MULTIOBJECTIVE OPTIMIZATION INVOLVING QUADRATIC FUNCTIONSReport as inadecuate




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1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

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 bi-objective optimization defined in the bi-dimensional 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 non-iterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.

Keywords : Multiobjective optimization Quadratic functions Continuous Pareto set





Author: Oscar Brito - Fouad Bennis - Stephane Caro -

Source: https://hal.archives-ouvertes.fr/



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