On the performance of multi-objective estimation of distribution algorithms for combinatorial problems

TL;DR

This paper analyzes the performance of multi-objective estimation of distribution algorithms, specifically mBOA, on combinatorial problems, using fitness landscape analysis and comparing it with NSGA-III, to understand their efficiency and behavior.

Contribution

It introduces a fitness landscape analysis for mBOA on MNK-landscape problems and compares its performance with NSGA-III, providing insights into their convergence and diversity.

Findings

mBOA's performance is moderately influenced by problem features.

The proposed regression model can predict algorithm runtime.

Probabilistic model analysis helps understand convergence and diversity.

Abstract

Fitness landscape analysis investigates features with a high influence on the performance of optimization algorithms, aiming to take advantage of the addressed problem characteristics. In this work, a fitness landscape analysis using problem features is performed for a Multi-objective Bayesian Optimization Algorithm (mBOA) on instances of MNK-landscape problem for 2, 3, 5 and 8 objectives. We also compare the results of mBOA with those provided by NSGA-III through the analysis of their estimated runtime necessary to identify an approximation of the Pareto front. Moreover, in order to scrutinize the probabilistic graphic model obtained by mBOA, the Pareto front is examined according to a probabilistic view. The fitness landscape study shows that mBOA is moderately or loosely influenced by some problem features, according to a simple and a multiple linear regression model, which is being proposed to predict the algorithms performance in terms of the estimated runtime. Besides, we conclude that the analysis of the probabilistic graphic model produced at the end of evolution can be useful to understand the convergence and diversity performances of the proposed approach.