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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: The Fractal Geometry of Fitness Landscapes at the Local Optima Level
Author(s): Thomson, Sarah L
Ochoa, Gabriela
Verel, Sébastien
Keywords: Fitness landscapes
Fractal analysis
Local optima networks
Issue Date: 19-Dec-2020
Date Deposited: 12-Jan-2021
Citation: Thomson SL, Ochoa G & Verel S (2020) The Fractal Geometry of Fitness Landscapes at the Local Optima Level. Natural Computing.
Abstract: A local optima network (LON) encodes local optima connectivity in the fitness landscape of a combinatorial optimisation problem. Recently, LONs have been studied for their fractal dimension. Fractal dimension is a complexity index where a non-integer dimension can be assigned to a pattern. This paper investigates the fractal nature of LONs and how that nature relates to metaheuristic performance on the underlying problem. We use visual analysis, correlation analysis, and machine learning techniques to demonstrate that relationships exist and that fractal features of LONs can contribute to explaining and predicting algorithm performance. The results show that the extent of multifractality and high fractal dimensions in the LON can contribute in this way when placed in regression models with other predictors. Features are also individually correlated with search performance, and visual analysis of LONs shows insight into this relationship.
DOI Link: 10.1007/s11047-020-09834-y
Rights: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Notes: Output Status: Forthcoming/Available Online
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