A Vision of Middle-earth: Contemporary views in Peter Jackson's Lord of the Rings trilogy 1

David Goldie (Aix-Marseille)

In The Gods Return to Earth2 , C.S. Lewis opens his review of LotR by acclaiming the return of Heroic Romance, comparing Tolkien"s work with stories stretching back to The Odyssey (and beyond). Indeed he goes on to make the claim that the book also represents a revolution for this genre. This point of view in fact reflects a dialectic argument which has faced artistic creation since ancient times. Should we look backwards taking classical inspiration, "standing on the shoulders of giants", as Isaac Newton put it, or forwards, always aiming to "make it new" as Ezra Pound proclaimed, with a modern approach? Of course our own reaction probably says more about us than the work in question. This argument is still relevant today however. As far as Tolken"s works are concerned, now relates to six new films.

Firstly a there is a new version of LotR in Peter Jackson"s original trilogy from 2001 to 2003 and more recently another trilogy based on H, scheduled for annual release between 2012 and 20143 . The "right" approach becomes a lot more than just a philosophical or aesthetic argument when you are in charge of major Hollywood productions, particularly ones aiming to adapt two of the most popular books in the world.

While many of the aesthetic points we intend to raise here would apply to both the adaptations LotR and H, we will concentrate our analysis on LotR and consider the implications of approach in three ways. Firstly we examine the question of fidelity in relation to the original texts. Secondly we analyse how Peter Jackson responds to some of the major differences between text and image. Finally we take a thematic approach to focus on changes to two important characters. The overall aim is to see how far we can find a modernising or "Romantic" spirit running through Jackson"s vision of Middle-earth.

The Problem of Fidelity

In addition to enormous commercial success4 , the LotR trilogy received widespread recognition within the cinematic industry, winning a total of 17 Oscars. Among critics, the website www.metacritic.com lists a total of 110 positive reviews to just 3 negatives.5 Empire Magazine, for example, gave all three films 5 star "classic" status, hailing LotR (2003) as "The resounding climax to a landmark in cinema history." Hannah McGill sums up this mainstream appeal thus:

Shot back-to-back, the three instalments have a glorious stylistic unity. With imaginative casting, superb special effects, gorgeous landscape photography and nail-biting action, this is riveting stuff, even for those not customarily drawn to elfin fantasy.

On the other hand, Scull and Hammond, in The J.R.R. Tolkien Companion and Guide, acknowledge the popular success of the series yet also highlight sharp divisions in the reception of the trilogy among Tolkien enthusiasts. These range from "high praise" to "travesty".

Points frequently argued include the diminishing or alteration of characters in the film relative to their portrayal in Tolkien"s book, emphasis on violent action, the over-use of special effects, and the omission of scenes from the book while incidents invented by the screenwriters have been inserted.

Criticisms of the films relate chiefly to missing or changed elements of the plot. In other words, viewers expecting a close fidelity in terms of a copy of events and dialogue from the original text were inevitably disappointed.

Fidelity requires clarification. Philosophically speaking, should mimesis be the aim of artistic endeavour, a perfect reproduction of reality or is art in fact too far removed from the original idea to be able to represent it accurately? If we regard the original source text as the "real" version, we return to this philosophical problem. Which is more important: the object or the idea?

Dudley Andrew identifies three basic approaches to adaptation.

1. Transforming: the film creates a mimetic copy of the events of the text.

2. Borrowing: the film represents the themes and ideas of the text 3. Intersecting: the text defies either of the approaches above.

We could equate transforming with a classical approach, maintaining the primacy of the text over the film, whereas borrowing could be said to be a more modern approach, unafraid to break with the original source to create a new version. It may be reasonably assumed that an audience with knowledge of the text would prefer the transforming approach in deference to the source. Film theorists and academics, on the other hand, often tend towards the borrowing approach. Cinema takes the essence (in other words, the most important elements) of the narrative and makes use of its specific visual and sensory qualities to "improve" on the book.

Kate Egan and Martin Barker analyse the rhetoric employed by Jackson and his production team in DVD bonus documentaries and interviews to present their versions of the story. Initially wary of alienating their audience, the filmmakers err on the side of caution. As such, a spirit of "deference" was applied to producing LotR I (2001). Following its success, their confidence gradually grew to the point that they felt justified in making stark changes.

By the time LotR III (2003) was released they were able to claim not only to have found the heart of the narrative but to have improved on it. Therefore, while the films begin by transforming, they move increasingly towards borrowing. 6How can we define fidelity? Is a cinematic copy which reproduces the action and dialogue of a book any more faithful to it than a film which focuses more on getting to the heart of the text? Here we find a choice which can only reflect our personal taste. However, we should perhaps note the logical conclusion as highlighted by Brian Mcfarlane that the likelihood of any one reader"s mental image of the text corresponding with that of its film adaptation"s director is extremely small. While he argues that film adaptation should be regarded in the context of intertext and therefore not unjustly compared with literature, it is nonetheless unsurprising that the process and the product of adaptation in general is so often and so fiercely criticised. An adaptation of such a popular work as LotR would inevitably split audiences, according to their own taste and point of view. Any number of individual commentators could find any number of points with which they would not agree. Martin

Barker underlines these tensions in his essay On Being a 60's Tolkien Reader. In his own views and criticisms, as well as in his discussion of interpretative communities, he points out that since the story means so much, to so many people and in so many different ways; it would be impossible to find one "true" way to appreciate it.

Tom Shippey"s 7 contributions to documentaries accompanying the DVD releases of the films, provide them with critical credibility. While he recognizes some of the essential differences between cinema and literature, his appraisals elsewhere 8 of the films also provide comparison of the text and the films. Shippey dismisses a number of the changes in the action and the characters as merely "playing to the gallery". Events such as Legolas firing off arrows while surfing on a shield down the outer steps of Helm"s Deep in LotR II (2002), and more importantly, the increased role of Arwen are examples of unnecessary concessions to a contemporary and youthful audience.

In their own interviews to be found on the same DVD releases, Jackson, the cast and production team take great pains to underline the authenticity of the films in relation to

Tolkien"s vision. This can be seen in the care and attention devoted to making weaponry and costumes for orcs and men at the WETA worshop, the natural proximity of New Zealand"s landscape to Middle-earth or by highlighting the "Prime Action" of Frodo"s journey with the Ring while providing insight on the "Subsidiary Action" concerning battles and heroes.

However, given the age in which the films were made, a more contemporary feel is hard to avoid. While the Medieval setting of the books is recreated in sometimes painstaking detail, many of the most dramatic scenes could only have been made with the most modern of special effects technology. Jackson has acknowledged the debt he owes to special effects pioneers like Ray Harryhausen 9 . 10 Yet he has also pointed out that he is glad to be working in cinema now with the benefits that twenty-first century technology brings to the process of image creation. For example the scale of the battles at Helm"s Deep and Pelennor Fields was We will concentrate the next part of our analysis on some of the perhaps more visually obvious differences between the text and the films. With this in mind, we now turn our attention to the problems created for a filmmaker by some of the more essential differences between cinema and literature.

Showing and telling: from the Sublime to the ridiculous?

While both cinema and literature are narrative arts, the fact remains that cinema can

only show what literature has to tell. Hamburger demonstrates the limits of images as narrative. Even if an extract of text contains no dialogue and consists entirely of description of setting or objects which can be filmed, there will always be something missing from the text in the on-screen image. She demonstrates this with an example of an extract from Joseph and His Brothers by Thomas Mann. Word play and associations create linguistic effects which quite simply can never appear in an image, even with an exact representation of the setting and objects within the passage. In this way Hamburger highlights, very effectively, the fundamental opposition and problems that exist between telling a tale and showing its events.

In an article for Cinéma Action: Contes et légendes à l'écran , the French aesthetician, Isabelle Smadja, praises the high quality of landscape photography in LotR I (2001) which frequently creates a vision of the Sublime. At the same time, however, she also highlights the challenge for Jackson of representing the beauty and depth of Tolkien"s language. In her opinion, Jackson cannot match it and therefore replaces it with the recurrent theme of sublime and grandiose landscapes, striking in their savage beauty. The landscapes evoke a journey towards the infinite, just like the journey that Frodo is on. The fertile cultivated land of the Shire is opposed to the wild and untamed lands into which he travels. In another striking example from the opening shot of LotR II (2002), the audience is treated to a vision of magnificent mountains while hearing Gandalf defying the Balrog in Moria from LotR I (2001) as a voiceover. In Smadja"s opinion, instances such as these give a visual expression of Rilke"s phrase: "For beauty is nothing but the beginning of terror". precisely what information to give. The director is at a disadvantage in this respect as his images can only show a scene. He will never be able to provide the direct access to a character"s inner life as is possible for the author. In cinema, rather than seeing through the eyes of a character, it may be more accurate to say that we are invited to try to see into their eyes. Close-up views and other visual effects may give clues to their thoughts but otherwise the limits of the image for representation of thought are plain to see.

