Differential Evolution Versus Genetic Algorithms in Multiobjective

This paper presents a comprehensive comparison between the performance of state-of-the-art genetic algorithms NSGA-II, SPEA2 and IBEA and their differential evolution based variants DEMO NS-II , DEMO SP2 and DEMO IB . Experimental results on 16 numerical multi-objective test problems show that on the majority of problems, the algo-rithms based on differential evolution perform significantly better than the corresponding genetic algorithms with regard to applied quality in- dicators. This suggests that in numerical multiobjective optimization, differential evolution explores the decision space more efficiently than genetic algorithms. 1 Introduction Differential Evolution

(DE) [1] is a simple yet powerful algorithm that outper- forms Genetic Algorithms (GAs) on many numerical singleobjective optimiza- tion problems [2]. In this paper we show that DE can achieve better results than GAs also on numerical multiobjective optimization problems (MOPs). To this end, we compare three state-of-the-art Multiobjective Evolutionary Algorithms (MOEAs), namely NSGA-II [3], SPEA2 [4] and IBEA [5], to their counterparts – algorithms that use the same environmental selection, but DE instead of GAs for exploring the decision space. While DE-based algorithms for multiobjective optimization have already been proposed in the past (see Related Work in Sec- tion 3), comparisons between these approaches and GA-based algorithms lack: (a) a wide choice of difficult test problems with more than two objectives, (b) performance assessment with Pareto compliant indicators, and (c) inferences about algorithm performance based on statistical tests. The comparison in this paper includes all these usually omitted features. The paper is further organized as follows. Section 2 introduces the basic GA as the underlying algorithm for NSGA-II, SPEA2 and IBEA, while the proposed algorithm DEMO is explained in detail in Section 3. Section 4 outlines the ex- periments, whose results are presented and discussed in Section 5. Section 6 concludes the paper with a summary of the results. 2 Multiobjective Optimization with the Basic GA Most of the efforts spent on adapting GAs to multiobjective optimization have been focusing on finding new approaches for environmental selection. These S. Obayashi et al. (Eds.): EMO 2007, LNCS 4403, pp. 257–271, 2007. c© Springer-Verlag Berlin Heidelberg 2007 258 T. Tuˇsar and B. Filipiˇc approaches try to produce good approximations of the Pareto optimal front by incorporating different preferences. For example, the environmental selection in NSGA-II [3] first ranks the individuals using nondominated sorting. To distin- guish between individuals with the same rank, the crowding distance metric is used, which prefers individuals from less crowded regions of the objective space. SPEA2 [4] works similarly, calculating the raw fitness of the individuals accord- ing to Pareto dominance relations between them and using a density measure to break the ties. The individuals that reside close together in the objective space are discouraged from entering the archive of best solutions. IBEA [5], on the other hand, uses a different approach. The fitness of individuals is determined only according to the value of a predefined indicator. This indicator has to be dominance preserving and no...

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