42 research outputs found

    Analyse et conception de recherches locales génériques pour l'optimisation combinatoire à un ou plusieurs objectifs

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    Lorsque l’on cherche à résoudre des problèmes d’optimisation combinatoire difficiles, trouver une solution optimale par les méthodes complètes peut s’avérer impraticable. Dans un tel contexte, on peut déterminer des solutions approchées grâce à l’utilisation d’heuristiques. Parmi elles, les métaheuristiques sont une forme générique d’algorithmes approchés facilement applicables à une large gamme de problèmes.Nos travaux de recherche sur les métaheuristiques cherchent à s’abstraire au maximum des spécificités des problèmes d’optimisation en les modélisant notamment sous forme de paysages de recherche à explorer. Cette abstraction, proposée en 1932 en biologie pour modéliser la relation entre génotype des individus et chances de reproduction, a été reprise plus récemment en optimisation combinatoire afin de mettre en relation la qualité des solutions avec les valeurs prises par les variables de décision. Dans ce contexte, nous avons étudié principalement la résolution de problèmes d’optimisation par les algorithmes de recherche locale.En optimisation mono-objectif, l’étude des climbers classiques de la littérature combinée avec l’analyse de la structure des paysages de recherche nous a permis d’obtenir des résultats parfois à contre-courant de ce qui est fait usuellement dans la communauté. Grâce à ces observations, nous nous sommes proposé d’étudier des stratégies originales pour ces algorithmes de recherche. Les résultats obtenus permettent d’entrevoir des perspectives de recherche importantes dans ce domaine.En optimisation multiobjectif, nous avons proposé des algorithmes de type recherche locale basés sur la notion d’indicateur de qualité. Ces algorithmes, en plus d’être génériques, se sont montrés efficaces sur divers types de problèmes tout en étant peu sensibles au paramétrage. L’utilisation d’indicateurs de qualité permet de surcroît de reformuler les problèmes d’optimisation multiobjectif sous forme de problèmes d’optimisation mono-objectif sur des ensembles et ainsi ouvrir diverses perspectives de recherche

    Metaheuristics for NP-hard combinatorial optimization problems

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    Ph.DDOCTOR OF PHILOSOPH

    Design of Heuristic Algorithms for Hard Optimization

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    This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content

    Mixed-integer linear programming based approaches for the resource constrained project scheduling problem.

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    Programa de P?s-Gradua??o em Ci?ncia da Computa??o. Departamento de Ci?ncia da Computa??o, Instituto de Ci?ncias Exatas e Biol?gicas, Universidade Federal de Ouro Preto.Resource Constrained Project Scheduling Problems (RCPSPs) without preemption are well-known NP-hard combinatorial optimization problems. A feasible RCPSP solution consists of a time-ordered schedule of jobs with corresponding execution modes, respecting precedence and resources constraints. First, in this thesis, we provide improved upper bounds for many hard instances from the literature by using methods based on Stochastic Local Search (SLS). As the most contribution part of this work, we propose a cutting plane algorithm to separate five different cut families, as well as a new preprocessing routine to strengthen resource-related constraints. New lifted versions of the well-known precedence and cover inequalities are employed. At each iteration, a dense conict graph is built considering feasibility and optimality conditions to separate cliques, odd-holes and strengthened Chv?tal-Gomory cuts. The proposed strategies considerably improve the linear relaxation bounds, allowing a state-of-the-art mixed-integer linear programming solver to nd provably optimal solutions for 754 previously open instances of different variants of the RCPSPs, which was not possible using the original linear programming formulations

    Development and application of hyperheuristics to personnel scheduling

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    This thesis is concerned with the investigation of hyperheuristic techniques. Hyperheuristics are heuristics which choose heuristics in order to solve a given optimisation problem. In this thesis we investigate and develop a number of hyperheuristic techniques including a hyperheuristic which uses a choice function in order to select which low-level heuristic to apply at each decision point. We demonstrate the effectiveness of our hyperheuristics by means of three personnel scheduling problems taken from the real world. For each application problem, we apply our hyperheuristics to several instances and compare our results with those of other heuristic methods. For all problems, the choice function hyperheuristic appears to be superior to other hyperheuristics considered. It also produces results competitive with those obtained using other sophisticated means. It is hoped that - hyperheuristics can produce solutions of good quality, often competitive with those of modern heuristic techniques, within a short amount of implementation and development time, using only simple and easy-to-implement low-level heuristics. - hyperheuristics are easily re-usable methods as opposed to some metaheuristic methods which tend to use extensive problem-specific information in order to arrive at good solutions. These two latter points constitute the main contributions of this thesis
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