlich constants K f and 1/n can be determined from the intercept and slope of the linear plot of ln Q e versus ln C e , respectively. K f is related to adsorption capacity, n is the intensity of adsorption and C e is the equilibrium concentration of ions (mg.L -1 ).

The Freundlich model in linear form is given by the following equation:

ln Q e = ln K f + 1 n ln C e (11)

Results and discussion

Adsorption lead isotherms on the four palygorskite samples obtained by grinding processes, in mortar, air jets mill and Pul-verisette0 or by acid treatment are displayed in Fig. 5.

All adsorption isotherms obtained with the four palygorskite samples displayed the same shape: in the case of low concentrations of Pb(II) in the solution at equilibrium, C e , a rapid increase in the adsorption capacity, Q e , was observed towards C e , whereas at high C e values, Q e tended towards a constant value. The constant value indicates the saturation of high energy sites involved in the adsorption process. The values of the isotherm parameters obtained from both linearized Langmuir and Freundlich models, for the adsorption of Pb(II) on modified palygorskite, are gathered in Table 5.

The correlation coefficients (R 2 ) obtained by applying the linear Langmuir model closer to the unity as compared to those obtained by applying the Freundlich model, means that the adsorption process of Pb(II) on palygorskite samples is governed by the Langmuir isotherm model. Then, according to the Langmuir isotherm model, the maximum monolayer adsorption capacity, Q m , of palygorskite samples are classified as follows: Q m sample milled in Pulverisette0 > Q m sample milled in air jet mill > Q m sample treated with HCl > Q m sample milled in mortar. Whatever the palygorskite samples, Q m appears to be higher than those obtained in literature for some natural adsorbents under optimal adsorption conditions (Table 6).

Maximum adsorption capacities Q m of the samples under test were compared to different parameters characterizing the particles. For example, the specific surface areas, a N 2 , of palygorskite samples measured with nitrogen adsorption do not seem to explain the difference in their lead adsorption capacities. The sample milled in Pulverisette0 with the lowest specific surface area (Table 1), has the highest Q m . Previous works [START_REF] Frini-Srasra | Acid treatment of south Tunisian palygorskite: removal of Cd(II) from aqueous and phosphoric acid solutions[END_REF][START_REF] Shirvani | Sorption-desorption of cadmium in aqueous palygorskite, sepiolite, and calcite suspensions: isotherm hysteresis[END_REF] on the same clay led to opposite results, i.e. the adsorption capacity increased with specific surface area.

The external specific surface area, a ext , calculated from the Sauter diameter d 32 gives us information on the external diffusion of Pb(II) ions towards the particles surface because it determines the number of sites available to lead ions adsorption. This parameter can explain the enhanced adsorption capacity of milled samples. Indeed, for milled adsorbents, Q m increases with increasing a ext (Table 1). A large a ext may promote a larger diffusion of Pb(II) ions at the particles surface. But the acid activated sample does not obey this variation because it presents the smallest a ext with a Q m higher than that of the sample milled in a mortar. If a ext can be linked to Q m , it does not seem to be the only factor involved. Q m could also be related to the variations of porous volumes. It can reasonably be thought that large pores volume will promote the retention of Pb(II) ions and hence their removal from the solution. Comparing the different samples, whatever the porous volume considered (micro, meso or macro), the highest porous volume was observed for the sample treated with hydrochloric acid, despite its lower Q m compared to the other adsorbents. Once again, porous volume could not be linked to adsorption capacity. Another parameter characterizing the surface, the cation exchange capacity (CEC) was determined (Table 7). It is a relevant indicator of the cations number accessible to ions exchange. The variation of this parameter was compared to those of the irreversibility index (I irr ) determined by IGC with isopropanol (Table 3).

It can be noticed that the two parameters, CEC and I irr measured with isopropanol, increase simultaneously with Q m (Fig. 6).

CEC and I irr involve specific interactions. I irr corresponds to a measurement of hydrogen bond between the isopropanol probe molecule and silanol or aluminol groups on the palygorskite surface (Fig. 7a). These sites contribute in part to CEC (Fig. 7b). Indeed, CEC is a measurement of exchanged cations, which can have two origins: -Counterions of the negative charges on the palygorskite surface as Fe 2+ , Al 3+ contained in the palygorskite structure [START_REF] Chahi | Infrared evidence of dioctahedral-trioctahedral site occupancy in palygorskite[END_REF][START_REF] Suarez | FTIR spectroscopic study of palygorskite: influence of the composition of the octahedral sheet[END_REF]. -The variable charge due to the presence of silanol or aluminol sites that can bind H 3 O + ions depending on the pH value.

