Pareto Local Optima of Multiobjective NK-Landscapes with Correlated Objectives

TL;DR

This paper analyzes the structure of local optima in multiobjective NK-landscapes with correlated objectives, revealing how problem parameters influence the number of Pareto local optima and impacting metaheuristic performance.

Contribution

It extends fitness landscape analysis to multiobjective NK-landscapes using Pareto dominance, exploring how various factors affect Pareto local optima.

Findings

Number of Pareto local optima varies with problem dimension

Correlation degree influences the landscape ruggedness

Non-linearity impacts the distribution of local optima

Abstract

In this paper, we conduct a fitness landscape analysis for multiobjective combinatorial optimization, based on the local optima of multiobjective NK-landscapes with objective correlation. In single-objective 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 non-linearity, the number of objectives and the correlation degree between objective functions on the number of Pareto local optima.