Section: New Results

On the Structure of Multiobjective Combinatorial Search Space: Multiobjective NK-Landscapes with Correlated Objectives

Participants : S. Verel, A. Liefooghe, L. Jourdan, C. Dhaenens.

The structure of the search space explains the behavior of multiobjective search algorithms, and helps to design well-performing approaches. In this work, we analyze the properties of multiobjective combinatorial search spaces, and we pay a particular attention to the correlation between the objective functions. To do so, we extend the multiobjective NK-landscapes in order to take the objective correlation into account. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives, and the objective correlation on the structure of the Pareto optimal set, in terms of cardinality and number of supported solutions [45] , as well as on the number of Pareto local optima [46] . This work concludes with guidelines for the design of multiobjective local search algorithms, based on the main fitness landscape features. All our results show that no expectation on the performance of multiobjective local search algorithms can be drawn without taking the problem properties into account very precisely. Indeed, it has now become clear that the number of objectives is one of the key issue to explain a problem complexity, but we also pointed out that the objective correlation is at least as important. Multiobjective fitness landscape analysis plays a central role to explain the performance of local search algorithms, and to design more efficient methods, that suit better the problem features.