Multiobjective optimization involving quadratic functions
type: Item
instance of: scholarly article
title: Multiobjective optimization involving quadratic functions
zbMATH Open document ID: 1460.90162
DOI: 10.1155/2014/406092
author: Oscar Brito Augusto
author: Fouad Bennis
author: Stéphane Caro
published in: Journal of Optimization
publication date: 2019-02-18T00:00:00Z
review text: Summary: Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in \(n\)-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C59
zbMATH DE Number: 7024755
Wikidata QID: Q59060759
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/406092
OpenAlex ID: W1990240408
cites work: Multicriteria optimization in engineering and in the sciences
cites work: Q4692508
cites work: Multi-objective optimization using evolutionary algorithms
cites work: Survey of multi-objective optimization methods for engineering
description: scientific article; zbMATH DE number 7024755