Smadja feels that Jackson may have struggled with this aspect, almost trying too hard to fit modern concerns into the Tolkien"s narrative context. She criticises the way Jackson chooses to show the Ring"s effect on those who come into contact with it. For example when Bilbo and Frodo experience sudden feelings of jealousy over it, their voices, eyes and faces begin to eerily resemble Gollum. These physical transformations on screen in reaction to the Ring seem almost comical caricatures, like cartoon animations of shock.

Yet this is a rather harsh judgement. Physical transformation accompanying psychological anguish around the Ring is a repetitive visual element in the trilogy. Jackson provides a full representation of Gollum"s story that allows the viewer to make a definite comparison between him and his former self in Sméagol. The full physical horror of the Ring"s power is thus demonstrated in a way that is implied in the text. Gollum in fact represents one of Jackson"s major successes. His duality is rendered very effectively on screen. At several points his inner battle is made obvious as he talks to himself; Sméagol arguing with Gollum. At one time this is done through reflection in a pool; at another the screen is effectively split by a tree trunk where each half of his personality addresses the other. Here as much is imparted by the construction of the image as the dialogue. Despite the comparatively limited possibilities of description in film images, Jackson makes a real attempt to live up to the heights achieved by the text. However the characters" relationship with their surroundings is only partially successful as it leads simultaneously towards conclusions about their inner lives and also serves to highlight one of the inherent problems of translating text into images.

A Romantic Spirit?

How far then could we regard the film versions as modern interpretations of Tolkien"s original and does a borrowing approach automatically mean something is lost from the original source? Lewis invites us not to overlook the "Romantic" spirit running through LotR and indeed makes a claim for Tolkien"s own revolutionary status within the genre of Romance. Let us consider briefly how nineteenth century Romanticism could relate to a borrowing approach.

In contrast to the idea of educating people through literature and classical studies, the nineteenth century Romantics wished for a return to nature. They tried to rediscover the lost world of tales, legends and folklore of the Middle Ages. Inasmuch as they sought to break with the past, the Romantics were taking the first steps towards Modernism, reaching beyond classicism and elevating a revived medievalism. Tolkien"s universe clearly has much in common with the aims of the nineteenth century Romantics. Could we say that Peter Jackson has, in some ways, adopted an equally "Romantic" spirit in his vision of Middle Earth in comparison with Tolkien"s original source? His borrowing approach already places him in rupture with the text. We have also seen how his use of sublime landscape photography seeks to point out certain themes.

We will now consider the effect of some of the most radical changes made in the films and ask whether they automatically mean concession to a new audience or in fact serve the story better. Since Shippey provides much analysis on a variety of themes in his essay Peter Jackson's Film Versions12 , we propose to take up one of his points: the position of women, a theme on which Tolkien"s works have received much criticism, to discuss the potential significance of such changes in the films.

The story of Aragorn and Arwen is played out on screen via flashbacks and insertions into the main narrative. From a commercial point of view, a love interest caters for the female viewers and therefore significantly increases the potential audience, thereby creating a completely new interpretative community. Yet is the elevation of a female character in respect of her position in the text merely a commercial ploy? The female characters, as a whole, are substantially different in the films and we should not forget that while Jackson directed the trilogy he co-wrote the screenplay with his wife Fran Walsh and their collaborator Philippa Boyens. Were their decisions based on demographics or a real will to "correct" the narrative in a way they saw would better serve the story?

Arwen"s role is significantly altered in the films. She appears much more regularly and in two guises. The first is as an ethereal being. Frodo sees her in a vision after his wounding at Weathertop. She calls to him, giving him the strength to withstand the poison of the Morgul blade. She appears again in a similar fashion to Aragorn in an event invented for LotR II (2002). As the people of Rohan come under attack by Warg Riders on their way to Helm"s Deep, Aragorn is lost in battle, seemingly tumbling to his death over a cliff. We soon learn, however, that he is floating unconsciously down a river, eventually coming to rest on a shore, far from his comrades. It would seem that he is seriously injured and while still unconscious Arwen visits him in a vision. She apparently breathes life back into him with a kiss. Though this may just indicate the deep union of Aragorn and Arwen"s souls, this episode also inverts the story of Sleeping Beauty. Peter Jackson here reverses the roles traditionally ascribed to the princess and the handsome prince, while also adding another layer of interest to Arwen"s character as she seems to possess magical healing powers.

At these times, she appears as an ethereal Pre-Raphaelite beauty, a fairy tale princess bathed in a soft white light. She maintains these qualities when we see the story of her love for Aragorn on screen. She also becomes a somewhat tragic heroine. She is willing to give up her mortality for the man she loves and even disobeys Elrond"s wishes when the elves begin their exodus from Middle-earth. Under these circumstances we can see her both as an ideal of feminine beauty and a woman asserting her own opinion over her father"s, no matter the consequences. This aspect of her character may not be vastly different from the books.

However the reality of choosing mortality is seen on screen in a lucid vision which brings vividly home to the viewer the consequences of aging and losing her lover.

Although not actually present at the muster of Rohan in either the book or the film of

LotR III (2003), Arwen contributes symbolically to Aragorn accepting the mantle of the King.

She asks Elrond to re-forge "The sword that was broken" and thus, like Arthur and The Lady of the Lake, becomes instrumental in calling Aragorn to meet his destiny. From this point onwards Aragorn will increasingly take his rightful place as Isildur"s heir. Producing Andúril in front of the King of the Dead proves his right to command the Army of the Dead which is decisive in the battle of Pelennor fields. Following this, Aragorn increasingly takes a lead in decisions. In fact in the film he (and not Gandalf) instigates the final march on the Black Gate.

This chain of events is again somewhat different from the book where Halbarad the ranger arrives in the aftermath of the battle at Helm"s Deep bringing a gift from Arwen. She has remade the King"s banner which will eventually be unfurled as Aragorn arrives by river to save Gondor. Substituting both the object and the time it is presented in the film serves a dramatic purpose. While a coat of arms is of course symbolically significant, it is probably not as strikingly powerful an object as a sword.

In another instance we see Arwen in a substantially different way, as active against the forces of the Dark Lord as the male characters. She takes the place of Glorfindel in LotR I (2001). She has gone out to search for Aragorn and the hobbits despite the danger of the Ringwraiths. She then proceeds to outride the nine Black Riders and causes their downfall by invoking the power of the Ford at Rivendell. This is the first time the viewer meets Arwen in person. Dressed like a ranger she strikes the viewer as adventurous and heroic, in stark contrast to the ethereal beauty we see at other times. As the Ringwraiths begin to ford the river she sits on her white horse, sword aloft, defying them, shouting that if they want Frodo they will have to come and take him by force.

Gender politics being substantially different now than at the time of Tolkien"s writing, Shippey13 consigns this incident in particular to the level of "playing to the gallery". However in conjunction with the other instances previously mentioned, it seems clear that Arwen"s enhanced role is more than simply symbolic. Despite this, the increased presence and participation of the female characters is perhaps even more remarkable with Éowyn.

In her commentary of LotR, Smadja is scathing of Tolkien"s treatment of women, arguing that he uses the Medieval context to portray an outmoded and outdated view of them.

Concentrating her analysis on Éowyn in LotR II, Smadja emphasises how she is required to stay in Edoras while the Riders go out to face Saruman"s forces at Helm"s Deep. In other words, it is the women"s duty to stay at home while the men decide their futures on the battlefield. In response to such charges, Curry"s reply is "guilty as charged". However, he goes on to point out that, "…there are the characters of Galadriel and Éowyn, without whom

The Lord of the Rings would be seriously impoverished…".

The screenwriters go some way to try to redress this problem. In the films, Éowyn"s role is promoted. While the book narrative does allow her to assert herself and join the men, albeit secretly, it also places a good deal more emphasis on her love interest. After this initially remains unrequited with Aragorn, she eventually falls for the courtly love of Faramir. This is all but removed in the films. The audience is therefore guided to focus on her as an assertive female. She rejects the suggestion of being forced into union with Wormtongue and once he has been disposed of, we see her increasingly as a warrior princess. She knows how to ride and fight. Her attraction to Aragorn could even be described as assertive, since she recognises him as a kindred spirit and chooses to make her feelings known.

As Edoras is evacuated in the film, the whole of the city moves to Helm"s Deep, including the women and children. Despite the fact that she is left in charge, Éowyn is left behind in the book and her role is diminished as the battle rages. Furthermore, in the film, leadership is thrust upon her, when the company comes under the attack of Warg riders. As the Riders of Rohan fly to the attack, King Théoden asks Éowyn to lead the rest of the company through the wilderness to Helm"s Deep. Although she wishes to join the attack, she responds with firm action and immediately begins marshalling the convoy. Finally, perhaps more symbolically significant than anything else, Théoden chooses to name her (and not Éomer) as his successor before the ride to Gondor. We should note, however, that the effect of this is slightly undone by him then wishing her happiness in love and that this twist in the plot remains undeveloped.

