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Application des algorithmes ´ evolutionnaires aux probl` emes d’optimisation multi-objectif avec contraintes. Olga Roudenko To cite this version: Olga Roudenko. Application des algorithmes ´ evolutionnaires aux probl` emes d’optimisation multi-objectif avec contraintes.. Optimisation et contrˆ ole [math.OC]. Ecole Polytechnique X, 2004.Fran¸cais. <pastel-00000967> HAL Id: pastel-00000967 https://pastel.archives-ouvertes.fr/pastel-00000967 Submitted on 23 Jul 2010 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destin´ ee au d´ epˆ ot et ` a la diffusion de documents scientifiques de niveau recherche, publi´ es ou non, ´ emanant des ´ etablissements d’enseignement et de recherche fran¸cais ou ´ etrangers, des laboratoires publics ou priv´ es.

Application des algorithmes évolutionnaires aux problèmes … · 2017. 1. 29. · Application des algorithmes evolutionnaires aux probl emes d’optimisation multi-objectif avec

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Page 1: Application des algorithmes évolutionnaires aux problèmes … · 2017. 1. 29. · Application des algorithmes evolutionnaires aux probl emes d’optimisation multi-objectif avec

Application des algorithmes evolutionnaires aux

problemes d’optimisation multi-objectif avec contraintes.

Olga Roudenko

To cite this version:

Olga Roudenko. Application des algorithmes evolutionnaires aux problemes d’optimisationmulti-objectif avec contraintes.. Optimisation et controle [math.OC]. Ecole Polytechnique X,2004. Francais. <pastel-00000967>

HAL Id: pastel-00000967

https://pastel.archives-ouvertes.fr/pastel-00000967

Submitted on 23 Jul 2010

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

Page 2: Application des algorithmes évolutionnaires aux problèmes … · 2017. 1. 29. · Application des algorithmes evolutionnaires aux probl emes d’optimisation multi-objectif avec

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Remerciements

J’ai eu la chance de faire ma these sous la direction de Marc, qui m’a apporte sonsoutien et son aide dans tous les moments difficiles, depuis mon inscription jusqu’a monpot de soutenance. Des le debut du travail, Marc m’a laisse la liberte de faire mes propreschoix concernant ma recherche (les pistes a explorer, les applications a traiter...), ce qui apu etre difficile au debut mais s’avere aujourd’hui precieux. Une des choses agreables auraete cette facon que Marc a de partager ses connaissances et son experience de chercheursans jamais rien imposer, en laissant croire, l’air de rien, que tout vient de soi. Enfin, c’esttoujours un plaisir de discuter avec quelqu’un qui sait lire a travers les tatonnements etcomprendre l’essentiel malgre l’imprecision.

J’en arrive a croire que si j’ai pris mon temps pour faire cette these, c’est qu’incon-sciemment, je voulais repousser le moment, ou je devrais m’eloigner du maıtre TAO pouraller trouver ma propre voie...

Je suis tres reconnaissante a Jin Kao-Hao et a Jacques Periaux, les premiers lecteursde ma these, qui ont ecrit des rapports agreablement favorables malgre “quelques coquillesdans le manuscrit”, coquilles dont je crains d’avoir conserve quelques exemplaires pour lapresente edition.

J’adresse mes remerciements les plus sinceres et respectueux a Jean-Claude Nedelecpour avoir ete le plus gentil President du plus gentil Jury que je pouvais esperer pour masoutenance.

Je tiens a exprimer ma grande reconnaissance a Francois Jouve, qui a non seulementaccepte de faire partie de ce Jury, mais qui a egalement eu la patience d’ecouter mescommentaires confus la veille de la soutenance et la sympathie de m’aider pour la logistiquede derniere minute, au moment ou le trac confine a la febrilite.

Mes remerciements vont a toutes les personnes qui travaillent (ou travaillaient) au Cen-tre de Mathematiques Appliquees et qui m’ont aidee au cours des annees de ma presencedans ce laboratoire par un geste amical ou par une parole encourageante. Merci a SylvainFerrand pour tous les portables et les ordinateurs fixes qu’il a fait marcher, typiquementaux moments critiques. Merci a Geo Boleat, a Jeanne Bailleul, a Aja Mazari, a NatachaBereux, a Erwan Le Pennec ainsi qu’a toute personne que j’ai pu deranger a intervallesplus ou moins reguliers pour la resolution de mes petits problemes tres importants. Mercia Vincent Giovangigli, directeur du CMAP, pour sa bonne humeur, sa disponibilite et sestres nombreux autographes (que je collectionnais depuis mon DEA) !

