Multiobjective optimization involving quadratic functions

Oscar Brito (1) , Fouad Bennis (1) , Stéphane Caro (1)

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

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.

Mots clés: Continuous Pareto set; Quadratic functions; Multiobjective optimization

Domaines: Sciences de l'ingénieur [physics]; Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]; Electronique

Oscar Brito, Fouad Bennis, Stéphane Caro. Multiobjective optimization involving quadratic functions. SIAM Journal on Optimization, 2014, 2014, pp.1-11. ⟨10.1155/2014/406092⟩. ⟨hal-01081821⟩