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Journal of Optimization
Volume 2014, Article ID 406092, 11 pages
http://dx.doi.org/10.1155/2014/406092
Research Article

Multiobjective Optimization Involving Quadratic Functions

1Escola Politécnica da Universidade de São Paulo, Av. Prof. Mello Moraes 2231, 05508-030 São Paulo, SP, Brazil
2École Centrale de Nantes, Institut de Recherche en Communications et Cybernétique de Nantes, 1 rue de la Noë, 44300 Nantes, France
3Institut de Recherche en Communications et Cybernétique de Nantes, 1 rue de la Noë, 44321 Nantes, France

Received 4 May 2014; Accepted 26 July 2014; Published 15 September 2014

Academic Editor: Manuel Lozano

Copyright © 2014 Oscar Brito Augusto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.