PPSN XIII (2014) - LNCS 8672

Using a Family of Curves to Approximate the Pareto Front of a Multi-Objective Optimization Problem

Saúl Zapotecas Martínez¹, Víctor A. Sosa Hernández², Hernán Aguirre¹, Kiyoshi Tanaka¹, and Carlos A. Coello Coello²

¹Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano, 380-8553, Japan
saul.zapotecas@gmail.com
ahernan@shinshu-u.ac.jp
ktanaka@shinshu-u.ac.jp

²Computer Science Department, CINVESTAV-IPN, Av. IPN 2508, San Pedro Zacatenco, C.P. 07360, Mexico D.F., Mexico
msosa@computacion.cs.cinvestav.mx
ccoello@cs.cinvestav.mx

Abstract. The design of selection mechanisms based on quality assessment indicators has become one of the main research topics in the development of Multi-Objective Evolutionary Algorithms (MOEAs). Currently, most indicator-based MOEAs have employed the hypervolume indicator as their selection mechanism in the search process. However, hypervolume-based MOEAs become inefficient (and eventually, unaffordable) as the number of objectives increases. In this paper, we study the construction of a reference set from a family of curves. Such reference set is used together with a performance indicator (namely _p) to assess the quality of solutions in the evolutionary process of an MOEA. We show that our proposed approach is able to deal (in an efficient way) with problems having many objectives (up to ten objective functions). Our preliminary results indicate that our proposed approach is highly competitive with respect to two state-of-the-art MOEAs over the set of test problems that were adopted in our comparative study.

LNCS 8672, p. 682 ff.

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