Abstract. In this paper, we conduct a fitness landscape analysis for multiobjective combinatorial optimization, based on the local optima of multiobjective N K-landscapes with objective correlation. In singleobjective optimization, it has become clear that local optima have a strong impact on the performance of metaheuristics. Here, we propose an extension to the multiobjective case, based on the Pareto dominance. We study the co-influence of the problem dimension, the degree of nonlinearity, the number of objectives and the correlation degree between objective functions on the number of Pareto local optima. The aim of fitness landscape analysis is to understand the properties of a given combinatorial optimization problem in order to design efficient search algorithms. One of the main feature is related to the number of local optima, to their distribution over the search space and to the shape of their basins of attraction. For instance, in single-objective optimization, it has been shown that local optima tend to be clustered in a 'central massif' for numerous combinatorial problems, such as the family of N K-landscapes [1]. A lot of methods are designed to 'escape' from such local optima. However, very little is known in the frame of multiobjective combinatorial optimization (MoCO), where one of the most challenging question relies on the identification of the set of Pareto optimal solutions. A Pareto Local Optima (PLO) [2] is a solution that is not dominated by any of its neighbors. The description of PLO is one of the first fundamental step towards the description of the structural properties of a MoCO problem. Surprisingly, up to now, there is a lack of study on the number and on the distribution of PLO in MoCO. Like in single-objective optimization, the PLO-related properties clearly have a strong impact on the landscape of the problem, and then on the efficiency of search algorithms. In particular, local search algorithms are designed in order to take them into account. For instance, the family of Pareto Local Search (PLS) [2] iteratively improves a set of solutions with respect to a given neighborhood
Later, Verel et al. REF conducted a study on the landscape of local optima in such problems.
Pareto Local Optima of Multiobjective NK-Landscapes with Correlated Objectives
Lecture Notes in Computer Science
Lecture Notes in Computer Science
Computer Science