Marie-Eléonore Marmion

On the neutrality of flowshop scheduling fitness landscapes

Solving efficiently complex problems using metaheuristics, and in particular local search algorithms, requires incorporating knowledge about the problem to solve. In this paper, the permutation flowshop problem is studied. It is well known that in such problems, several solutions may have the same fitness value. As this neutrality property is an important issue, it should be taken into account during the design of search methods. Then, in the context of the permutation flowshop, a deep landscape analysis focused on the neutrality property is driven and propositions on the way to use this neutrality in order to guide the search efficiently are given.

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.

Automatic Design of Hybrid Stochastic Local Search Algorithms

Many stochastic local search (SLS) methods rely on the manipulation of single solutions at each of the search steps. Examples are iterative improvement, iterated local search, simulated annealing, variable neighborhood search, and iterated greedy. These SLS methods are the basis of many state-of-the-art algorithms for hard combinatorial optimization problems. Often, several of these SLS methods are combined with each other to improve performance. We propose here a practical, unified structure that encompasses several such SLS methods. The proposed structure is unified because it integrates these metaheuristics into a single structure from which we can not only instantiate each of them, but we also can generate complex combinations and variants. Moreover, the structure is practical since we propose a method to instantiate actual algorithms for practical problems in a semi-automatic fashion. The method presented in this work implements a general local search structure as a grammar; an instantiation of such a grammar is a program that can be compiled into executable form. We propose to find the appropriate grammar instantiation for a particular problem by means of automatic configuration. The result is a semi-automatic system that, with little human effort, is able to generate powerful hybrid SLS algorithms.

Neutral but a Winner! How Neutrality Helps Multiobjective Local Search Algorithms

This work extends the concept of neutrality used in single-objective optimization to the multi-objective context and investigates its effects on the performance of multi-objective dominance-based local search methods. We discuss neutrality in single-objective optimization and fitness assignment in multi-objective algorithms to provide a general definition for neutrality applicable to multi-objective landscapes. We also put forward a definition of neutrality when Pareto dominance is used to compute fitness of solutions. Then, we focus on dedicated local search approaches that have shown good results in multi-objective combinatorial optimization. In such methods, particular attention is paid to the set of solutions selected for exploration, the way the neighborhood is explored, and how the candidate set to update the archive is defined. We investigate the last two of these three important steps from the perspective of neutrality in multi-objective landscapes, propose new strategies that take into account neutrality, and show that exploiting neutrality allows to improve the performance of dominance-based local search methods on bi-objective permutation flowshop scheduling problems.

A template for designing single-solution hybrid metaheuristics

Single-solution metaheuristics are among the earliest and most successful metaheuristics, with many variants appearing in the literature. Even among the most popular variants, there is a large degree of overlap in terms of actual behavior. Moreover, in the case of hybrids of different metaheuristics, traditional names do not actually reflect how the hybrids are composed. In this paper, we discuss a template for single-solution hybrid metaheuristics. Our template builds upon the Paradiseo-MO framework, but restricts itself to a pre-defined structure based on iterated local search (ILS). The flexibility is given by generalizing the components of ILS (perturbation, local search and acceptance criterion) in order to incorporate components from other metaheuristics. We give precise definitions of these components within the context of our proposed template. The template proposed is flexible enough to reproduce many classical single-solution metaheuristics and hybrids thereof, while at the same time being sufficiently concrete to generate code from a grammar description in order to support automatic design of algorithms. We give examples of three IG-VNS hybrids that can be instantiated from the proposed template.

Neutrality in the Graph Coloring Problem

In this paper, the neutrality of some hard instances of the graph coloring problem GCP is quantified. This neutrality property has to be detected as it impacts the search process. Indeed, local optima may belong to plateaus that represent a barrier for local search methods. Then, we also aim at pointing out the interest of exploiting neutrality during the search. Therefore, a generic local search dedicated to neutral problems, NILS, is performed on several hard instances.

Feature Selection Using Tabu Search with Learning Memory: Learning Tabu Search

Feature selection in classification can be modeled as a combinatorial optimization problem. One of the main particularities of this problem is the large amount of time that may be needed to evaluate the quality of a subset of features. In this paper, we propose to solve this problem with a tabu search algorithm integrating a learning mechanism. To do so, we adapt to the feature selection problem, a learning tabu search algorithm originally designed for a railway network problem in which the evaluation of a solution is time-consuming. Experiments are conducted and show the benefit of using a learning mechanism to solve hard instances of the literature.

The road to VEGAS: guiding the search over neutral networks

VEGAS (Varying Evolvability-Guided Adaptive Search) is a new methodology proposed to deal with the neutrality property that frequently appears on combinatorial optimization problems. Its main feature is to consider the whole evaluated solutions of a neutral network rather than the last accepted solution. Moreover, VEGAS is designed to escape from plateaus based on the evolvability of solutions, and on a multi-armed bandit by selecting the more promising solution from the neutral network. Experiments are conducted on NK-landscapes with neutrality. Results show the importance of considering the whole identified solutions from the neutral network and of guiding the search explicitly. The impact of the level of neutrality and of the exploration-exploitation trade-off are deeply analyzed.

Multi-objective Neutral Neighbors': What could be the definition(s)?

There is a significant body of research on neutrality and its effects in single-objective optimization. Particularly, the neutrality concept has been precisely defined and the neutrality between neighboring solutions efficiently exploited in local search algorithms. The extension of neutrality to multi-objective optimization is not straightforward and its effects on the dynamics of multi-objective optimization methods are not clearly understood. In order to develop strategies to exploit neutral neighbors in multi-objective local search algorithms, it is important and necessary to clearly define neutrality in the multi-objective context. In this paper, we propose several definitions of the neutrality property between neighboring solutions. A natural definition comes from the Pareto-dominance, widely used in multi-objective optimization. In addition, definitions derived from epsilon and hypervolume indicators are also proposed as such indicators are usually used to compare sets of solutions. We analyze permutation problems under the proposed definitions of neutrality and show that each definition of neutrality leads to a particular structure of the problem.

Fitness Landscape of the Factoradic Representation on the Permutation Flowshop Scheduling Problem

Because permutation problems are particularly challenging to model and optimise, the possibility to represent solutions by means of factoradics has recently been investigated, allowing algorithms from other domains to be used. Initial results have shown that methods using factoradics can efficiently explore the search space, but also present difficulties to exploit the best areas. In the present paper, the fitness landscape of the factoradic representation and one of its simplest operator is studied on the Permutation Flowshop Scheduling Problem (PFSP). The analysis highlights the presence of many local optima and a high ruggedness, which confirms that the factoradic representations is not suited for local search. In addition, comparison with the classic permutation representation establishes that local moves on the factoradic representation are less able to lead to the global optima on the PFSP. The study ends by presenting directions for using and improving the factoradic representation.