The silanol or aluminol groups, neutral or ionized, seem to be the common factor between the two parameters, CEC and I irr obtained with isopropanol. The higher the CEC and the I irr , the more silanol groups there are on the surface increasing its reactivity and its adsorption capacity leading to a higher Q m .

Upon grinding of muscovite, Papirer already observed a correlation between CEC and another IGC parameter [START_REF] Papirer | Variation of the surface energy characteristics of mica muscovite upon grinding[END_REF], the dispersive component of the surface energy, d s , determined by IGC at infinite dilution. They concluded that the variation of the grinding conditions can lead to significant changes of the surface characteristics of muscovite involved in applications like the use of micas as filler for polymers, as mentioned by the authors, or in the adsorption process, the subject of the present work.

It may be thought that grinding in Pulverisette0 contributes to generate silanol sites [START_REF] Boudriche | Influence of different dry milling processes on the properties of an attapulgite clay, contribution of inverse gas chromatography[END_REF]. These silanol sites can develop hydrogen interactions with the injected isopropanol, which contributes to increase irreversibility index. Furthermore, in aqueous medium, they can be ionized depending on pH and greatly contribute to enhancement of the lead adsorption capacity also measured by the CEC.

Conclusion

The adsorption capacity of palygorskite Q m in contact with a solution of toxic metal ion, lead, was investigated. The adsorbents used were palygorskite powders modified by an acid treatment or different grinding processes.

The adsorption isotherms obtained were consistent with the Langmuir model in the range of lead concentrations studied.

All the adsorbents used exhibited very good adsorption properties towards lead. However, Q m varied depending on the different samples. It was demonstrated that the type of treatment influenced significantly the behaviour of the adsorbents in solution. Specific surface area, porous volumes, or external surface were not the parameters explaining the Q m variation of the samples. This last one was related to the cation exchange capacity, CEC, and the irreversibility index, I irr , determined by IGC at finite concentration with the isopropanol probe. Despite the complete disappearance of the fibrous structure, the sample obtained by grinding in the Pul-verisette0 had the highest Q m in correlation with the highest CEC and I irr probably due to the new sites generated by grinding like silanol groups.

Fig. 1 .Fig. 2 .

 12 Fig. 1. (a) Crystal structure of palygorskite "from Galan [20, Fig. 1]. Reproduced with kind permission of the Mineralogical Society, publisher of Clay Minerals" and (b) its polyhedral representation "from McKeown et al. [19, Fig. 1]. Reproduced with kind permission of the Clay Minerals Society, publisher of Clays and Clay Minerals."

Fig. 3 .

 3 Fig. 3. Experimental chromatogram and the associated thermodesorption peak obtained on palygorskite with isopropanol probe at 316 K.

Fig. 4 .

 4 Fig. 4. Distribution functions of the adsorption energies with n-octane (left) and isopropanol (right) probes measured on adsorbent samples.

Fig. 5 .

 5 Fig. 5. Adsorption isotherms of Pb(II) at 298 K on modified palygorskite powders.

Fig. 6 .

 6 Fig.6. Correlation between cation exchange capacity and irreversibility indexes of palygorskite samples.

Fig. 7 .

 7 Fig. 7. (a) Hydrogen bonds between palygorskite surface and isopropanol probe involved in the I irr determined by IGC and (b) electrostatic interactions between palygorskite surface and hydronium.

Table 1

 1 Characteristic parameters of modified palygorskite samples.

	Sample	d50 (m)	d32 (m)	(g.mL -1 )	aext (m 2 .g -1 )	aBET N 2 (m 2 .g -1 )	V micro (mL.g -1 )	Vmeso (mL.g -1 )	Vporous (mL.g -1 )
	Raw palygorskite	143	23.56	2.57	0.09	125	0.018	0.302	-
	Milled in mortar	25	10.65	2.46	0.23	89	0.007	0.297	0.272
	Milled in air jet mill	6	2.66	2.87	0.78	93	0.010	0.330	0.324
	Milled in Pulverisette0 (60 h)	3	1.77	2.40	1.41	66	0.013	0.253	0.303
	Treated with HCl (0.5 M)	265	97.27	2.40	0.02	273	0.046	0.397	0.356

Table 2

 2 Variation of the dispersive components of the surface energies ( d s ), the nanomorphological indexes IM( t ), and the specific free energies of adsorption of acidic probes (-G sp a ) of modified palygorskite samples, determined by IGC-ID at 403 K.