Merci beaucoup a Sana Ben Hamida et Hatem Hamda (qui ont fait egalement leurstheses avec Marc) pour leur aide, leur disponibilite, leur gentillesse et leurs conseils. Avoirleur exemple devant moi m’a reelement aidee a mener mon propre travail de these a bien.Je remercie Kamal Abboud pour sa bonne humeur en toutes circonstances et lui souhaitebon courage pour la fin de sa these !

Je me rappelerai toujours l’ambiance familiale, gaie et chaleureuse d’un bureau cos-mopolite au possible : merci a Paola Goatin, Shiva Zamani, Javier Abadia, Ignacio Muga,Mai Duc Thanh et Snorre Cristiansen pour y avoir chacun joue un role particulier etirremplacable.

Il y a eu des moments, ou j’ai cru de plus pouvoir terminer ma these et je suis heureuse,aujourd’hui, d’exprimer toute ma reconnaissance a Sergio Basso Ricci : c’est en grandepartie a son influence et a son soutien que je dois de ne pas avoir craque dans ces moments-la.

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Je suis particulierement sensible a toute l’aide dont j’ai beneficie pendant la derniereannee de these, qui a ete tres dure pour moi a plusieurs egards. Je n’aurais jamais pumener a bien ce travail sans la comprehension et la generosite de Marc pendant cetteperiode. Il m’est egalement difficile d’imaginer les mois qui ont precede la soutenancesans le soutien de Anne Auger qui m’a constamment aide pour la resolution de petites etgrandes difficultes. L’acces au “bureau convivial” cree par Anne, Yann Semet et NicolasGodzik a ete l’une des rares choses a posseder la force de me remonter le moral pendantcette periode epuisante.

J’ai trouve au sein de l’equipe TAO une ambiance particulierement favorable pourpreparer“l’accouchement” : merci a Michele Sebag de ses conseils et sa disponibilite, graziea Nico e Mara del loro buonissimo tiramisu, et merci a Mary Felkin, Nicolas Bredeche,Antoine Cornuejols, Nicolas Baskiotis, Vijay Pratap Singh, Celso Ishida, Aurora RamirezPozo et a tous les gens qui ont trouve pour moi une parole encourageante en francais,anglais, russe ou dans une quelconque autre langue.

Je tiens egalement a remercier les membres de l’equipe Fractales de l’INRIA Rocquen-court de leur accueil chaleureux et leurs encouragements pour l’etape aussi importanteque difficile du “demarrage” de la redaction. Parmi eux Amine Boumaza tient une placeparticuliere.

J’adresse mes remerciements les plus sinceres et chaleureux a Olga Chestiperova etSamir El Mouala, mes amis depuis mon arrive en France, pour m’avoir toujours donneleur appui et plus particulierement pendant ces derniers mois. Je suis egalement tres recon-naissante a Jose Emilio Soto pour avoir ete disponible dans les moments difficiles ! KatyaIakovleva et Maxime Eremenko ont ma gratitude profonde pour avoir partage toutes mesjoies et tristesses !

Je suis heureuse aujourd’hui d’exprimer toute ma reconnaissance et tout mon respect amon premier responsable scientifique et mon premier co-auteur Yuri Mironovitch Laevskypour m’avoir initiee a la recherche et pour m’avoir encouragee a continuer dans cette voie.

C’est un grand plaisir pour moi de dire merci a Franci Kluzer, qui a montre une reservede patience sans fond et qui m’a aide a prendre la confiance en moi : les choses qui parais-saient impossibles se sont alors realisees comme par magie. – Hvala, soncek, da si bil takpotrpezljiv in si me vedno podpiral! Pa zlasti sem ti hvalezna, da si mi pomagal pridobitisamozavest!

Je ne remercierai jamais suffisamment ma maman, qui m’a apporte un soutien enormemalgre un eloignement difficile. Elle a toujours su trouver le mot juste pour m’aider arassembler les forces qui me faisaient defaut. J’espere seulement avoir la chance de luirendre un millieme de l’aide que j’ai recu d’elle...

