On a stochastic differential equation approach for multiobjective optimization up to pareto-criticality

Ricardo H.C. Takahashi, Eduardo G. Carrano, Elizabeth F. Wanner

Research output: Chapter in Book/Report/Conference proceedingConference publication

Abstract

Traditional Evolutionary Multiobjective Optimization techniques, based on derivative-free dominance-based search, allowed the construction of efficient algorithms that work on rather arbitrary functions, leading to Pareto-set sample estimates obtained in a single algorithm run, covering large portions of the Pareto-set. However, these solutions hardly reach the exact Pareto-set, which means that Pareto-optimality conditions do not hold on them. Also, in problems with high-dimensional objective spaces, the dominance-based search techniques lose their efficiency, up to situations in which no useful solution is found. In this paper, it is shown that both effects have a common geometric structure. A gradient-based descent technique, which relies on the solution of a certain stochastic differential equation, is combined with a multiobjective line-search descent technique, leading to an algorithm that indicates a systematic solution for such problems. This algorithm is intended to serve as a proof of concept, allowing the comparison of the properties of the gradient-search principle with the dominance-search principle. It is shown that the gradient-based principle can be used to find solutions which are truly Pareto-critical, satisfying first-order conditions for Pareto-optimality, even for many-objective problems.

Original languageEnglish
Title of host publicationEvolutionary Multi-Criterion Optimization - 6th International Conference, EMO 2011, Proceedings
PublisherSpringer
Pages61-75
Number of pages15
ISBN (Print)9783642198922
DOIs
Publication statusPublished - 14 Apr 2011
Event6th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2011 - Ouro Preto, Brazil
Duration: 5 Apr 20118 Apr 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6576 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2011
CountryBrazil
CityOuro Preto
Period5/04/118/04/11

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    Takahashi, R. H. C., Carrano, E. G., & Wanner, E. F. (2011). On a stochastic differential equation approach for multiobjective optimization up to pareto-criticality. In Evolutionary Multi-Criterion Optimization - 6th International Conference, EMO 2011, Proceedings (pp. 61-75). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6576 LNCS). Springer. https://doi.org/10.1007/978-3-642-19893-9_5