	Samples	d s (mJ.m -2 ) ± 4%	IM( t ) ± 5%		-G a kJ.mol -1 ± 4% sp
			2,3,4-TMP	Cyclo8	CHCl3	CH2Cl2
	Raw palygorskite	164	0.69	0.22	14	17
	Milled in mortar	147	0.67	0.24	13	17
	Milled in air jet mill	159	0.59	0.20	14	17
	Milled in Pulverisette0 (60 h)	116	0.73	0.33	14	17
	Treated with HCl (0.5 M)	133	0.71	0.26	12	14

Table 3

 3 Values of the specific surface areas (aBET) and irreversibility indexes (I irr ) of modified palygorskite, obtained by nitrogen adsorption and IGC-FC (with n-octane C8 and isopropanol IP).

		Adsorption N2	IGC-FC
			C8 (326 K)		IP (316 K)
		aBET ± 0.3 (m 2 .g -1 )	aBET ± 2.8 (m 2 .g -1 )	I irr ± 0.2 (%)	aBET ± 4.1 (m 2 .g -1 )	I irr ± 0.6 (%)
	Raw palygorskite	125.2	114.5	0.1	70.9	8.3
	Milled in mortar	85.8	84.2	1.8	65.7	10.8
	Milled in air jet mill	93.3	75.6	1.2	60.0	15.9
	Milled in Pulverisette0 (60 h)	66.3	62.6	1.2	47.0	23.4
	Treated with HCl (0.5 M)	272.6	135.4	2.1	100.0	10.4

Table 4

 4 Heterogeneity (I hete ) index values, measured by IGC-FC for n-octane and isopropanol probes, on modified palygorskite.

	Samples	C8 (326 K)	IP (316 K)
		I hete (%) ± 1.2	I hete (%) ± 4.9
	Raw palygorskite	13.6	41.2
	Milled in mortar	11.7	34.5
	Milled in air jet mill	13.8	41.9
	Milled in Pulverisette0 (60 h)	15.3	46.5
	Treated with HCl (0.5 M)	20.7	40.7

Table 5

 5 Values of Langmuir and Freundlich isotherm parameters (Qm, b, K f , n and R 2 ), for the adsorption of Pb(II) on modified palygorskite samples.

		Langmuir isotherm model			Freundlich isotherm model
		Qm (mg.g -1 )	b (L.mg -1 )	R 2	K f (mg.g -1 )	n	R 2
	Milled in mortar	142.8	0.057	0.999	9.64	2.849	0.844
	Milled in air jet mill	333.3	0.008	0.997	14.93	2.564	0.946
	Milled in Pulverisette0 (60 h)	500.0	0.023	0.998	157.27	8.264	0.748
	Treated with HCl (0.5 M)	200.0	0.006	0.996	8.66	2.638	0.919

Table 6

 6 Maximum adsorption capacity Qm towards Pb(II) for adsorbents of natural origin.

	Adsorbent	Qm (mg.g -1 )	Refs.
	Zeolite	70.6	[30]
	Active carbon	47.6	[31]
	Bioadsorbent	37.5	[13]
	Kaolinite	13.3	[32]
	Palygorskite (South Africa)	62.1	[1]
	Palygorskite (China)	104.3	[33]

Table 7

 7 Cation exchange capacities (CEC) for the four palygorskite powders.

	Adsorbents	CEC (Meq/100 g)
	Treated with HCl (0.5 M)	20.45
	Milled in mortar	15.11
	Milled in air jets mill	25.12
	Milled in Pulverisette0 (60 h)	30.11


Nassima Keddari
email: keddarinassima@yahoo.frz_sari@mail.univ-tlemcen.dz

Mebarki Nasser
email: nasser.mebarki@univ-nantes.fr

Shahzad Atif
email: bia.atifshahzad@gmail.com

Sari Zaki

Solving an integration process planning and scheduling in a flexible job shop using a hybrid approach