Of course Tolkien had already allowed Éowyn to be integral to the plot when she secretly accompanied the Riders to the Battle of Pelennor fields. It is foretold that no man can defeat the Witch-King yet two apparently weak individuals, a woman and a hobbit, are chosen to defeat the leader of the Nazgûl. Quantitatively in comparison with the deeds of the male characters, this may seem like a small concession. However, placing Éowyn and Merry in such crucial roles could be seen to be particularly forward-looking by Tolkien. He was not some sort of proto-feminist of course. Yet one of the most important messages that comes through the narrative is not to underestimate anyone, especially those outwardly appearing weak and insignificant. The reader is constantly reminded how hobbits have hidden resources and resolve. Ultimately they are the ones upon whom the whole future of Middle-earth depends. Through affirmative action a female character is able to empathise with another marginalised one, joining forces with them. Éowyn is recognised as being as courageous as any man, she possesses the essentially feminine quality of empathy which gives her another kind of strength and permits her to ultimately succeed where men would have failed.

Texts are rarely entirely independent from previous creations. Even if a director wants to stamp his own mark on his creation, it is impossible to erase the traces of what has gone before. Genette points this out with the term palimpsest to discuss the concept of intertext. In the Middle Ages, when parchment was in short supply, scribes would use pieces with text already on them. Carefully erasing the original text left a fresh page. However, the traces of what had been written before still existed under the surface. Cinematic adaptation of literature further demonstrates this and requires the audience to consider the question of intertext.

Writers, their texts and their readers are inter-dependent and not separate from directors, their films and their audience.

As (1967), Fritz Lang was recorded in conversation with the French filmmaker 15 . Among the subjects of their conversation was their differing styles of filmmaking. At one point, Lang, who was most definitely a classical narrative director, labels Godard a "Romantic". While the LotR trilogy remains predominantly in this classical tradition, Jackson"s vision of Middle-earth is unafraid to make changes to the original text and to modernise it. Whether this is a result of essential differences between cinematic and literary narrative, a desire to reach the heart of the story or a pragmatic approach to attracting a contemporary audience, it seems clear that this "Romantic" spirit also prevails in his interpretations.

Does this mean that in C.S. Lewis" eyes, the film versions of LotR would be regarded as equally revolutionary as the original texts? In terms of popular success, they are on a par with Tolkien"s work. In the book when Frodo and Sam discuss their own story on the Stairs of Cirith Ungol, the point is made that each of us has our favourite versions of tales. We attach our own significance to them and characters which attract us. Underlining the role of our personal taste in such questions reminds us that whether it is a case of an aesthetic opposition such as classicism versus modernity or something as simple as preferring one character over another, our appreciation of any work of art is subjective.

The question of adaptation reveals that there are many factors involved in bringing a literary work to the screen, not the least of which are the essential differences between literary 14 Noel Brown, " "Family" Entertainment and Contemporary Hollywood Cinema" in Scope: An Online Journal of Film and Television Studies, Issue 25, February 2013 15 André S. Labarthe « Cinéastes de notre temps » Le dinosaure et le bébé, dialogue en huit parties entre Fritz Lang et Jean-Luc Godard (1967).

and cinematic narratives. Peter Jackson has made a huge effort in this respect. Although not always successful, he has managed to introduce a certain psychological depth to the characters despite the problem faced by showing the story rather than telling it. While it may be difficult for us to accept Jackson positioning himself as a "corrector", emboldening

Tolkien"s original vision, he is not merely "playing to the gallery". Jackson"s vision of Middle-earth certainly demands serious consideration and should not be dismissed simply because of a lack of fidelity to our own. Even if we do not agree with all his changes, the fact that we notice them and react to them cannot fail but to reengage us with Tolkien"s story. As such, the discussion and evaluation of the text that the changes in the films provoke can only be positive.

7

  "Tolkien"& "Book to Script", Extended version DVD"s, Wingnut Films, The Saul Zaentz Company 2006 8 Tom Shippey Peter Jackson's Film Versions, Appendix C in The Road to Middle-Earth Revised and Expanded edition, HarperCollins, London, 2005 9 His numerous works include: The 7th Voyage of Sinbad (1958), Jason and the Argonauts (1963), First Men in the Moon (1964), One Million Years B.C. (1966), The Golden Voyage of Sinbad (1974), Sinbad and the Eye of the Tiger (1977), Clash of the Titans (1981) 10 See: The Hobbit Interview Special, Interview, Film 4, UK, broadcast 12/01/13 and On The Lord of the Rings Trilogy, Interview, Film 4, UK, broadcast 27/03/1 only possible with the invention of the Massive 11 artificial intelligence program while Gollum was the first CGI character brought to life through motion-capture of an actor.

11

  Multiple Agent Simulation System in Virtual EnvironmentSmadja continues by highlighting the importance of fairytale. The Medieval setting of LotR serves to enhance the atmosphere of an ancient tale that yet contains hidden depths and universal truths. This is true for the early part of Peter Jackson"s trilogy. The idyllic Shire shares many of the characteristics of a marvellous fairytale setting. Describing the genesis of the book, Carpenter highlights the fact that as the narrative progresses, the aesthetic turns darker, reflected not only by the passage of the characters towards greater danger and darker times, but also a linguistic development in Tolkien"s prose towards more archaic terms, indicating the growing seriousness of the situation and the themes treated by the text.To some extent these changes are reflected in the films. Mirroring the characters" individual journeys, the general aspect of the landscapes and settings changes over the course of the trilogy. At the beginning the viewer is struck by the verdant lushness and simple beauty of the Shire which gives way to progressively darker and more desolate landscapes. In LotRIII (2003) rapid shifts of time and place are accompanied by radical shifts of colour and atmosphere. For example Gondor"s defeat at Osgiliath is represented in harsh grey, followed similarly in tone by Frodo and Sam on the Stairs of Cirith Ungol, before warmer colours return as the forces of Rohan muster at Dunharrow, where hope, albeit slim, remains.From the moment the hobbits leave the Shire in LotR I (2001), the narrative continues almost exclusively in darkness. A pleasant walk through Farmer Maggot"s field in the sunlight ends abruptly as Frodo, Sam, Merry and Pippin are chased onto the Road and their first encounter with a Black Rider. The whole environment darkens in reaction to the presence of evil. The film cuts to night as the hobbits are chased through thick forest before a temporary reprieve at the Buckland Ferry. From now on darkness reigns almost exclusively until the arrival of Arwen. Making her appearance after Frodo is struck on Weathertop, she appears like an angel in white, bathed in glorious light. Day has dawned again as she outrides the Black Riders to Rivendell. The contrast in luminosity upon Frodo"s re-awakening there is striking. This continues for the majority of the time the hobbits spend in Rivendell, firmly contrasting this place of temporary rest with the evil to be encountered in the world outside. This technique serves to underline one way in which Jackson answers the problem of showing rather than telling. The natural world of Middle-earth consistently reflects the tone of the narrative. Both Isengard and Mordor are represented predominantly in the dark.Saruman"s evil industry takes place in the depths of the earth and it is almost pitch black when Frodo and Sam climb the stair of Cirith Ungol to enter Mordor. Despite the apparent hurdles presented by the description of Tolkien"s settings in print, the images should not be automatically considered inferior to the text. Jackson manages to give authentic physical portrayals of place while at the same time create differing and contrasting atmospheres which do reflect the overall development of the narrative.In 1956 George Bluestone highlighted a central paradox of literary adaptations when he classified their relationship as "overtly compatible, secretly hostile". For Bluestone particular problems arise in the representation of thought and time on film. The reader is in a privileged position compared to the film viewer. Through his words an author can choose

Finally, as

 as Frodo refuses to throw the Ring into the Crack of Doom in LotR III(2003), we recognise that it has finally taken possession of him. The text gives a precise description, without recourse to monstrous transformation. In the films, it is possible to compare the innocent young hobbit of the Shire with the emaciated individual we now see. However, Jackson does not treat the viewer to visual pyrotechnics here. The image of Frodo before the Crack of Doom does reflect Tolkien"s text while adding an expression in his eyes suggestive of demonic possession and transformation. This is reminiscent of the look we see in Isildur"s eyes as Elrond recounts the first failure to destroy the Ring in LotR I (2001). In the end though, perhaps it is the fact that Frodo has undergone a prolonged and subtle change, progressively portrayed over the three films, which makes this final realisation that he has succumbed all the more powerful.

  one of the most technically and politically audacious of the New Wave directors, Jean-Luc Godard helped to create a rupture with cinema"s past, rewriting the rules of narrative. In comparison with New Wave cinema the LotR trilogy forms a central part of the Hollywood movement of "family" movies as described by Brown 14 which includes other series like Disney"s The Chronicles of Narnia and Warner Brothers" Harry Potter. According to Brown LotR represents classic Hollywood narrative cinema focussing on spectacle, emotion, an overall optimistic message and broad audience suitability. After collaborating with Godard on Le Mépris

To distinguish between the identical titles of Tolkien"s books and Jackson"s films, the following abbreviations are used: LotR = the book series; LotR = the film series. Individual films are abbreviated in italics accompanied by the year of their release in brackets. For example: LotR I = "The Fellowship of the Rings" by J.R.R Tolkien; LotR I (2001) = "The Fellowship of the Rings" by Peter Jackson.

