Please use this identifier to cite or link to this item:
Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Multifractality and Dimensional Determinism in Local Optima Networks
Author(s): Thomson, Sarah
Verel, Sébastien
Ochoa, Gabriela
Veerapen, Nadarajen
Cairns, David
Contact Email:
Keywords: Fitness Landscapes
Quadratic Assignment Problem
Local Optima Networks
Fractal Dimension
Issue Date: 31-Dec-2018
Citation: Thomson S, Verel S, Ochoa G, Veerapen N & Cairns D (2018) Multifractality and Dimensional Determinism in Local Optima Networks. In: Proceedings of the Genetic and Evolutionary Computation Conference 2018. 2018 Genetic and Evolutionary Computation Conference (GECCO 2018), Kyoto, Japan, 15.07.2018-19.07.2018. New York: ACM, pp. 371-378.
Abstract: We conduct a study of networks of local optimas 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 stochastic 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.
DOI Link: 10.1145/3205455.3205472
Rights: This item has been embargoed for a period. During the embargo please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study. Publisher policy allows this work to be made available in this repository. Published in Proceedings of the Genetic and Evolutionary Computation Conference 2018 by ACM. The original publication is available at:

Files in This Item:
File Description SizeFormat 
SarahLThomson.pdfFulltext - Published Version1.19 MBAdobe PDFView/Open

This item is protected by original copyright

Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

If you believe that any material held in STORRE infringes copyright, please contact providing details and we will remove the Work from public display in STORRE and investigate your claim.