MultiGLODS: global and local multiobjective optimization using direct search

A. L. Custódio, J. F. A. Madeira

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The optimization of multimodal functions is a challenging task, in particular when derivatives are not available for use. Recently, in a directional direct search framework, a clever multistart strategy was proposed for global derivative-free optimization of single objective functions. The goal of the current work is to generalize this approach to the computation of global Pareto fronts for multiobjective multimodal derivative-free optimization problems. The proposed algorithm alternates between initializing new searches, using a multistart strategy, and exploring promising subregions, resorting to directional direct search. Components of the objective function are not aggregated and new points are accepted using the concept of Pareto dominance. The initialized searches are not all conducted until the end, merging when they start to be close to each other. The convergence of the method is analyzed under the common assumptions of directional direct search. Numerical experiments show its ability to generate approximations to the different Pareto fronts of a given problem.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Global Optimization
Volume72
Issue number2
DOIs
Publication statusPublished - 1 Oct 2018

Fingerprint

Direct Search
Local Optimization
Multiobjective optimization
Multi-objective Optimization
Derivative-free Optimization
Multistart
Pareto Front
Derivatives
Particular derivative
Objective function
Multimodal Optimization
Multimodal Function
Pareto
Merging
Alternate
Global Optimization
Numerical Experiment
Optimization Problem
Generalise
Optimization

Keywords

  • Direct search methods
  • Global optimization
  • Multiobjective optimization
  • Multistart strategies
  • Nonsmooth calculus

Cite this

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abstract = "The optimization of multimodal functions is a challenging task, in particular when derivatives are not available for use. Recently, in a directional direct search framework, a clever multistart strategy was proposed for global derivative-free optimization of single objective functions. The goal of the current work is to generalize this approach to the computation of global Pareto fronts for multiobjective multimodal derivative-free optimization problems. The proposed algorithm alternates between initializing new searches, using a multistart strategy, and exploring promising subregions, resorting to directional direct search. Components of the objective function are not aggregated and new points are accepted using the concept of Pareto dominance. The initialized searches are not all conducted until the end, merging when they start to be close to each other. The convergence of the method is analyzed under the common assumptions of directional direct search. Numerical experiments show its ability to generate approximations to the different Pareto fronts of a given problem.",
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MultiGLODS: global and local multiobjective optimization using direct search. / Custódio, A. L.; Madeira, J. F. A.

In: Journal of Global Optimization, Vol. 72, No. 2, 01.10.2018, p. 1-23.

Research output: Contribution to journalArticle

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