C.S. Lewis "The Gods Return to Earth", Time andTide, 14 August 1954.pp.1082-3

At the time of writing only An Unexpected Journey (2012) has appeared in cinemas.

At the time of writing LotR III (2003) is 9 th in the list of all time worldwide box office earnings with $1,119.9m, LotR II (2002) is 23 rd with £926m, LotR I (2001) is 31 st with $871.5m. See: http://boxofficemojo.com/alltime/world/ (consulted 25/04/13)

It also gives 1,153 positive user reviews to 174 negatives (consulted 25/04/13)

This trend continues to an even greater degree with the release of An Unexpected Journey (2012). The much shorter original story is now a trilogy, cinematically, at least, of as grand a scale as LotR.

Tom Shippey Peter Jackson's Film Versions, Appendix C in The Road to Middle-Earth Revised and Expanded edition, HarperCollins, London, 2005

Tom Shippey Peter Jackson's Film Versions, Appendix C in The Road to Middle-Earth Revised and Expanded edition, HarperCollins, London, 2005.


Phan T H Nguyen
email: nguyenthihongphan@gmail.com

Thang H Bui

A Multiple Refinement Approach in Abstraction Model Checking

) an error refinement approach using multiple abstraction in symbolic model checking. The experimentation shows that the new approach has a great performance in checking both 'buggy' and 'correct' models.

Introduction

In model checking, a model is a specification of the under-the-check system for detecting violations of desired properties. When a violation is found, a counterexample is generated to help system engineers in allocating defects. Unfortunately, when the size and the complexity of system-under-check grows up, the state space will be exposed, the checking process is more intractable. To deal with the explosion, abstraction can be used to reduce the size of the model, and thus the effort. However, abstraction may introduce a 'fake' behavior that violates the specification, but that behavior is not present in the original system (false alarm).

When abstracting a system, domain abstraction [START_REF] Menzies | The strangest thing about software[END_REF], that reduces domains of the model, and predicate abstraction, that uses (pre-defined) predicates in reducing the model, are mostly employed. The research in [START_REF] Menzies | The strangest thing about software[END_REF] has discovered that in most system there are some collar variables that play an important role in representing the behavior of the system. Base on that idea, Qian et al. proposed that some 'weak' system variables that almost play no role in the system can be abstracted away [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF]. A simple variable dependency analysis [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF] can be used to classified variables based on their impact to the system. Note that, the research focused only on directed model checking [START_REF] Edelkamp | Directed explicit model checking with HSF-SPIN[END_REF]. The research in [START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF] proposed a propagation variable dependency analysis method to discover the impact of variables to each other. The experimentation has shown that, it outperforms the simple analysis method.

However, good abstract methods still introduce spurious counter-examples. Clarke et al. [START_REF] Clarke | Counterexample-guided abstraction refinement[END_REF] states that refinement on a false alarm counter-example can eliminate it. Whenever a counter-example is found on the abstraction, it should be refined in the concrete system to validate the error. Therefore, abstraction refinement approach must deal with the state explosion on the concrete model when the abstraction is too bad to generate many 'fake' counter-examples.

Qian et al. [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF] instead uses multiple abstraction and indicates that if there is no error on some abstraction, the system is verified without examine the original one. Of course, if all abstractions contain errors, the concrete system should be checked. When a defect is found on an abstraction, the next abstraction will be used. However, the multiple abstraction does not reduce the state space of the next search as in abstraction refinement [START_REF] Clarke | Counterexample-guided abstraction refinement[END_REF].

In this report, we propose a new analysis method as an improvement of the former method [START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF] to analyze system variables so that weak ones are eliminated to make the model simpler. It takes the convergence into account to analyze the variable dependency in domain abstraction. Moreover, we applied the methods to symbolic model checking when states (and the transition relation) of the model can be represented as an expression of system variables, and then can be simply abstracted by domain abstraction.

Besides, a method that takes the advantages of the abstraction refinement [START_REF] Clarke | Counterexample-guided abstraction refinement[END_REF] and multiple abstraction [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF] is also proposed. In other words, the new so-called multiple abstraction refinement (MAR) method is a combination of multiple abstraction and abstraction refinement. It currently supports only for directed model checking, a research direction that considers only invariant properties.

The rest of paper is constructed as follows: Section 2 is to provide some technical background, Section 3 is for the convergent propagation variable dependency analysis, Section 4 is for multiple abstraction refinement. The conclusion and future work is in the last section.

2 Technical Background and Related work

Symbolic model checking

Model checking is a problem to answer is a given model M satisfies the checking property.The problem has two related sub-problem: model representation and model checking approach. There are two main model representation: symbolic model checking, that represents the state space as symbolic expressions, and explicit state model checking, that represent states explicitly. When the state spaces in symbolic model checking are in expressions, In symbolic model checking, the state spaces are in symbolic expressions. one can capture more states than that of the explicit state model checking [START_REF] Burch | Symbolic model checking: 10 20 states and beyond[END_REF].

Definition 1 (Transition systems). A finite state transition system is a tuple M = (S, S 0 , T ), where S is a finite set of states, S 0 ⊆ S is a set of initial states and T ⊆ S × S is a transition relation.

In symbolic model checking, a state s i ∈ S is represented as an expression over a non-empty set of system (or state) variables X = (x 0 , x 1 , . . . , x n ), where each variable x i ranges over a finite domain D i , s i = f (x 0 , x 1 , . . . , x n ).

Abstraction

Abstraction is the concept using in model checking to make the model smaller. In general, if the abstract system is correct, so does the concrete system [START_REF] Clarke | Model checking and abstraction[END_REF]. But there is no guarantee that there is an error in the concrete system if there is an error in the abstraction. For example, an abstraction of the concrete system [START_REF] He | Integrating evolutionary computation with abstraction refinement for model checking[END_REF] is depicted in Fig. 1, in which the error concrete state 10 is unreachable in Fig. 1. An abstraction system [START_REF] He | Integrating evolutionary computation with abstraction refinement for model checking[END_REF] the concrete system even though its abstract state IV is reachable from the (abstract) initial state.

Support that, there is a set of surjections H = (h 1 , h 2 , . . . , h n ), where each h i maps a finite domain D i to another domain Di with | Di | ≤ |D i |. An domain abstraction of a transition system is defined as follows [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF].

Definition 2 (Homomorphic abstraction). A homomorphic abstraction of a transition system

M is M = ( Ŝ, Ŝ0 , T ), where Ŝ = H(S) = { ŝi | ŝi = h i (s)}, Ŝ0 = H(S 0 ), and T = {( ŝi , ŝj ) | (s i , s j ) ∈ T, ŝi = h i (s i ), ŝj = h j (s j )}.
For example, if we want to omit a system variable x k of a model in making an abstraction, we can simply abstract its domain to an empty domain, and apply the above definition. It has been proved that, the (homomorphic) abstraction preserves the checking properties of the concrete system [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF].

Based on that definition, the restriction operation can be defined as: let S M is a set of states of a model M , S M is a set of abstract states of an abstract model

M of M , the restriction of S M according to S M is {s i ∈ S M | ŝi = h i (s i ), ŝi ∈ S M }.

Variable Dependency Analysis

There are many way to abstract a model such as predicate abstraction [START_REF] Ball | Automatic predicate abstraction of C programs[END_REF], that uses predefined predicates to abstract the system, and lazy abstraction [START_REF] Henzinger | Lazy abstraction[END_REF], that prunes branches of execution by abstracting and refines the pruning to allocate errors. Suppose that, the state space of a model in symbolic model checking can be defined over a set of system variables, Qian et al. [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF] proposed that, pruning 'weak' system variables will set off the main features of the model. They have shown that, a simple variable dependency analysis can be used to find 'important' and 'weak' variables. The research in [START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF] suggested to use a propagation approach to the variable dependency analysis and achieved good results.

E(x0) = 1, E(x1) = E(x0)/3 = 0.33, E(x2) = E(x0)/3 = 0.33, E(x3) = E(x1)/3 = 0.11, E(x4) = E(x1)/3 + E(x2)/2 -0.01/(1 + Lv(x0)) -0.01/(1 + Lv(x2)) = 0.26 E(x5) = E(x2)/2 = 0.17.

Fig. 2. A variable dependency graph [5] and its importance factors

Let Prv (x i ) be the set of all variables that defines x i in the relation transition, Nxt(x i ) be the set of variables that are defined by x i , varOf (f ) be the set of variables in the expression f and ϕ be the checking property of the model. The variable dependency graph is defined as follows.

Definition 3 (Variable Dependency Graph). A (variable) dependency graph is a directed graph VDG = (V, E), where V is a set of variables as vertices, E is a set of edges

E = {x i → x j | x j ∈ Nxt(x i )}.
We also defined a mapping Lv to map each variable to a 'layer'. It is defined as Lv(x j ) = 0 iff x j ∈ varOf(ϕ) and Lv(x j ) = Lv(x i ) + 1 if x i ∈ Prv(x j ).

