DE/RM-MEDA: A New Hybrid Multi-Objective Generator

TL;DR

This paper introduces DE/RM-MEDA, a hybrid multi-objective optimization algorithm combining differential evolution and estimation of distribution, which adaptively adjusts solutions and outperforms existing methods in convergence and diversity.

Contribution

The paper presents a novel hybrid algorithm, DE/RM-MEDA, that adaptively adjusts solutions based on covariance eigenvalues, improving multi-objective optimization performance.

Findings

DE/RM-MEDA outperforms NSGA-II-DE and RM-MEDA in convergence.

The algorithm achieves better diversity in solutions.

Experimental results on nine benchmark problems demonstrate its effectiveness.

Abstract

Under the condition of Karush-Kuhn-Tucker, the Pareto Set (PS) in the decision area of an m-objective optimization problem is a piecewise continuous (m-1)-D manifold. For illustrate the degree of convergence of the population, we employed the ratio of the sum of the first (m-1) largest eigenvalue of the population's covariance matrix of the sum of all eigenvalue. Based on this property, this paper proposes a new algorithm, called DE/RM-MEDA, which mix differential evolutionary (DE) and the estimation of distribution algorithm (EDA) to generate and adaptively adjusts the number of new solutions by the ratio. The proposed algorithm is experimented on nine tec09 problems. The comparison results between DE/RM-MEDA and the others algorithms, called NSGA-II-DE and RM-MEDA, show that the proposed algorithm perform better in terms of convergence and diversity metric.