Set-based Multiobjective Fitness Landscapes: A Preliminary Study

TL;DR

This paper introduces a set-based framework for analyzing multiobjective fitness landscapes, providing insights into their geometry to improve search algorithms, with experimental analysis on multiobjective NK-landscapes.

Contribution

It offers a general definition of set-based multiobjective fitness landscapes and applies this analysis to enhance multiobjective search approaches.

Findings

Set-based fitness landscapes provide new insights into multiobjective problem structure.

Experimental analysis on NK-landscapes reveals landscape properties relevant for search.

Framework aids in designing more effective multiobjective optimization algorithms.

Abstract

Fitness landscape analysis aims to understand the geometry of a given optimization problem in order to design more efficient search algorithms. However, there is a very little knowledge on the landscape of multiobjective problems. In this work, following a recent proposal by Zitzler et al. (2010), we consider multiobjective optimization as a set problem. Then, we give a general definition of set-based multiobjective fitness landscapes. An experimental set-based fitness landscape analysis is conducted on the multiobjective NK-landscapes with objective correlation. The aim is to adapt and to enhance the comprehensive design of set-based multiobjective search approaches, motivated by an a priori analysis of the corresponding set problem properties.