In the case when x i and x j depend on each other, the propagation will be applied to calculate Lv. In the graph in Fig. 2, variable x 0 depends on itself and on x 4 , x 2 and x 4 depends on each other.

Let in(y) be the in-degree of the vertex y, the importance factor of a variable is defined as follows.

E(x) =      1 Lv(x) = 0 y∈Nxt (x)-{x} E(y) in(y) -α(x) Lv(x) > 0 (1)
where α(x) is the counter-effect on x and is defined as

α(x) = β y∈Prv, Lv(y) < Lv(x)(x) 1 1 + Lv(y) (2)
and β ∈ [0 . . . 1] is an adjustment, that controls how much the variables in a higher level affects a variable in a lower level. For example, let β = 0.01, the importance of variables in the graph in the left of Fig. 2 are given on the right of it.

Counter-example Guided Abstraction Refinement -CEGAR

In order to find out the truth about a counter-example in an abstraction, Clarke et al. [START_REF] Clarke | Counterexample-guided abstraction refinement[END_REF] proposed a method so-call Counter-Example Guided Abstraction Refinement (CEGAR). It is to determine if a counter-example on an abstract model can be confirmed on the concrete system. The main idea is that the search is performed on an abstraction and any found counter-example will be refined and confirmed on the concrete system to report an error. If there is no error on the abstraction, the concrete system has been proved its correctness. In this case, the performance of the model checking depends on the quality of the abstraction and the refinement algorithm. Moreover, the method faces the non-strong connectivity inside abstract state (See Fig. 4 in [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF]), when an abstract state represents a set of non-strong connected concrete states. The abstract state III in Fig. 1 is an example of the the issue.

Multiple Abstraction

Another abstraction approach had also been proposed by Qian et al. in [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF].

It is a multiple abstraction strategy to reduce verification efforts. Based on an assumption that there are a series of abstractions M 0 M 1 . . . such that some states s 1 i , s 2 i , . . . in M i+1 (more concrete) are abstracted into only one abstract state s i in M i (more abstract). The model checking searches through abstractions from M 0 , M 1 , . . . for any violation (in those abstraction). It can stop if there is no error found in any M i . Otherwise, the search continuing detects the error on the remanding abstractions and even at last on the concrete system. The proposed method treats all abstractions as separated models and in the sequential order. However, it can take into account the counter-example found on the previous search as a heuristic to guide the search on the next abstraction (or concrete model). Of course, the problem of non-strong connected abstract state mentioned above still exists when it may lead the next search into the wrong direction. In the worst case, the search must be executed on the concrete model to find the actual counter-example. Although its performance is very good [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF], it can be improved by concentrating on (only) dangerous areas in the next abstraction.

Other Direction on Reducing Model Checking Effort

There are some other directions on reducing model checking effort such as Partial Order Reduction [START_REF] Peled | Combining partial order reductions with on-the-fly model-checking[END_REF], SAT-solving [START_REF] Eén | Temporal induction by incremental SAT solving[END_REF]. The latter is known as Bound Model Checking -BMC. In this work, we only focus on abstraction approach to reduce the size of the state space. We may try to apply the idea in this work to some other directions, including BMC in the future. algorithm proposed in [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF] to compare the abstractions made from our new approach and the previous ones. When [START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF] has shown that the propagation analysis is generally better than the simple analysis proposed in [2, 3], we will only compare the new algorithm named VRK with the one in [START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF] named PG in this experiment. The experiment is taken on a Core 2 Duo 2.93 GHz with 2 GB of RAM computer running Ubuntu 13.10. The results are the average of running time in seconds. The experimentation is in Fig. 3.

In this experiment, 40% of the least important variables ('weak' variables) are abstracted away to make the abstraction. It is easy to see that, the searching time of A* using abstraction generated from VRK is generally smaller than that of from PG. The chart on the figure also shows that, the strength of running time of A* using VRK is smoother than that of PG.

Note that, a other configuration may results differently with that experimentation. The experimentation of abstracting away 90% of 'weak' variables is in Fig. 4. In this case, they are almost identical. We believe that, the topology of the Fig. 4. A* with 90% of weak variables abstracted away dependency graphs (of those models) may effect the calculation on convergent. For example, after analyzing, some first variables of the most important ones are the same in both approaches, thus the removing of them makes similar abstrac-tions in both case and the checking will have the same effort. Therefore, the PG algorithm that has lest analysis computation effort, may take advantages. The similar issue has also been reported in [START_REF] Bui | Heuristic sensitivity in guided random-walk based model checking[END_REF].

Discussion: The VRK method in general has more computation effort than the PG method when it takes into account the relationship on all related variables in the system. This effort sometime effective, but in some other cases, it gives no advantages to the whole checking process. But when the development strength of the running time on the abstraction using VRK is smooth, it is likely better than other methods in general. We suggest to use VRK in general.

Multiple Abstraction Refinement -MAR

In this section, we present our new proposed approach named MAR that takes advantages from both CEGAR [START_REF] Clarke | Counterexample-guided abstraction refinement[END_REF] and multiple abstraction methods [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF].

MAR algorithm

Suppose that there is a series of abstractions M 0 M 1 . . . as in Section 2.5. The search is started in the M 0 . If there is a violation (of the checking property), a series of counter-example refinements will be performed on the rest of abstraction M i . If the counter-example is confirmed on all abstractions and then on the concrete system S, it is the actual counter-example. Otherwise, the search will continue on M 0 for another error. If there is no (or no more) counter-example, the concrete system S is proved to satisfy the checking property.

The flows of the algorithm are in Fig. 5. On the right, it is to show how to refine error on all abstraction M i , and even on the concrete system S. The restriction operation is applied on the state space of the checking model based on the counter-example of the previous (more abstract) model. The difference to that of CEGAR is that instead of refining the error on the concrete system S immediately when an error is found on the abstraction M 0 , it refines the error on the 'more concrete' abstraction M 1 (and then on M 2 and so on). In the worst case, the concrete system will be used to search. General speaking, it delays the refinement on the concrete system as long as possible. So, if there is a false alarm, this algorithm may have a chance to find out the truth without searching on the concrete 'huge' state space. In fact, MAR and CEGAR have the same idea when we only have only one abstraction M 0 such that they will refine the counter-example on the concrete state space immediately when it is found on the abstraction. Technically, they are not the same when CEGAR refines error on the concrete system using some complicated algorithms, and our MAR just search on the restricted area made from the (abstract) counter-example on the concrete state space. In this work, we assume that our MAR with one abstraction is CEGAR.

The MAR algorithm also differs to the multiple abstraction proposed in [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF] when it uses the abstractions only for validating an error found on the previous abstraction. At every iteration, instead of searching the state space of M i for a (new) error as in multiple abstraction method, it restricts the state space of M i to the area that comes from the previous counter-example. The idea is that, when the counter-example found from the previous search is small, the restriction will help the algorithm to reduces the verification effort.

Remark 1. The MAR algorithm is sound and complete.

It is easy to prove the remark. When the algorithm returns no error, based on the algorithm, if there is no error on the abstraction M 0 , or if there are some errors on M 0 but were rejected in the validation step, the concrete system has no error. When the algorithm returns a counter-example, it is confirmed on the concrete system, hence it is a counter-example.

Experimental Results on Multiple Abstraction Refinement

In this section, we compare our algorithm (MAR) to the that of [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF] (named SAGA) using the variable dependency analysis VRK. To compare to CEGAR, we assume that our algorithm acts similar to CEGAR if there is only one abstraction M 0 . We named that algorithm is MAR-1 in this experiment. The benchmark we use in this section is provided on the main page of NuSMV. They are named brp, dme, gigamax, msi_wtra, periodic. All of them are correct models, so we can expect that only a few level of abstraction is enough to find the truth. The environment is the same as stated in Section 3.2.

In Fig. 6, we compare the algorithms. The abstractions are built by removing 80%, 60%, 40% and 20% of 'weak' variables, respectively. It is easy to see that, they almost have the same performance, when (in many cases) only the first abstraction is searched and no error ever returned. We also re-use the benchmark in Section 3.2. When they are 'buggy' systems, Fig. 7. MAR vs. SAGA vs. MAR-1 on 'buggy' systems the search in M 0 will return some error and the validation step will search on all the abstractions and the concrete system. The experimentation results in Fig. 7 confirms that the proposed method outperform both multiple-abstraction search (SAGA [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF]) and single-abstraction refinement (MAR-1 as CEGAR). Only one exception that SAGA is extremely good on sender systems. [START_REF] Bui | Heuristic sensitivity in guided random-walk based model checking[END_REF] mentioned that this is a special case when the topology of the state space is skew to some buggy locations and thus the guided search algorithms like SAGA are the best to be used.