Keywords: Integration, Process planning, Scheduling, Metaheuristics, Shifting Bottleneck Heuristic, Tabu search, Kangaroo Algorithm

Traditionally, process planning and scheduling functions are performed sequentially, where scheduling is implemented after process plans has been generated. Recent research works have shown that the integration of these two manufacturing system functions can significantly improve scheduling objectives. In this paper, we present a new hybrid method that integrates the two functions in order to minimize the makespan. This method is made up of a Shifting Bottleneck Heuristic as a starting solution, Tabu Search (TS) and the Kangaroo Algorithm metaheuristics as a global search. The performance of this newly hybrid method has been evaluated and compared with an integrated approach based on a Genetic Algorithm. Thereby, the characteristics and merits of the proposed method are highlighted.

Introduction

The concept of Industry 4.0 promotes the integration of all aspects of production for greater efficiency. The factory of the future will be a smart manufacturing, holistic and flexible, where Internet of Things, augmented reality, automation and artificial intelligence will enable to adapt quickly the production system to a constantly changing environment. It necessitates a high level of enterprise integration. Yet, in most of manufacturing systems, two distinct functions are still handled independently to manage the production: the process planning function and the scheduling function.

Process planning determines how a product will be manufactured from its initial to a finished product, in other words, which sequence to use and which resource to select [START_REF] Kumar | Integration of process planning and scheduling in a job shop environment[END_REF]. The scheduling is another manufacturing function that finds a mapping between jobs and resources to achieve some relevant criteria. The output of process planning is an input of scheduling. Therefore, scheduling is based on a fixed process planning. Moreover, process planning doesn't consider the current capacity of the resources while it is a strict constraint for the scheduling function. This sequential organization doesn't permit to take fully advantage of the flexibility provided by modern manufacturing systems. Research on scheduling has focused primarily in the construction of efficient algorithms to solve different types of scheduling problems: flow shop, job shop, open shop, and so on. However, research works show that the integration of the process planning function and the scheduling function permits to gain valuable insights [START_REF] Tan | Integration of process planning and scheduling[END_REF][START_REF] Tan | Integration of process planning and scheduling -a review[END_REF][START_REF] Li | A simulated annealing-based optimization approach for integrated process planning and scheduling[END_REF].

The Flexible Job Shop Scheduling Problem (FJSSP) is an extension of the classical job shop scheduling problem (JSSP), where each operation Oj can be processed by a set of alternative machines, subset of the set of machines M. In that case, pjk denotes the processing time of operation Oj on machine Mk .Machines are always available and while operations are being processed, preemption is not allowed. The aim is to find a schedule for processing these n jobs on the m machines. The quality of a schedule is given by a performance measure objective function f, based on the jobs completion times denoted Ci. One of the most classical objective functions is to minimize the makespan, which measures the total length of the schedule [START_REF] Samur | An Evolutionary Solution to a Multi-objective Scheduling Problem Proceedings of the World Congress on Engineering[END_REF]. The makespan, denoted Cmax is computed as Cmax=max .. C . Following the Lawler notation [START_REF] Lawler | Chapter 9 Sequencing and scheduling: algorithms and complexity[END_REF], this problem is noted J||Cmax.

The integration of process planning and scheduling in a flexible job shop system (FJSSP-PPF) considers alternative machines for the operations, called operation flexibility (OF), and alternative operations' sequence, called sequencing flexibility (SF).

