A Memetic Procedure for Global Multi-Objective Optimization

TL;DR

This paper introduces NSMA, a memetic algorithm that combines evolutionary and descent methods to improve global multi-objective optimization over a box, demonstrating superior performance in numerical tests.

Contribution

A novel memetic algorithm that integrates evolutionary and descent strategies for enhanced multi-objective optimization.

Findings

NSMA outperforms existing methods on standard test functions.

The hybrid approach balances exploration and exploitation effectively.

Theoretical properties support the algorithm's robustness.

Abstract

In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary methods, which are usually very good at exploring the feasible region and retrieving good solutions even in the nonconvex case, and descent methods, which excel in efficiently approximating good quality solutions. In this paper, first we confirm, through numerical experiments, the advantages and disadvantages of these approaches. Then we propose a new method which combines the good features of both. The resulting algorithm, which we call Non-dominated Sorting Memetic Algorithm (NSMA), besides enjoying interesting theoretical properties, excels in all of the numerical tests we performed on several, widely employed, test functions.