Novel Metric based on Walsh Coefficients for measuring problem difficulty in Estimation of Distribution Algorithms

TL;DR

This paper introduces a new metric based on Walsh coefficients to assess problem difficulty in Estimation of Distribution Algorithms, aiming to better predict algorithm performance on various benchmark problems.

Contribution

It proposes a novel difficulty metric using Walsh coefficients, addressing limitations of existing measures and improving prediction of EDA success.

Findings

The metric accurately predicts EDA performance across benchmark problems.

It outperforms existing metrics like Fitness Distance Correlation in measuring problem difficulty.

The approach highlights the role of variable dependencies in problem difficulty assessment.

Abstract

Estimation of distribution algorithms are evolutionary algorithms that use extracted information from the population instead of traditional genetic operators to generate new solutions. This information is represented as a probabilistic model and the effectiveness of these algorithms is dependent on the quality of these models. However, some studies have shown that even multivariate EDAs fail to build a proper model in some problems. Usually, in these problems, there is intrinsic pairwise independence between variables. In the literature, there are few studies that investigate the difficulty and the nature of problems that can not be solved by EDAs easily. This paper proposes a new metric for measuring problem difficulty by examining the properties of model-building mechanisms in EDAs. For this purpose, we use the estimated Walsh coefficients of dependent and independent variables. The proposed metric is used to evaluate the difficulty of some well-known benchmark problems in EDAs. Different metrics like Fitness Distance Correlation (FDC) are used to compare how well the proposed metric measures problem difficulty for EDAs. Results indicate that the proposed metric can accurately predict the EDA's performance in different problems.