Set-based Multiobjective Fitness Landscapes: A Preliminary Study

Fitness landscape analysis aims to understand the geometry of a given optimization problem in order to design more efficient search algorithms. However, there is a very little knowledge on the landscape of multiobjective problems. In this work, following a recent proposal by Zitzler et al. (2010), we consider multiobjective optimization as a set problem. Then, we give a general definition of set-based multiobjective fitness landscapes. An experimental set-based fitness landscape analysis is conducted on the multiobjective NK-landscapes with objective correlation. The aim is to adapt and to enhance the comprehensive design of set-based multiobjective search approaches, motivated by an a priori analysis of the corresponding set problem properties

Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes

In multiobjective combinatorial optimization, there exists two main classes of metaheuristics, based either on multiple aggregations, or on a dominance relation. As in the single objective case, the structure of the search space can explain the difficulty for multiobjective metaheuristics, and guide the design of such methods. In this work we analyze the properties of multiobjective combinatorial search spaces. In particular, we focus on the features related the efficient set, and we pay a particular attention to the correlation between objectives. Few benchmark takes such objective correlation into account. Here, we define a general method to design multiobjective problems with correlation. As an example, we extend the well-known multiobjective NK-landscapes. By measuring different properties of the search space, we show the importance of considering the objective correlation on the design of metaheuristics.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

NILS: a Neutrality-based Iterated Local Search and its application to Flowshop Scheduling

This paper presents a new methodology that exploits specific characteristics from the fitness landscape. In particular, we are interested in the property of neutrality, that deals with the fact that the same fitness value is assigned to numerous solutions from the search space. Many combinatorial optimization problems share this property, that is generally very inhibiting for local search algorithms. A neutrality-based iterated local search, that allows neutral walks to move on the plateaus, is proposed and experimented on a permutation flowshop scheduling problem with the aim of minimizing the makespan. Our experiments show that the proposed approach is able to find improving solutions compared with a classical iterated local search. Moreover, the tradeoff between the exploitation of neutrality and the exploration of new parts of the search space is deeply analyzed

A new distance measure based on the exchange operator for the HFF-AVRP

The Heterogeneous Fixed Fleet Asymmetric Vehicle Routing Prob- lem (HFF-AVRP) is a N P-hard optimization problem. Instances analysis and in particular, fitness landscape analysis, may help problem solving. Such anal- ysis require the definition of a distance between feasible solutions. Such a dis- tance does not exist for the HFF-AVRP and this report aims at proposing a new distance measure defined from the exchange operator. In order to compute the exchange-distance between two solutions, four algorithms are suggested and then experimented. One of them is proved to be robust and to give the exact distance whereas others only compute an upper bound

Parallel partitioning method (PPM): A new exact method to solve bi-objective problems

International audienceIn this paper, we propose a new exact method, called the parallel partitioning method (PPM), able to solve efficiently bi-objective problems. This method is based on the splitting of the search space into several areas leading to elementary exact searches. We compare this method with the well-known two-phase method (TPM). Experiments are carried out on a bi-objective permutation flowshop problem (BOFSP). During experiments the proposed PPM is compared with two versions of TPM: the basic TPM and an improved TPM dedicated to scheduling problems. Experiments show the efficiency of the new proposed method

Combining Evolutionary Algorithms and exact approaches for multi-objective knowledge discovery

International audienceAn important task of knowledge discovery deals with discovering association rules. This very general model has been widely studied and efficient algorithms have been proposed. But most of the time, only frequent rules are seeked. Here we propose to consider this problem as a multi-objective combinatorial optimization problem in order to be able to also find non frequent but interesting rules. As the search space may be very large, a discussion about different approaches is proposed and a hybrid approach that combines a metaheuristic and an exact operator is presented

A Parallel Adaptive GA for Linkage Disequilibrium in Genomics.

In this paper, we treat the linkage disequilibrium, used to discover haplotypes, candidate to explain multi-factorial diseases such as diabetes or obesity, as an optimization problem where a given objective function has to be optimized. In order to determine what kind of algorithm will be able to solve this problem, we first study the specificities and the structure of the problem. Results of this study show that exact algorithms are not adapted to this specific problem and lead us to the development of a parallel dedicated adaptive multipopulation genetic algorithm that is able to find several haplotypes of different sizes. After describing the biological problem, we present the dedicated genetic algorithm, its specificities, such as the use of several populations and its advanced mechanisms such as the adaptive choice of operators, random immigrants, and its parallel implementation. We give results on a real dataset

Rules extraction in linkage disequilibrium mapping with an adaptive genetic algorithm

Paris, FranceIn this paper, we present an evolutionary approach to discover candidate haploty pes in a linkage disequilibrium study. This work takes place into the study of f actors involved in multi-factorial diseases such as diabetes and obesity. A firs t study on the linkage disequilibrium problem structure led us to use a genetic algorithm to solve it. Due to the particular, but classical, evaluation function given by the biologists, we design our genetic algorithm with several populatio ns. This model lead us to implement different cooperative operators such as muta tion and crossover. Probabilities of application of those mechanisms are set ada ptively. In order to introduce some diversity, we also implement a random immigr ant strategy and to cover up the cost of the evaluation computation we paralleli ze it in a master / slave model. Different combinations of the presented mechani sms are tested on real data and compared in term of robustness and computation c ost. We show that the most complete strategy is able to find the best solutions and is the most robust

Contraintes d'optimisation pour les problèmes d'arbres couvrants sous restrictions

Bien que des méthodes de filtrage basées sur les coûts existent depuis peu pour les problèmes d'arbres couvrants sous incertitudes \cite{Aron2002,Dooms2006}, elles ne permettent pas la prise en compte de. restrictions additionnelles. Nous présentons dans cet article une contrainte d'optimisation pour les problèmes d'arbres couvrants de poids optimal sous restrictions fondée sur les travaux de \cite{Sellmann2004}. Nous améliorons tout d'abord la contrainte d'optimisation proposée par \cite{Aron2002,Dooms2006} pour les problèmes d'arbres couvrants en mettant en évidence l'analogie entre recherche de cycles, recherche de ponts et calcul de remplaçants. Puis nous décrivons les problèmes posés par l'ajout de restrictions lors de l'utilisation de ce type d'algorithme pour proposer ensuite, grâce aux travaux de Sellmann, une nouvelle contrainte d'optimisation basée sur une relaxation Lagrangienne. Nous fournissons une première expérimentation de cette contrainte sur un problème d'arbre couvrant sous restriction de degré

Coopération entre Optimisation Combinatoire et Statistiques pour la Sélection animale

National audienceL'objectif de cette étude est d'élaborer des modèles prédictifs permettant, à partir de données génomiques, de déterminer les individus les plus performants selon certains critères quantitatifs. L'approche proposée allie les forces des méthodes statistiques et des méthodes d'optimisation combinatoire