Metaheuristics for multiobjective optimisation: Cooperative approaches, uncertainty handling and application in logistics

International audienceThis is a summary of the author's PhD thesis supervised by Laetitia Jourdan and El-Ghazali Talbi and defended on 8 December 2009 at the Université Lille 1. The thesis is written in French and is available from http://sites.google.com/site/arnaudliefooghe/. This work deals with the design, implementation and experimental analysis of metaheuristics for solving multiobjective optimisation problems, with a particular interest on hard and large combinatorial problems from the field of logistics. After focusing on a unified view of multiobjective metaheuristics, we propose new cooperative, adaptive and parallel approaches. The performance of these methods are experimented on a scheduling and a routing problem involving two or three objective functions. We finally discuss how to adapt such metaheuristics during the search process in order to handle uncertainty that may occur from many different sources

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

An Analysis on Selection for High-Resolution Approximations in Many-Objective Optimization

This work studies the behavior of three elitist multi- and many-objective evolutionary algorithms generating a high-resolution approximation of the Pareto optimal set. Several search-assessment indicators are defined to trace the dynamics of survival selection and measure the ability to simultaneously keep optimal solutions and discover new ones under different population sizes, set as a fraction of the size of the Pareto optimal set.Comment: apperas in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

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

CoBRA: A cooperative coevolutionary algorithm for bi-level optimization

International audienceThis article presents CoBRA, a new evolutionary algorithm, based on a coevolutionary scheme, to solve bi-level optimization problems. It handles population-based algorithms on each level, each one cooperating with the other to provide solutions for the overall problem. Moreover, in order to evaluate the relevance of CoBRA against more classical approaches, a new performance assessment methodology, based on rationality, is introduced. An experimental analysis is conducted on a bi-level distribution planning problem, where multiple manufacturing plants deliver items to depots, and where a distribution company controls several depots and distributes items from depots to re- tailers. The experimental results reveal significant enhancements, particularly over the lower level, with respect to a more classical approach based on a hierarchical scheme

CoBRA: A Coevolutionary Meta-heuristic for Bi-level Optimization

This article presents CoBRA, a new parallel coevolutionary algorithm for bi-level optimization. CoBRA is based on a coevolutionary scheme to solve bi-level optimization problems. It handles population-based meta-heuristics on each level, each one cooperating with the other to provide solutions for the overall problem. Moreover, in order to evaluate the relevance of CoBRA against more classical approaches, a new performance assessment methodology, based on rationality, is introduced. An experimental analysis is conducted on a bi-level distribution planning problem, where multiple manufacturing plants deliver items to depots, and where a distribution company controls several depots and distributes items from depots to retailers. The experimental results reveal significant enhancements with respect to a more classical approach, based on a hierarchical scheme.Cet article présente CoBRA, un nouvel algorithme paralléle et coévolutionnaire pour l'optimisation bi-niveau. CoBRA se base sur un modèle coévolutionnaire pour faire face aux problèmes d'optimisation bi-niveau. Il manipule une méta-heuristique à base de population sur chaque niveau, chacune coopérant avec l'autre de manière à garder une vue générale sur le problème complet. De plus, afin d'étudier la pertinence de CoBRA par rapport aux approches plus classique, une nouvelle méthodologie, basée sur la rationalité est introduite. Est conduite ensuite une étude expérimentale sur un problème bi-niveau de distribution-production, dans lequel des usines contrôlées par une entreprise produisent des marchandises pour des dépôts, et une autre entreprise contrôlant les dépôts se charge de livrer les marchandises à des clients. Cet article se conclut sur l'observation d'un réel gain de performance par rapport à une approche plus classique, basée sur un modèle hiérarchique

Metaheuristics and cooperative approaches for the Bi-objective Ring Star Problem

International audienceThis paper presents and investigates different approaches to solve a new bi-objective routing problem called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a graph while optimizing two kinds of cost. The first objective is the minimization of a ring cost that is related to the length of the cycle. The second one is the minimization of an assignment cost from non-visited nodes to visited ones. In spite of its obvious bi-objective formulation, this problem has always been investigated in a single-objective way. To tackle the bi-objective ring star problem, we first investigate different stand-alone search methods. Then, we propose two cooperative strategies that combine two multi-objective metaheuristics: an elitist evolutionary algorithm and a population-based local search. We apply these new hybrid approaches to well-known benchmark test instances and demonstrate their effectiveness in comparison to non-hybrid algorithms and to state-of-the-art methods

A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEO-MOEO

International audienceThis paper presents a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. A concise overview of evolutionary algorithms for multiobjective optimization is given. A substantial number of methods has been proposed so far, and an attempt of conceptually unifying existing approaches is presented here. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. This model is then incorporated into the ParadisEO-MOEO software framework. This framework has proven its validity and high flexibility by enabling the resolution of many academic, real-world and hard multiobjective optimization problems

Metaheuristics and Their Hybridization to Solve the Bi-objective Ring Star Problem: a Comparative Study

This paper presents and experiments approaches to solve a new bi-objective routing problem called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a graph while optimizing two kinds of cost. The first objective is the minimization of a ring cost that is related to the length of the cycle. The second one is the minimization of an assignment cost from non-visited nodes to visited ones. In spite of its obvious bi-objective formulation, this problem has always been investigated in a single-objective way. To tackle the bi-objective ring star problem, we first investigate different stand-alone search methods. Then, we propose two cooperative strategies that combines two multiple objective metaheuristics: an elitist evolutionary algorithm and a population-based local search. We apply this new hybrid approaches to well-known benchmark test instances and demonstrate their effectiveness in comparison to non-hybrid algorithms and to state-of-the-art methods