To not be bias to the variable analysis methods, we repeated out experiments using random abstraction, in which the importances of system variables are assigned randomly. The experimentation results in Fig. 8 shown that the MAR Discussion: When we model check a system in practice, we actually do not known it is correct or not. The abstraction method MAR is a good choice when it works similarly to CEGAR or SAGA in correct systems and outperforms them in buggy systems. Moreover, it also works well on arbitrary abstraction such as random abstraction.

Future Work and Conclusions

In this paper, a new convergent variable analysis method has been proposed to enrich abstraction technique in model checking. It employees the idea of the convergent computation using in the Page Rank algorithm [START_REF] Brin | The anatomy of a large-scale hypertextual web search engine[END_REF] to calculate the importance of system variables in domain abstraction. The less important variables can be omitted to make abstractions to reduce the state space. The experimentation shows that the new analysis generally gives a better solution in abstraction than some algorithm proposed in previous work. The study on when to use the new analysis and when to use the others is not carried out in this work and should be in the near future.

A new model checking based on counter-example refinement and multiple abstraction has also been proposed. It takes advantages from both methods such that it uses multiple abstraction to confirm a counter-example found on the finest abstraction and the idea of counter-example refinement to refine the counter-example. The modification is instead of refining the error on the concrete system, the new method validates it in the abstractions first. The modification allows the checking process works around the abstractions which are smaller than the concrete system and hence reduces the effort. The experimental results confirmed our assumption. Of course, our algorithm still faces the same problem with CEGAR and multiple abstraction algorithms that if there are errors, it still has to refer to the concrete system in generating a real counter-example.

Nevertheless, when we only support for directed model checking, we need to extend our approach to support other checking direction. It should be in our future work.

Fig. 3 .

 3 Fig. 3. Experimentation on A* using VRK and PG variable analysis methods

Fig. 5 .

 5 Fig. 5. The MAR algorithm

Fig. 6 .

 6 Fig. 6. MAR vs. SAGA vs. MAR-1 on correct systems

Fig. 8 .

 8 Fig. 8. MAR vs. SAGA vs. MAR-1 on 'buggy' systems using random abstraction

Acknowledgment

This research was supported by Vietnam National University -Ho Chi Minh City (Ho Chi Minh City, Vietnam) under the grant number C2013-20-07.

This section is to propose the convergent variable dependency analysis and some experimentation.

The Method -VRK

In this section, we try to add the convergent approach to the propagation approach mentioned in Section 2.3. In this approach, it captures the counter-effect from all related (or connected) variables. The idea of the convergent is actually came from the Page Rank algorithm [START_REF] Brin | The anatomy of a large-scale hypertextual web search engine[END_REF], that had been used in the Google search engine to calculate the degree of related web pages for each web page.

Let d be the damping factor to the convergent (default value is 0.85), the formula to calculate the importance factors of a variable dependency graph V DG = (V, E, Lv) is as follows.

Let try to apply the new formula to the graph in Fig. 2.

(+) Apply equation ( 3): P E(x 0 ) = 0.16243, P E(x 1 ) = 0.17687, P E(x 2 ) = 0.1017, P E(x 3 ) = 0.025, P E(x 4 ) = 0.13348, P E(x 5 ) = 0.025. (+) Apply equation ( 4):

E(x 0 ) = 1.16243, E(x 1 ) = 0.67687, E(x 2 ) = 0.6017, E(x 3 ) = 0.025, E(x 4 ) = 0.13348, E(x 5 ) = 0.025. Discussion: (1) It easy to see that the relationship among variables in this case is different to that of the proposed method in [START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF] (See Fig. 2). We captured more about the inter-effect between any two variables. (2) Especially, the variable's level on the graph still has its effects to the variable important degree similar to the method in [START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF]. Convergent variable dependency analysis simply has focused on both sides.

Experimentation

To compare our new proposed variable analysis in abstraction with previous work [START_REF] Qian | Abstraction-based model checking using heuristical refinement[END_REF][START_REF] Qian | Experiments in multiple abstraction heuristics in symbolic verification[END_REF][START_REF] Bui | Yet another variable dependency analysis for abstraction guided model checking[END_REF], we re-use models from those works. They are peterson, leaderelection, needham protocols and sender-receiver communication system. They are actually 'buggy' models.

The variable analysis algorithm is made into NuSMV (http://nusmv.fbk.eu), a famous symbolic model checking tool. We also re-use the guided search (A*)


Michal Pluhacek
email: pluhacek@fai.utb.cz

Roman Senkerik
email: senkerik@fai.utb.cz

Ivan Zelinka
email: zelinka@fai.utb.cz

Tomas Bata

Chaos Driven Particle Swarm Optimization with Basic Particle Performance Evaluation -An Initial Study

In this paper, the novel concept of particle performance evaluation is introduced into the chaos driven particle swarm optimization algorithm (PSO). The discrete chaotic dissipative standard map is used here as a chaotic pseudo-random number generator (CPRNG). In the novel proposed particle performance evaluation method the contribution of each particle to the process of obtaining the global best solution is investigated periodically. As a reaction to the possible poor performance of a particular particle, its velocity calculation is thereafter altered. Through utilization of this approach the convergence speed and overall performance of PSO algorithm driven by CPRNG based on Dissipative map is improved. The proposed method is tested on the CEC13 benchmark set with two different dimension settings.

Introduction

Since its introduction in 1995 [START_REF] Kennedy | Particle swarm optimization[END_REF], the PSO algorithm [START_REF] Kennedy | Particle swarm optimization[END_REF], [START_REF] Kennedy | Swarm Intelligence[END_REF] has become one of the leading representatives of evolutionary computational techniques (ECTs) and also of the Swarm intelligence [START_REF] Kennedy | Swarm Intelligence[END_REF]. Various modifications have been proposed over the time [START_REF] Liang | Dynamic multi-swarm particle swarm optimizer[END_REF][START_REF] Liang | Comprehensive learning particle swarm optimizer for global optimization of multimodal functions[END_REF][START_REF] Nickabadi | A novel particle swarm optimization algorithm with adaptive inertia weight[END_REF][START_REF] Zhi-Hui | Orthogonal Learning Particle Swarm Optimization[END_REF][START_REF] Yuhui | A modified particle swarm optimizer[END_REF] and the inner dynamic of the PSO has been subject of many detailed studies e.g. [START_REF] Kennedy | Population structure and particle swarm performance[END_REF][START_REF] Van Den Bergh | A study of particle swarm optimization particle trajectories[END_REF]. One of the more recent trends with very satisfactory results is represented through the implementation of chaotic sequences into the PSO dynamic [START_REF] Caponetto | Chaotic sequences to improve the performance of evolutionary algorithms[END_REF][START_REF] Araujo | Particle swarm approaches using Lozi map chaotic sequences to fuzzy modelling of an experimental thermal-vacuum system[END_REF][START_REF] Alatas | Chaos embedded particle swarm optimization algorithms[END_REF][START_REF] Pluhacek | On the behavior and performance of chaos driven PSO algorithm with inertia weight[END_REF][START_REF] Pluhacek | Particle Swarm Optimization Algorithm Driven by Multichaotic Number Generator[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF][START_REF] Pluhacek | Extended Initial Study on the Performance of Enhanced PSO Algorithm with Lozi Chaotic Map, In Proceedings of Nostradamus 2012: International conference on prediction, modeling and analysis of complex systems[END_REF][START_REF] Pluhacek | Designing PID Controller for DC Motor by Means of Enhanced PSO Algorithm with Dissipative Chaotic Map, In Proceedings of SOCO 2012: Soft Computing Models in Industrial and Environmental Applications[END_REF]. Within the previous research [START_REF] Pluhacek | On the behavior and performance of chaos driven PSO algorithm with inertia weight[END_REF][START_REF] Pluhacek | Particle Swarm Optimization Algorithm Driven by Multichaotic Number Generator[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF][START_REF] Pluhacek | Extended Initial Study on the Performance of Enhanced PSO Algorithm with Lozi Chaotic Map, In Proceedings of Nostradamus 2012: International conference on prediction, modeling and analysis of complex systems[END_REF][START_REF] Pluhacek | Designing PID Controller for DC Motor by Means of Enhanced PSO Algorithm with Dissipative Chaotic Map, In Proceedings of SOCO 2012: Soft Computing Models in Industrial and Environmental Applications[END_REF], the strong evidences have been collected to support the claim that utilization of CPRNGs based on different chaotic systems may lead to significantly different behavior of the swarm and overall performance of the algorithm. The dissipative standard map [START_REF] Sprott | Chaos and Time-Series Analysis[END_REF] in particular seems to be very promising chaotic sequence for the usage as the CPRNG inside the PSO algorithm. The performance of such algorithm has been investigated deeply in previous studies e.g. [START_REF] Pluhacek | On the behavior and performance of chaos driven PSO algorithm with inertia weight[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF][START_REF] Pluhacek | Designing PID Controller for DC Motor by Means of Enhanced PSO Algorithm with Dissipative Chaotic Map, In Proceedings of SOCO 2012: Soft Computing Models in Industrial and Environmental Applications[END_REF].

In this research a simple method called the "Particle Performance Evaluation" is designed to improve the performance of PSO algorithm driven by dissipative chaotic map and to address some of the main issues that were discovered during previous research.

