Matthieu Basseur

Hybridizing exact methods and metaheuristics: A taxonomy

The interest about hybrid optimization methods has grown for the last few years. Indeed, more and more papers about cooperation between heuristics and exact techniques are published. In this paper, we propose to extend an existing taxonomy for hybrid methods involving heuristic approaches in order to consider cooperative schemes between exact methods and metaheuristics. First, we propose some natural approaches for the different schemes of cooperation encountered, and we analyse, for each model, some examples taken from the literature. Then we recall and complement the proposed grammar and provide an annotated bibliography.

ParadisEO-MOEO: a framework for evolutionary multi-objective optimization

This paper presents ParadisEO-MOEO, a white-box object-oriented generic framework dedicated to the flexible design of evolutionary multi-objective algorithms. This paradigm-free software embeds some features and techniques for Pareto-based resolution and aims to provide a set of classes allowing to ease and speed up the development of computationally efficient programs. It is based on a clear conceptual distinction between the solution methods and the multi-objective problems they are intended to solve. This separation confers a maximum design and code reuse. ParadisEO-MOEO provides a broad range of archive-related features (such as elitism or performance metrics) and the most common Pareto-based fitness assignment strategies (MOGA, NSGA, SPEA, IBEA and more). Furthermore, parallel and distributed models as well as hybridization mechanisms can be applied to an algorithm designed within ParadisEO-MOEO using the whole version of ParadisEO. In addition, GUIMOO, a platform-independant free software dedicated to results analysis for multi-objective problems, is briefly introduced.

Design of multi-objective evolutionary algorithms: application to the flow-shop scheduling problem

Multi-objective optimization using evolutionary algorithms has been extensively studied in the literature. We propose formal methods to solve problems appearing frequently in the design of such algorithms. To evaluate the effectiveness of the introduced mechanisms, we apply them to the flow-shop scheduling problem. We propose a dynamic mutation Pareto genetic algorithm (GA) in which different genetic operators are used simultaneously in an adaptive manner, taking into account the history of the search. We present a diversification mechanism which combines sharing in the objective space as well as in the decision space, in which the size of the niche is automatically calculated. We also propose a hybrid approach which combines the Pareto GA with local search. Finally, we propose two performance indicators to evaluate the effectiveness of the introduced mechanisms.

Multi‐objective optimization using metaheuristics: non‐standard algorithms

In recent years, the application of metaheuristic techniques to solve multi-objective optimization problems has become an active research area. Solving this kind of problems involves obtaining a set of Pareto-optimal solutions in such a way that the corresponding Pareto front fulfils the requirements of convergence to the true Pareto front and uniform diversity. Most of the studies on metaheuristics for multi-objective optimization are focused on Evolutionary Algorithms, and some of the state-of-the-art techniques belong this class of algorithms. Our goal in this paper is to study open research lines related to metaheuristics but focusing on less explored areas to provide new perspectives to those researchers interested in multi-objective optimization. In particular, we focus on non-evolutionary metaheuristics, hybrid multi-objective metaheuristics, parallel multi-objective optimization and multi-objective optimization under uncertainty. We analyze these issues and discuss open research lines.

Combinatorial optimization of stochastic multi-objective problems: an application to the flow-shop scheduling problem

The importance of multi-objective optimization is globably established nowadays. Furthermore, a great part of real-world problems are subject to uncertainties due to, e.g., noisy or approximated fitness function(s), varying parameters or dynamic environments. Moreover, although evolutionary algorithms are commonly used to solve multi-objective problems on the one hand and to solve stochastic problems on the other hand, very few approaches combine simultaneously these two aspects. Thus, flow-shop scheduling problems are generally studied in a single-objective deterministic way whereas they are, by nature, multi-objective and are subjected to a wide range of uncertainties. However, these two features have never been investigated at the same time. In this paper, we present and adopt a proactive stochastic approach where processing times are represented by random variables. Then, we propose several multi-objective methods that are able to handle any type of probability distribution. Finally, we experiment these methods on a stochastic bi-objective flow-shop problem.

Path relinking in pareto multi-objective genetic algorithms

Path relinking algorithms have proved their efficiency in single objective optimization. Here we propose to adapt this concept to Pareto optimization. We combine this original approach to a genetic algorithm. By applying this hybrid approach to a bi-objective permutation flow-shop problem, we show the interest of this approach. In this paper, we present first an Adaptive Genetic Algorithm dedicated to obtain a first well diversified approximation of the Pareto set. Then, we present an original hybridization with Path Relinking algorithm, in order to intensify the search between solutions obtained by the first approach. Results obtained are promising and show that cooperation between these optimization methods could be efficient for Pareto optimization.

A preliminary study on handling uncertainty in indicator-based multiobjective optimization

Real-world optimization problems are often subject to uncertainties, which can arise regarding stochastic model parameters, objective functions and decision variables. These uncertainties can take different forms in terms of distribution, bound and central tendency. In the multiobjective context, several studies have been proposed to take uncertainty into account, and most of them propose an extension of Pareto dominance to the stochastic case. In this paper, we pursue a slightly different approach where the optimization goal is defined in terms of a quality indicator, i.e., an objective function on the set of Pareto set approximations. We consider the scenario that each solution is inherently associated with a probability distribution over the objective space, without assuming a ’true’ objective vector per solution. We propose different algorithms which optimize the quality indicator, and preliminary simulation results indicate advantages over existing methods such as averaging, especially with many objective functions.

Indicator-based multi-objective local search

This paper presents a simple and generic indicator-based multi-objective local search. This algorithm is a direct extension of the IBEA algorithm, an indicator- based evolutionary algorithm proposed in 2004 by Zitzler and Kuenzli, where the optimization goal is defined in terms of a binary indicator defining the selection operator. The methodology proposed in this paper has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on different binary indicators: Those used in IBEA experiments, and also the indicators derived from classical Pareto ranking methods taken from well-known multi-objective evolutionary algorithms of the literature. Experiments show that the best results are obtained using selection indicators which are not only based on Pareto dominance relation. Moreover, the generic local search algorithm presented in this paper and the proposed indicators obtain promising results which lead to a number of future research directions.

Hypervolume-based multi-objective local search

This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Künzli in 2004, where the optimization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contribution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experimental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators.

The efficiency of indicator-based local search for multi-objective combinatorial optimisation problems

In the last few years, a significant number of multi-objective metaheuristics have been proposed in the literature in order to address real-world problems. Local search methods play a major role in many of these metaheuristic procedures. In this paper, we adapt a recent and popular indicator-based selection method proposed by Zitzler and Künzli in 2004, in order to define a population-based multi-objective local search. The proposed algorithm is designed in order to be easily adaptable, parameter independent and to have a high convergence rate. In order to evaluate the capacity of our algorithm to reach these goals, a large part of the paper is dedicated to experiments. Three combinatorial optimisation problems are tested: a flow shop problem, a ring star problem and a nurse scheduling problem. The experiments show that our algorithm can be applied with success to different types of multi-objective optimisation problems and that it outperforms some classical metaheuristics. Furthermore, the parameter sensitivity analysis enables us to provide some useful guidelines about how to set the parameters.