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Multifractality and Dimensional Determinism in Local Optima Networks

Abstract : We conduct a study of local optima networks (LONs) in a search space using fractal dimensions. The fractal dimension (FD) of these networks is a complexity index which assigns a non-integer dimension to an object. We propose a fine-grained approach to obtaining the FD of LONs, using the probabilistic search transitions encoded in LON edge weights. We then apply multi-fractal calculations to LONs for the first time, comparing with mono-fractal analysis. For complex systems such as LONs, the dimensionality may be different between two sub-systems and multi-fractal analysis is needed. Here we focus on the Quadratic Assignment Problem (QAP), conducting fractal analyses on sampled LONs of reasonable size for the first time. We also include fully enumerated LONs of smaller size. Our results show that local optima spaces can be multi-fractal and that valuable information regarding probabilistic self-similarity is encoded in the edge weights of local optima networks. Links are drawn between these phenomena and the performance of two competitive metaheuristic algorithms.
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Contributor : Sébastien Verel Connect in order to contact the contributor
Submitted on : Monday, September 13, 2021 - 9:47:25 AM
Last modification on : Wednesday, May 25, 2022 - 1:30:03 PM


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Sarah Thomson, Sébastien Verel, Gabriela Ochoa, Nadarajen Veerapen, David Cairns. Multifractality and Dimensional Determinism in Local Optima Networks. Genetic and Evolutionary Computation Conference, Jul 2018, Kyoto, Japan. ⟨10.1145/3205455.3205472⟩. ⟨hal-01823551⟩



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