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A ma maman

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Paramétres de controle

Timing de l’injection principale de commande

Unité

Moteur

Reponses du système

Performances

(NOx, particules, ...)Emissions

Pression

Timing de la pré−injection

Durée de la pré−injection

(consommation, bruit)Timing de la post−injection

Durée de la post−injection

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Resume

Ce travail est une contribution au developpement des Algorithmes Evolutionnaires Multi-objectif. Lahausse remarquable d’ineret pour ces methodes recentes constatee depuis la derniere decenie s’expliquenotamment par leur capacite de trouver une (bonne) approximation de l’ensemble des compromis dePareto en un seul essai de l’algorithme, a la difference des approches traditionnelles pour l’optimisationmulti-critere, qui ne trouvent qu’une solution-compromis a la fois (d’autant que cette solution dependfortement du choix subjectif de certains parametres). En effet, lors de la resolution des problemes reelsd’optimisation multi-critere, et en particulier, des problemes de conception, il est souvent preferable deprendre la decision finale a partir des informations les plus completes possibles, meme si cela necessiteun effort de calcul supplementaire.

Dans cette these, deux problemes de l’industrie automobile sont etudies. Le premier concerne l’op-timisation parametrique de la forme d’un pare-choc de voiture, un probleme a 10 objectifs issus de 3domaines mecaniques: crash, acoustique et statique. Le second probleme qui se pose lors du calibrage dumoteur diesel Common Rail (rampe commune) consiste a minimiser la consommation specifique du car-burant ainsi que le bruit de la combustion tout en respectant les normes europeennes de fonctionnementen terme de nuisances a l’environnement.

Une tendance remarquable des Algorithmes Evolutionnaires est que ces methodes “penetrent” au-jourd’hui dans de nombreux nouveaux domaines d’application malgre l’absence de bases theoriques(notamment, de preuves de convergence) aussi solides que celles qu’on peut trouver pour des approchesalternatives. Inspiree par cette observation, la motivation principale de ce travail etait de contribuerau developpement des Algorithmes Evolutionnaires Multi-objectif de facon a rendre leur applicationaux problemes reels la plus efficace possible. Ainsi, une contribution originale de cette these consiste arepondre a un manque criant dans ce domaine, le manque de critere d’arret plus fin qu’une simple bornesur le nombre d’iterations. Le critere d’arret propose dans ce travail est destine a optimiser le rapportentre la qualite des solutions et le cout de calcul: dans la pratique c’est ce compromis qui est le plussouvent recherche. De meme, un nouvel operateur de croisement base sur la relation de la dominancede Pareto est propose et nous montrons l’acceleration de la progression vers la surface des compromisoptimaux qu’il apporte.

Abstract

This work contributes to the development of Evolutionary Multi-objective Algorithms. The increa-sing interest for these techniques observed since the last decade is mainly due to their ability to find a(good) sampling of the whole set of the Pareto compromises in a single run unlike the traditional multi-objective optimization approaches that provide only one compromise solution which, what is more,highly depends on the subjective choice of certain parameters. Indeed, when solving the real-worldmulti-objective optimization problems and, in particular, design problems, it is often preferable to makethe final decision from the informations as complete as possible even if an additional computation effortis needed.

In this thesis, two problems from car industry are studied. The first one is the optimization ofthe shape of the car front end taking into account 10 objectives issued from the crash, acoustic andstatic mechanical domains. The second problem consists in optimizing the parameters controlling thefuel injection for the Common Rail diesel engine in order to minimize the specific consumption andcombustion noise subject to the European Emission Standard constraints.

An important tendency of the Evolutionary Algorithms is that these methods today “penetrate”into numerous new applicative domains in spite of the absence of a solid theoretical basis (notably,convergence proofs) as can be found for the alternative approaches. Inspired by this observation, themain motivation of this work was to contribute to the development of Evolutionary Multi-objectiveAlgorithms in such a way as to make their application to the real-world problems most efficient. Thus,one original contribution of this thesis consists in responding to a very important lack in this domain,the lack of a stopping criterion finer then just the bounding of the number of iterations. The stoppingcriterion proposed in this work is intended to optimize the ratio between the solutions quality and thecomputation cost: indeed, in practice this is what is very often sought. Then, a new crossover operatorbased on the Pareto dominance relation is proposed and we show that it accelerates the progress towardthe Pareto surface.