─ In this paper, we address the problem of integrating process planning and scheduling on a flexible job shop. The main contribution of this paper is to propose a very effective hybrid method to evaluate and explore the search space intelligently in a reasonable time frame in order to solve the FJSSP-PPF problem. This method has been evaluated on a manufacturing model from the literature, with objective to find a schedule which minimizes the makespan. This hybrid method, described more precisely in section 3, is based on three stages:Generation of an initial solution using an innovative local search procedure called Shifting Bottleneck Heuristic (SBH). ─ The second stage is based on an exploration of the solutions' space using a Tabu Search method. The solution found by the SBH procedure becomes the initial solution of the Tabu Search. An efficient initialization of the solution is an essential aspect of a metaheuristic's performance in terms of solution quality and computing time. As the SBH is one of the most successful heuristics for the J||Cmax problem, it is of the greatest interest to use it as initial solution for the Tabu Search method. ─ Tabu Search gives very effective results to solve the JSSSP, but it is a neighborhood method that may be trapped in local optimum. To avoid this, the solution obtained from the Tabu Search becomes the initial solution of an iterated solution improvement metaheuristic called Kangaroo Algorithm. The Kangaroo method is a combination of local and global search. The algorithm tries to improve the current solution by exploring its neighborhood using an iterative stochastic descent procedure. When a new improvement is no longer possible a "jump" procedure is performed in order to escape from the attraction of a local minimum [START_REF] Serbencu | An ant colony system based metaheuristic for solving single machine scheduling problem[END_REF]. Within this hybrid approach, the SBH to provide an efficient solution, tabu search is used to define an effective neighborhood around the initial solution as a local search method and the kangaroo algorithm is used to perform the global search among neighborhood. The main positive effect of this hybridization is the convergence speed to local optimum and to intensify the local search and the intensification ability of the Kangaroo algorithm (KA) the of global optimum

The remainder of this paper is organized as follows: the second section proposes a literature review of hybrid methods for flexible scheduling job shop problems, section three describes the case study and the framework of our hybrid approach. In section four experimental results are reported and then discussed in section five. The last section concludes this work and proposes different research perspectives.

Literature review

To solve the FJSSP-PPF problems, which are harder than FJSSP, hybrid methods give promising results. [START_REF] Tan | Integration of process planning and scheduling[END_REF] Has developed a linear mixed-integer programming model (LMIPM) for integration problem that relates a Tabu Search (TS) heuristic with branchand-bound method. The TS algorithm is employed as a fast heuristic to find an initial solution for a branch-and-bound procedure in an LMIPM environment. The feasible initial solution is generated using a specially designed dispatching rule earliest completion time first. [START_REF] Kim | A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling[END_REF] Have proposed a symbiotic Genetic Algorithm, which uses an artificial intelligent search technique, to handle, at the same time, the process planning and the scheduling functions. [START_REF] Kumar | Integration of process planning and scheduling in a job shop environment[END_REF] Have analyzed the effect of changing flexible process plan of a part-type in a production order. They use a simulation-based Genetic Algorithm (GA) in order to select the key part-type so that a performance measure can be further improved. This approach generates near-optimal performance for the makespan. [START_REF] Haddadzade | Integration of process planning and job shop scheduling with stochastic processing time[END_REF] Have proposed a new hybrid algorithm to solve the FJSSP-PPF problem with stochastic processing time. This approach combines simulated annealing and Tabu Search heuristic. More recently, [START_REF] Botsali | Comparison of Simulated Annealing and Genetic Algorithm Approaches on Integrated Process Routing and Scheduling Problem[END_REF] have compared the performance of two different heuristics based on genetic algorithms and simulated annealing algorithm, for the FJSSP-PPF problem, in order to minimize the total completion time.

One of the key factors of hybrid methods is the synergetic between the different methods used. Another key factor is the quality of the initial solution. Due to its great efficiency to solve the J||Cmax problem, the Shifting Bottleneck Heuristic has been largely used in hybrid methods. [START_REF] Bulbul | A hybrid Shifting Bottleneck-Tabu Search heuristic for the job shop total weighted tardiness problem[END_REF] Have planned a hybrid method which combines a Shifting Bottleneck Heuristic and a Tabu Search algorithm. In their method, the reoptimization step in the Shifting Bottleneck algorithm is replaced by the Tabu search. [START_REF] Braune | Shifting Bottleneck scheduling for total weighted tardiness minimization: a computational evaluation of subproblem and re-optimization heuristics[END_REF] Have combined a Shifting Bottleneck Heuristic with an iterated local search method for re-optimizing already scheduled machines. Computational experiments show that this hybrid method improve existing results for benchmark instances. Moreover this combination of SBH with an iterated local search method is applicable to large instances of job shop (more than 100 jobs and 20 machines). [START_REF] Gen | Multistage-Based Genetic Algorithm for Flexible Job shop Scheduling Problem[END_REF] Have developed a hybrid method, combining the genetic algorithm with the SBH for the flexible job shop scheduling problem. They generate the initial population randomly in order to maintain the diversity of individuals.

