A memetic procedure for global multi-objective optimization

In this paper we consider multi-objective optimization problems over a box. Several computational approaches to solve these problems have been proposed in the literature, that broadly fall into two main classes: evolutionary methods, which are usually very good at exploring the feasible region and r...

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Bibliographic Details
Published in:Mathematical programming computation 2023-06, Vol.15 (2), p.227-267
Main Authors: Lapucci, Matteo, Mansueto, Pierluigi, Schoen, Fabio
Format: Article
Language:English
Subjects:
Full Length Paper
Mathematics
Mathematics and Statistics
Mathematics of Computing
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Sorting algorithms
Theory of Computation
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Summary:In this paper we consider multi-objective optimization problems over a box. Several computational approaches to solve these problems have been proposed in the literature, that 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, besides enjoying interesting theoretical properties, excels in all of the numerical tests we performed on several, widely employed, test functions.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-022-00231-3