Communities of minima in local optima networks of combinatorial spaces |
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Authors: | Fabio Daolio,Marco TomassiniSé bastien Vé rel,Gabriela Ochoa |
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Affiliation: | a Faculty of Business and Economics, Department of Information Systems, University of Lausanne, Switzerlandb INRIA Lille - Nord Europe and University of Nice Sophia-Antipolis / CNRS, Nice, Francec Automated Scheduling, Optimisation and Planning (ASAP) Group, School of Computer Science, University of Nottingham, Nottingham, UK |
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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. |
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Keywords: | Community structure Optima networks Combinatorial fitness landscapes |
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