Most of works related to application of Kangaroo Algorithm use it as a level of a hybridization method. [START_REF] Serbencu | An ant colony system based metaheuristic for solving single machine scheduling problem[END_REF] Have proposed a hybrid method formed by an Ant Colony System (ACS) and a Kangaroo Algorithm (KA) to solve the single machine scheduling problem. This work is based on the collaborative power of the ACS and the intensification ability of KA.

3

Framework of the approach

Case study

In order to evaluate our method and compare its performances, we have chosen a manufacturing model already used by [START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF] (see Table 1). [START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF] Have used a genetic algorithm to solve it and their results are presented in section 4.

Table 1. Representation of the integration problem

Jobi Oj Set of alternatives machines (pj,k)

Process plan number (operation sequence) This model presents two difficulties. The first one is to choose the order in which the operations of each job are sequenced (sequencing flexibility) and the second is to assign each operation Oj to a machine Mk selected from the set of alternative machines (operation flexibility).For instance, job J2 has three process plans, each one with a fixed sequence; furthermore, operation O8 may be processed by M3, M1 or M2, with processing time 5, 5 and 6, respectively, but it must be processed after operation O7.

J1 1 {M1(6), M2(6)} 1: (1-2-3) 2: (1-3-2) 2 {M2(5), M1(6), M3(6)} 3 {M3(4)} J2 4 {M1(3), M3 (4)

General framework

As the FJSSP-PPF problem is a highly combinatorial optimization problem we propose a hybrid procedure where the first stage (the Shifting Bottleneck heuristic) is dedicated to solve a part of the problem as shown in Figure 1. In our hybrid procedure, as the SBH doesn't take into account alternative machines and alternative sequences as well, it is used only once, with an instance of a JSSP derived from the FSP-PPF problem. Thus, at this stage, for each job a process plan is chosen arbitrarily and for each operation a machine is assigned arbitrarily. The Tabu Search (TS) and the Kangaroo Algorithm take into account both alternative sequences and alternative machines. The idea is that, at each stage, very good quality solutions are obtained permitting to improve this solution at the next stage.

Shifting Bottleneck Heuristic (SBH)

The Shifting Bottleneck Heuristic (SBH) was proposed by [START_REF] Adams | The Shifting Bottleneck procedure for job shop scheduling[END_REF] to solve the minimum makespan problem for the job shop problem. The principle of this heuristic is to iteratively determine a machine considered as bottleneck and to optimally schedule this machine only. For each machine, a single machine scheduling problem1|rj|Lmaxis solved using the branch and bound technique proposed by [START_REF] Carlier | The one-machine sequencing problem[END_REF]. The bottleneck machine is the one with the highest Lmax. Then, using a disjunctive graph, the machines already scheduled are re-sequenced to include the optimal sequence of the current bottleneck machine. For each operation Oj, a release date rj and a due date dj are computed iteratively: rj is the earliest beginning date of operation Oj, computed from its predecessors already scheduled; dj is the latest completion time of operation Oj. For a more complete presentation of the SBH, the reader may refer to [START_REF] Pinedo | Scheduling Theory, Algorithms, and Systems[END_REF].

Tabu Search

Tabu Search (TS) algorithms are among the most effective approaches for solving JSSP [START_REF] Jain | Deterministic job-shop scheduling: Past, present and future[END_REF]. They use a memory function to avoid being trapped in a local optimum [START_REF] Zhang | A very fast TS/SA algorithm for the job shop scheduling problem[END_REF].

Neighborhood structures and move evaluation strategies play the central role in the effectiveness and efficiency of the Tabu Search for the JSSP [START_REF] Jain | New and stronger job-shop neighborhoods: a focus on the method of Nowicki and Smutnicki[END_REF]. Most of the TS algorithms related to job shop scheduling are based on the pair-exchange method for generating neighborhood solutions. It depends on a permutation of operations placed on position i and i+1 on a given machine [START_REF] Tan | Integration of process planning and scheduling[END_REF]. During the Tabu Search exploratory, two types of neighborhood structures are added to take into account the two distinct decisions of the FJSSP-PPF problem: process plans' selection and machine's affectation. Finally, it gives the following movement operators:

• For a machine, permute the order of two sequential operations (operation exchange) when these two operations are on the critical path of the solution. • For a critical operation, assign an alternative machine (machine exchange).