The paper is structured as follows: In the next section the original PSO algorithm is described. Section three contains brief summary of the results and main points of previous research of PSO witch Dissipative map based CPRNG. The "Particle Performance Evaluation" is described in section four. Following sections contain the experiments design and results. The results discussion and conclusion follows afterwards.

Particle swarm optimization algorithm

The original (canonical) PSO algorithm was introduced in 1995 by Eberhart and Kennedy [START_REF] Kennedy | Particle swarm optimization[END_REF][START_REF] Kennedy | Swarm Intelligence[END_REF]. Each particle in the swarm is defined by its "position" -the combination of cost function (CF) parameters, and "velocity". The new position of the particle in the following iteration is then obtained as a sum of actual position and newly calculated velocity. The velocity calculation follows two natural tendencies of the particle: To move to the best solution found so far by the particular particle (known in the literature as personal best: pBest or local best: lBest). And to move to the overall best solution found in the swarm or defined sub-swarm (known as global best: gBest).

According to the method of selection of the swarm or subswarm for gBest information spreading, the PSO algorithms are noted as global PSO (GPSO) [START_REF] Yuhui | A modified particle swarm optimizer[END_REF] or local PSO (LPSO) [START_REF] Kennedy | Population structure and particle swarm performance[END_REF]. Within this research the PSO algorithm with global topology (GPSO) [START_REF] Kennedy | Particle swarm optimization[END_REF][START_REF] Kennedy | Swarm Intelligence[END_REF][START_REF] Yuhui | A modified particle swarm optimizer[END_REF] was utilized.

In the original GPSO the new velocity is calculated according to (1):

) ( ) ( 2 1 1 t ij j t ij ij t ij t ij x gBest Rand c x pBest Rand c v w v - ⋅ ⋅ + - ⋅ ⋅ + ⋅ = + (1)
Where: v i t+1 -New velocity of the ith particle in iteration t+1. w -Inertia weight value. v i t -Current velocity of the ith particle in iteration t. c 1 , c 2 -Priority factors (set to the typical value = 2 ). pBest i -Local (personal) best solution found by the ith particle. gBest -Best solution found in a population. x ij t -Current position of the ith particle (component j of the dimension D) in iteration t. Rand -Pseudo random number, interval (0, 1). The CPRNG is used here.

The maximum velocity of particles in the GPSO is typically limited to 0.2 of the range of the optimization problem and this pattern was followed in this study. The new position of a particle is then given by (2), where x i t+1 is the new position of the particle:

1 1 + + + = t i t i t i v x x ( 2
)
Finally the linear decreasing inertia weight [START_REF] Nickabadi | A novel particle swarm optimization algorithm with adaptive inertia weight[END_REF][START_REF] Yuhui | A modified particle swarm optimizer[END_REF] is used in the GPSO here. Its purpose is to slow the particles over time thus to improve the local search capability in the later phase of the optimization. The inertia weight has two control parameters w start and w end . A new w for each iteration is given by (3), where t stands for current iteration number and n stands for the total number of iterations. The values used for the GPSO in this study were w start = 0.9 and w end =0.4.

( ) (

)

n t w w w w end start start ⋅ - - = (3)

PSO with CPRNG based on Dissipative standard map

Within the previous research [START_REF] Pluhacek | On the behavior and performance of chaos driven PSO algorithm with inertia weight[END_REF][START_REF] Pluhacek | Particle Swarm Optimization Algorithm Driven by Multichaotic Number Generator[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF][START_REF] Pluhacek | Designing PID Controller for DC Motor by Means of Enhanced PSO Algorithm with Dissipative Chaotic Map, In Proceedings of SOCO 2012: Soft Computing Models in Industrial and Environmental Applications[END_REF] strong evidences have been gathered hinting that through using of CPRNG based on Dissipative standard map inside the velocity calculation formula (1) of PSO algorithm the performance may be improved (in some cases). The detailed investigations [13 -15] showed that the PSO driven by Dissipative map based CPRNG seems to achieve better results than canonical PSO in the cases of complex highly multimodal or high dimensional problems [START_REF] Pluhacek | On the behavior and performance of chaos driven PSO algorithm with inertia weight[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF][START_REF] Pluhacek | Designing PID Controller for DC Motor by Means of Enhanced PSO Algorithm with Dissipative Chaotic Map, In Proceedings of SOCO 2012: Soft Computing Models in Industrial and Environmental Applications[END_REF].

Recent research in chaos driven heuristics has been fueled with the predisposition that unlike stochastic approaches, a chaotic approach is able to bypass local optima stagnation. This one clause is of deep importance to evolutionary algorithms. A chaotic approach generally uses the chaotic map in the place of a pseudo random number generator. This causes the heuristic to map unique regions, since the chaotic map iterates to new regions. The task is then to select a very good chaotic map as the pseudo random number generator.

It seems that the performance of PSO is improved by altering the swarm behavior in such manner that the convergence speed is significantly slower, which may result in the lower chance of falling into local extremes. However the better achieved results are usually compensated by the significantly higher computational time demands given the higher number of iterations required for the algorithm to converge (for further details please see [13 -15]).

The aforementioned behavior lead to conclusion: when strict time restrictions are applied, the PSO driven by chaotic Dissipative map based CPRNG is not able to achieve good results. As a reaction to these issues, the novel "Particle performance evaluation" approach is investigated and implemented into the GPSO driven by Dissipative standard map in this presented research. The goal is to enhance the overall performance of the algorithm through the improvement of the convergence speed together with maintaining the advantages of the original PSO driven by Dissipative map based CPRNG.

The Dissipative standard map is a two-dimensional chaotic map [START_REF] Sprott | Chaos and Time-Series Analysis[END_REF]. The parameters used in this work are b = 0.6 and k = 8.8 based on previous experiments [START_REF] Pluhacek | Designing PID Controller for DC Motor by Means of Enhanced PSO Algorithm with Dissipative Chaotic Map, In Proceedings of SOCO 2012: Soft Computing Models in Industrial and Environmental Applications[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF] and suggestions in literature [START_REF] Sprott | Chaos and Time-Series Analysis[END_REF].The map equations are given in (4).

) 2 (mod sin ) 2 (mod 1 1 1 π π n n n n n n X k bY Y Y X X + = + = + + + (4)

PSO with Particle performance evaluation (PSO with PPE)

The novel approach proposed in this study is based on the simple premise that all particles should take part in the process of finding and improving of the final solution. The only way of communication among the particles in the GPSO design [START_REF] Kennedy | Particle swarm optimization[END_REF] represents the shared knowledge of the position of the best globally found solution (gBest). In other words: To be beneficial for the swarm, the particle has to update the gBest. Therefore the first step in the particle performance evaluation (PPE) is the exact monitoring of the gBest updaters. A counter is allocated to each particle. On the start of each iteration the counter is incremented by 1 and is set to 0 when the particle triggers a gBest update. In this way, it is possible to measure the number of iterations since the last gBest was found by particular particle. The second step in the PPE approach is to alter the performance of the particular particle when it has not triggered the gBest update for a given maximum number of iterations. In this initial research the simple constant c 1 (1) is modified to vector (see [START_REF] Nickabadi | A novel particle swarm optimization algorithm with adaptive inertia weight[END_REF]).

) ( ) ( 2 1 1 t ij j t ij ij i t ij t ij x gBest Rand c x pBest Rand c v w v - ⋅ ⋅ + - ⋅ ⋅ + ⋅ = + (5)
Where: c 1i -Priority factor 1 for the ith particle. Subsequently when the particular particle does not trigger a gBest update for 1/10 of the total number of iterations, the c 1 value for that particle is set to 1. The value of c 1 is set back to 2 when the particle reaches the gBest update.

Through the following of this very simple pattern it is possible to reduce the number of particles with no gBest updates (triggers), further to reduce the number of iteration between gBest updates for the each particle and to improve the overall performance of the PSO algorithm driven by Dissipative map based CPRNG in some cases as it is presented in the following sections.

Experiment setup

Within all performance testing three different GPSO versions were used. The first one was the original canonical GPSO with linear decreasing inertia weight (as described in the section 2), noted GPSO. The second version was the GPSO with Dissipative map based CPRNG in the velocity calculation (Noted GPSO Disi) and finally the third version represents the GPSO with Dissipative map based CPRNG and PPE as described in the section 4 (noted PSO Disi PPE).

For the performance tests the CEC 13 benchmark suite [START_REF] Liang | Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization[END_REF] was used. For each version, totally 20 separate runs were performed and statistically analyzed.

