Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes

TL;DR

This paper investigates how the correlation between objectives affects the structure of the search space in multiobjective combinatorial optimization, emphasizing its importance for designing effective metaheuristics.

Contribution

It introduces a general method to generate multiobjective problems with controllable objective correlation, extending NK-landscapes, and analyzes the impact on search space properties.

Findings

Objective correlation significantly influences the structure of the efficient set.

Considering objective correlation can improve the design of metaheuristics.

The proposed method allows systematic study of correlation effects in benchmark problems.

Abstract

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.