Communities of minima in local optima networks of combinatorial spaces

Fabio Daolio, Marco Tomassini, Sébastien Vérel and Gabriela Ochoa

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 9, 1684-1694

Abstract: In this work, we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two different classes of instances of a hard combinatorial optimization problem: the quadratic assignment problem (QAP). We provide evidence indicating that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the networks possess a clear modular structure, while the optima networks belonging to the class of random uniform instances are less well partitionable into clusters. This is convincingly supported by using several statistical tests. Finally, we briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.

Keywords: Community structure; Optima networks; Combinatorial fitness landscapes (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:9:p:1684-1694

DOI: 10.1016/j.physa.2011.01.005

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