• For a job with at least a critical operation, change the process plan (sequence exchange). These three movement operators will also be used during the stochastic descent of the Kangaroo Algorithm, described in the next section.

Kangaroo Algorithm

As most heuristics, there is no theoretical results ensuring the convergence of a Tabu Search procedure to a global optimum. Further progress is achieved by using a jump procedure to potentially move away from the previous local optimum. A very promising heuristic that includes a jump mechanism is the Kangaroo Algorithm proposed by [START_REF] Fleury | Application des méthodes stochastiques inspirées du recuit simulé à des problèmes d'ordonnancement[END_REF]. It is described in Figure4.The principle of the Kangaroo method is similar to the simulated annealing algorithm but with a different research strategy. It generates a solution by using an iterative procedure that contains two parts: the stochastic descent procedure and the jump procedure [START_REF] Serbencu | An ant colony system based metaheuristic for solving single machine scheduling problem[END_REF].

During the stochastic descent, Kangaroo Algorithm seeks a solution that minimizes a function f(S) in a neighborhood N(S) of the current solution S using a local uniform mutationη1. If the new solution S' is better than the previous solution, it is stored and a new solution is explored in the same neighborhood N(S'). The algorithm tries to improve the current solution A times, A being the maximum number of iterations in improving the current solution before a jump. If it is not possible to obtain a further improvement, the algorithm moves to another neighborhood with a jump procedure using a global uniform mutation η2.

Solution representation

To solve FJSSP-PPF using TS and KA, we first need to represent the solution of our problem as a chromosome. Each individual in FJSSP-PPF consists of three vectors with the same length, as shown in Figure 2. With this representation, by selecting a chromosome, the FJSSP-PPF problem is transformed into a JSSP problem formulation. Depending on the selection of each job's sequence and each operation's machine it produces different instances of a JSSP. For example, the chromosome presented in Figure 2 gives the following schedule (Figure 3): It can be noticed that the chromosome representation gives a semi-active schedule and not necessarily an active schedule. Active schedules are dominant for the makespan. For example, the example in Figure 3 gives a semi-active schedule but not an active schedule.

Results

Our hybrid approach was coded in JAVA software Intel(R),Core (TM) i7 with a 2.2 GHZ CPU. First, we present the solution obtained by the genetic algorithm developed by [START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF] in Figure 4. O [START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF] The solution proposed by [START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF] is not an active schedule. For example, operations O1, O2, O3, O9 and O8 could begin earlier, on the same machines, without delaying any other operation, giving an active schedule. However, their solution gives a makespan of 43. In the following, we present the different solutions, on the same case study, obtained at each stage of our method. The SBH runs with the selections shown in Table 2: for each job the first process plan is chosen and for each operation the first machine is assigned. The outcome of the SBH gives the following critical operations: O4, O7, O1, O2 and O9.Gantt chart of the SBH solution is shown in Figure 5. This solution is an active schedule. Table 3 shows the results obtained after the Tabu Search procedure. Only job J1 has been modified: its process plan number is now the second (sequence exchange) and there is a machine exchange on operations O1 and O2. The critical operations become: O4, O7, O8 and O6. Figure 6 gives the Gantt chart of the TS solution. 4 shows the outcome after the Kangaroo Algorithm. This time, the modifications are on job J2 (sequence exchange and machine exchange for operations O4 and O6). The critical operations become O7, O6, O5.Figure 7 gives the Gantt chart obtained after the KA procedure. 5 gives the number of generations, computational time and Cmax value obtained at each stage of our hybrid approach. The lowest Cmax value is found in 20seconds by the hybrid method (SBH+TS+KA).

Discussion

The solution provided by the GA is not well balanced (see Figure 4). Among nine operations, four of them are assigned to machine M2, which gives a workload of 22 for this machine, while machine M3, with only two operations, has a workload of 8. Two successive operations of job J1:O1 and O2 are performed on the same machine M2.

There is another cycle, with job J3 on machine M1. These cycles are one of the causes of the poor performance of the GA procedure proposed by [START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF].

