An Algorithm Based on Differential Evolution for Multi-Objective Problems

Abstract

Abstract: This paper presents a new multi-objective evolu-tionary algorithm based on differential evolution. The pro-posed approach adopts a secondary population in order to re-tain the nondominated solutions found during the evolution-ary process. Additionally, the approach also incorporates theconcept of † -dominance to get a good distribution of the solu-tions retained. The main goal of this work was to keep thefast convergence exhibited by Differential Evolution in globaloptimization when extending this heuristic to multi-objectiveoptimization. We adopted standard test functions and perfor-mance measures reported in the specialized literature to vali-date our proposal. Our results are compared with respect toanother multi-objective evolutionary algorithm based on differ-ential evolution (Pareto Differential Evolution) and with respectto two approaches that are representative of the state-of-the-artin the area: the NSGA-II and † -MOEA. I. Introduction Most real world problems involve the simultaneous opti-mization of two or more (often conflicting) objectives. Thesolution of such problems (called “multi-objective”) is differ-ent from that of a single-objective optimization problem. Themain difference is that multi-objective optimization problemsnormally have not one but a set of solutions which are allequally good.In the past, a wide variety of evolutionary algorithms (EA’s)have been used to solve multi-objective optimization prob-lems [5]. However, from the several types of EAs available,few researchers have attempted to extend Differential Evo-lution (DE) [25] to solve multi-objective optimization prob-lems. DE has been very successful in the solution of a va-riety of continuous (single-objective) optimization problemsin which it has shown a great robustness and a very fast con-vergence. These are precisely the characteristics of DE thatmake it attractive to extend it to solve multi-objective opti-mization problems.In this paper, we propose a new multi-objective evolution-ary algorithm based on differential evolution. Our approachuses an external archive in which the relaxed form of Paretodominance known as