An analysis of the effects of population structure on scalable multiobjective optimization problems

Abstract

Multiobjective evolutionary algorithms (MOEA) are an effective tool for solving search and optimization problems containing several incommensurable and possibly conflicting objectives. Unfortunately, many MOEAs face difficulties in solving problems when the number of objectives increases. In this paper, we investigate the efficacy of spatially structured MOEAs for scalable multiobjective problems. The algorithm is an extension of the standard cellular evolutionary algorithm, where the population is mapped to nodes of alternative complex networks. A selection regime based on a non-dominance rating and a crowding mechanism guides the evolutionary trajectory and an -dominance external archive is used to maintain a spread of solutions across the Paretooptimal front. An important outcome of this work is the classification of the network models based on their impact on convergence speed and solution quality as the number of objectives increases for a given problem.

Scale-free fully informed particle swarm optimization algorithm

“…Eqs. (20) and (21) are needed to be modified to facilitate the implementation of discrete version. 3.…”

“…Examples of such systems include the metabolic interactions [15], the neural networks [11], the scientific citation network [33], the financial market [12,37], the World Wide Web [5] and Internet [41], and the software engineering [44]. Recently, there has been a surge of interest in introducing scale-free networks into evolutionary optimization [13,14,20,21]. In particular, Kirley and Stewart [21] found that on specific multiobjective optimization problems, populations evolving on scale-free structures outperform populations evolving on random, small-world, and regular lattice population structures as the number of objectives increased.…”

Distributed evolutionary algorithms and their models: A survey of the state-of-the-art

“…In [50,48], Giacobini et al use takeover time analysis to investigate the selection intensity of cEAs based on small-world topology and scale-free topology, respectively. In [68], the performance of cEAs using four topologies, including the 2D regular lattice, small-world network, random graph, and scale-free network, is investigated. Their experimental results show that, with the increase of the problem complexity, the ideal topology should change from one with a high mean degree distribution (the regular topologies) to a network with a high clustering coefficient (the complex networks).…”

Weighted local sharing and local clearing for multimodal optimisation

“…The offspring produced from these parents then enter the population at the location upon which the deme was centred. Common topologies for the network used in an SSEA include rings and torii (e.g., Collins and Jefferson 1991), and scale-free networks (e.g., Kirley and Stewart 2007); in this work we focus local sharing models that incorporate a two-dimensional, toroidal topology.…”