The solution provided by the SBH is the most balanced solution of all obtained solutions (a workload of 16, 16 and 15 for machines M1, M2 and M3 respectively). As we can see in Table 5, the makespan is significantly improved by SBH w.r.t. to the solution obtained by [START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF]. This shows the importance of the initial solution when using metaheuristic. Moreover, as the SBH deals only with one JSSP instance, the solution is obtained immediately. Thanks to the high quality of the initial solution of the TS exploratory permits to improve again, and largely, the makespan (21%). With regards to the SBH solution, the new solution has permuted the machines ofoperationsO1 and O2 (M1 and M2) and has changed the process plan of J1. Thus, during the TS search, only the operation and sequence flexibility of J1 has been updated. Inside the hybrid system, SBH and TS methods are used to achieve local exploitation around, while the KA is used to achieve global exploration. Although the TS has already well explored the search space and has given a high quality solution, the KA achieves to improve this solution. The KA's final solution has reassigned operationsO4 and O6 to alternative machines M3 and M1 respectively. Thanks to its jump mechanism, the KA can explore globally the search space and finally the process plan flexibility is used for all jobs and permits to improve the solution. It can be noticed that at the end of the hybrid procedure (SBH+TS+KA), the final solution is improved by 24% w.r.t. the solution obtained with only the SBH.

Conclusion and future work

In this paper, we developed a new approach that simultaneously integrates process planning and scheduling functions in a flexible job shop in order to minimize the makespan. This approach consists of hybridizing three heuristics: Shifting Bottleneck Heuristic (SBH), Tabu Search (TS) and Kangaroo Algorithm (KA). This approach has been compared with an integrated approach based on a Genetic Algorithm.

Our strategy is to start from a feasible initial solution created by the SBH. This heuristic gives a very good performance for the makespan in less than one second. This solution becomes a starting point for the Tabu Search. TS improves the solution obtained from the SBH by integrating operation flexibility and sequence flexibility. Again, the obtained solution becomes the initial solution for the next phase. In this phase, the search area is expanded by a global search algorithm called Kangaroo Algorithm, which improves the current solution by performing a jump procedure. The best makespan is produced by the hybridation SBH+TS+KA and outperforms the Genetic Algorithm by a factor of 2.3.

Although the scheduling problem studied is in this paper has only three machines and three jobs, due to its high flexibility, it is hard to get an optimal solution. However, it will be of the greatest interest to evaluate the efficiency (in terms of quality and speed) of our approach with a more complex problem. Comparisons of this approach with various optimization algorithms, such as exact methods or other metaheuristics, should also be very interesting. Another future work is to propose a multi-objective framework for solving the FSSP-PPF problem in order to minimize simultaneously the makespan and the maximum lateness.

Fig. 1 .

 1 Fig. 1. General framework of our approach

Fig. 2 .

 2 Fig. 2. Solution structure

Fig. 3 .

 3 Fig. 3. Gantt chart of the solution derived from the chromosome selected in Figure2.

Fig. 4 .

 4 Fig. 4. Gantt chart of the solution proposed by[START_REF] Park | A genetic algorithm for integration of process planning and scheduling in a job shop0[END_REF]

Fig. 5 .

 5 Fig. 5. Gantt chart of the SBH solution

Fig. 6 .

 6 Fig. 6. Gantt chart of the SBH+TS solution

Table 2 .

 2 Solution for the SBH (critical operations are shaded)

	4 1 1	5 1 2	7 1 1	8 1 3	6 1 3	1 1 1	2 1 2	3 1 3	9 1 2	Operation number vector Assigned Process plan vector Assigned Machines vector	S(SBH)

Table 3 .

 3 Presentation of the obtained SBH+TS solution

	4 1 1	1 2 2	5 1 2	7 1 1	2 2 1	3 2 3	8 1 3	9 1 2	6 1 3	Operation number vector Assigned Process plan vector Assigned Machines vector	+TS)	S(SBH

Table 4 .

 4 Presentation of the obtained SBH+TS+KA solution

	4 2 3	1 2 2	7 2 1	6 2 1	3 2 3	2 2 1	9 2 2	8 2 3	5 2 2	Operation number vector Assigned Process plan vector Assigned Machines vector	+KA)	+TS	S(SBH

Table 5 .

 5 Computational results

	Method	Generations number	Comp.Time (sec-onds)	Cmax	Improvement of the solution
	GA [14]	Not provided	Not provided	44
	SBH	1	<1	25	43% (w.r.t. to GA)
	SBH+TS	100	11	21	21% (w.r.t. to SBH)
	SBH+TS+KA	100	20	19	5% (w.r.t. to SBH+TS)