Limitation of Small-world Topology for Application in Non-dominated Sorting Differential Evolution

Abstract:  In the context of complex network theory, the small-world network is famous for the small-world phenomenon, namely six degrees of separation. Different from its wide application in the social, physical and technological network analysis, it can be combined with the mathematical optimization algorithm recently. In this paper, the limitation of small-world network topology for application in multi-objective optimization algorithm is proposed. The optimization algorithm based on small-world network topology may be suitable for solving a few single-objective optimization problems, but has limitation and unobvious effectiveness to deal with many multi-objective optimization problems. This paper takes non-dominated sorting differential evolution algorithm (NSDE) based on small-world topology to solve eight multi-objective optimization problems (MOPs) for example. Compared with early NSDE algorithm, the limitation of the efficiency of small-world topology in NSDE is validated with the Matlab simulation results of eight MOEA test functions of early 2007. The results prove that small-world topology has limitation and unobvious effectiveness to improve a multi-objective optimization algorithm, not as good as to improve a single-objective optimization algorithm.
Keywords: complex network, MOP, network theory, NSDE, small-world network
Author: Jun-fang Li, Bu-han Zhang
Journal Code: jptkomputergg120064

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