Control parameters were set up based on the previous numerous experiments and literature sources [START_REF] Kennedy | Particle swarm optimization[END_REF][START_REF] Pluhacek | Particle Swarm Optimization Algorithm Driven by Multichaotic Number Generator[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF][START_REF] Liang | Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization[END_REF] as follows:

Population size: 30 Dimension: 10, 50 Iterations: 2500, 12500 (according to [START_REF] Liang | Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization[END_REF]) Runs: 20 v max = 0.2 • Range w start = 0.9 w end = 0.4

Results

The mean results for all versions of PSO described in the previous section are given and compared in Tables 1 and2. The bold numbers represents the best results. The mean results are presented alongside the total number of best results obtained. Furthermore the performance of pairs of algorithms is compared, where 1 stands for "win" of the "algorithm 1" (the first from the pair -left); number 2 stand for "win" of algorithm 2 (the second from the pair -right) and 0 stands for draw. The final score is also given in Tables 1 and2 as a sum of points for wins (1 point) and draws (0.5 point).

Furthermore Fig. 1 depicts the illustrative comparison of the number of iterations since the last gBest update for each particle for GPSO Disi and GOPSO Disi PPE. It can be clearly observed the positive influence of PPE approach.

Finally two examples of mean gBest history plots are given in Fig. 2 and3 to highlight the change in behavior of the chaos driven GPSO especially in terms of convergence speed. The results are further discussed in following section.

Results Discussion

The data presented in previous section seem to indicate that when the PPE is applied, the performance of GPSO driven by Dissipative standard map was in some cases significantly improved. In the first experiment (Table 1) the original chaotic GPSO (GPSO Disi) managed to obtain better results than the canonical version (GPSO) only for 8 functions. However when PPE was applied the number of better results (for the restricted number of iterations) has increased to 15. In direct comparisons the chaos driven GPSO with PPE (GPSO Disi PPE) managed to find better results for 19 different benchmark functions than the simple chaos driven GPSO (GPSO Disi). As an illustrative example, the effect of PPE (in case of f( 15)) can be further observed from Fig. 2, where the gBest history is depicted and the improvement of convergence speed is clearly visible. It also seems that the GPSO Disi would improve its performance further if the number of iterations was increased.

The second experiment (with higher dimension setting) has brought up surprising results (Table 2) that were unprecedented in any previous research [START_REF] Pluhacek | On the behavior and performance of chaos driven PSO algorithm with inertia weight[END_REF][START_REF] Pluhacek | Particle Swarm Optimization Algorithm Driven by Multichaotic Number Generator[END_REF][START_REF] Pluhacek | On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems[END_REF]. It seems that the performance of GPSO Disi is not satisfactory within the given dimension setting, function complexity and number of iterations. However when PPE is applied once again the performance was significantly improved. The example of mean gBest history for dim=50 and f( 4) is given in Fig. 3. It seems that on this type of problem [START_REF] Liang | Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization[END_REF] the chaos driven PSO with PPE manages to obtain significantly better results than both the canonical (GPSO) and original chaos driven version (GPSO Disi).

Conclusion

In this initial research the behavior of GPSO algorithm driven by Dissipative standard map based CPRNG was altered by applying the "Particle performance evaluation". The performance of newly designed algorithm was tested on the CEC 13 benchmark suite and compared to the performance of original GPSO with both canonical and chaotic PRNG.

It is necessary to mention, that the main aim of this paper was not to test the chaos embedding approach for evolutionary/swarm based algorithms, as the utilization of different CPRNGS and the very positive influence of inner chaotic dynamics to the performance of embedded algorithms was proved in many previous studies. Since the PPE approach was already successfully tested with canonical versions of PSO and with default PRNGs (no chaos embedded), the contribution of this paper is to show/prove the influence of PPE approach also in the different case of the chaos driven PSO algorithm, which takes advantages from the different swarm environment given by the chaotic dynamics.

The initial results presented in this paper seem to indicate that this approach may lead to significant performance improvements for certain types of optimization problems. Also it seems that the number of redundant cost function evaluations may be significantly reduced by using the PPE approach. There is however still a need for significant number of experiment with higher variety of problem types and control parameters settings to prove these claims. The future research will focus mainly on further improvements of this method by enhancing the PPE with variety of different behavior changes (rules) for the particles.

Fig. 1 .

 1 Fig. 1. Number of iterations since last gBest update for each particle (sorted). f(1), dim = 10; comparison of GPSO Disi-blue, GPSO Disi PPE -red

Fig. 3 .

 3 Fig. 3. Mean gBest history comparison f(4), dim = 50

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Table 1 :

 1 Mean results comparison for dim = 10

	f(x) GPSO	GPSO Disi GPSO Disi PPE		A1 vs. A2 A1 vs. A3 A2 vs. A3
	f(1)	-1400	-1400	-1400	0	0	0
	f(2)	116137.6 416672.8	238461.5	1	1	2
	f(3)	2.73E+06 1.90E+06	289907.1	2	2	2
	f(4)	-806.79	-471.1	-957.38	1	2	2
	f(5)	-1000	-1000	-1000	0	0	0
	f(6)	-894.08	-886	-890.78	1	1	2
	f(7)	-795.82	-796.74	-793.61	2	1	1
	f(8)	-679.67	-679.69	-679.67	2	0	1
	f(9)	-597.39	-596.65	-596.82	1	1	2
	f(10)	-499.51	-499.32	-499.6	1	2	2
	f(11)	-398.16	-397.14	-397.61	1	1	2
	f(12)	-287.02	-278.4	-288.41	1	2	2
	f(13)	-181.14	-177.32	-180.41	1	1	2
	f(14)	73.36	169.38	128.84	1	1	2
	f(15)	835.16	949.55	674.34	1	2	2
	f(16)	200.89	200.95	200.79	1	2	2
	f(17)	314.23	329.04	313.66	1	2	2
	f(18)	431.55	439.58	422.38	1	2	2
	f(19)	500.68	501.48	500.67	1	2	2
	f(20)	602.48	602.87	602.6	1	1	2
	f(21)	1100.19	1090.18	1100.19	2	0	1
	f(22)	1031.51	1045.12	1121.89	1	1	1
	f(23)	1623.05	1726.28	1711.32	1	1	2
	f(24)	1204.71	1209.16	1204.64	1	2	2
	f(25)	1307.02	1305.78	1306.93	2	2	1
	f(26)	1350.92	1345.93	1347.28	2	2	1
	f(27)	1640.26	1656.97	1691.26	1	1	1
	f(28)	1754.15	1737.21	1745.87	2	2	1
	Best:	12		8	12	Score:	20 : 8	13 : 15	9.0 : 19.0

Table 2 :

 2 Mean results comparison for dim = 50

	f(x) GPSO	GPSO Disi GPSO Disi PPE		A1 vs. A2 A1 vs. A3 A2 vs. A3
	f(1)	-1400 -1348.687	-1400	1	0	2
	f(2)	9.65E+06 6.29E+07	2.18E+07	1	1	2
	f(3)	3.01E+08 6.91E+09	2.45E+08	1	2	2
	f(4)	1964.64 8114.369	-742.66	1	2	2
	f(5)	-1000	-975.08	-1000	1	0	2
	f(6)	-846.59	-832.96	-853.21	1	2	2
	f(7)	-749.31	-732.56	-743.87	1	1	2
	f(8)	-678.88 -678.879	-678.9	0	2	2
	f(9)	-558.06	-550.86	-554.49	1	1	2
	f(10)	-498.69	-377.11	-499.88	1	2	2
	f(11)	-345.973 -202.754	-346.22	1	2	2
	f(12)	-38.699	120.79	-137.82	1	2	2
	f(13)	136.46	217.1	88.27	1	2	2
	f(14)	1582.63	5858.16	1657.56	1	1	2
	f(15) 12130.01 12897.36	7891.71	1	2	2
	f(16)	203.04	202.68	202.89	2	2	1
	f(17)	432.469	764.932	448.87	1	1	2
	f(18)	868.08	947.15	611.54	1	2	2
	f(19)	507.03	541.05	508.97	1	1	2
	f(20)	621.37	621.67	620.03	1	2	2
	f(21)	1615.7	1726.1	1661.8	1	1	2
	f(22)	2915.96	7466.41	3205.45	1	1	2
	f(23) 12395.47 14554.47	10168.74	1	2	2
	f(24)	1290.55	1314.49	1306.99	1	1	2
	f(25)	1484.49	1521.45	1510.91	1	1	2
	f(26)	1563.87	1582.17	1586.17	1	1	1
	f(27)	2687.23	2843.66	2863.93	1	1	1
	f(28)	1800 1861.448	1960.31	1	1	1
	Best:	13		1	12	Score: 26.5 : 1.5 14.0 : 14.0 4.0 : 24.0

Fig. 2. Mean gBest history comparison f(15), dim = 10

Acknowledgements

The following grants are acknowledged for the financial support provided for this research: Grant Agency of the Czech Republic -GACR P103/ 13/08195S, is partially supported by Grant of SGS No. SP2014/159, VŠB -Technical University of Ostrava, Czech Republic, by the Development of human resources in research and development of latest soft computing methods and their application in practice project, reg. no. CZ.1.07/2.3.00/20.0072 funded by Operational Programme Education for Competitiveness, co-financed by ESF and state budget of the Czech Republic, further was supported by European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089 and by Internal Grant Agency of Tomas Bata University under the project No. IGA/FAI/2014/010.