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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Mapping the global structure of TSP fitness landscapes
Author(s): Ochoa, Gabriela
Veerapen, Nadarajen
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Keywords: Fitness landscapes
Local optima network
Global structure
Travelling salesman problem
Lin-Kernighan heuristic
Iterated local search
Issue Date: 30-Jun-2018
Date Deposited: 30-May-2017
Citation: Ochoa G & Veerapen N (2018) Mapping the global structure of TSP fitness landscapes. Journal of Heuristics, 24 (3), pp. 265-294.
Abstract: The global structure of combinatorial landscapes is not fully understood, yet it is known to impact the performance of heuristic search methods. We use a so-called local optima network model to characterise and visualise the global structure of travelling salesperson fitness landscapes of different classes, including random and structured real-world instances of realistic size. Our study brings rigour to the characterisation of so-called funnels, and proposes an intensive and effective sampling procedure for extracting the networks. We propose enhanced visualisation techniques, including 3D plots and the incorporation of colour, sizes and widths, to reflect relevant aspects of the search process. This brings an almost tangible new perspective to the landscape and funnel metaphors. Our results reveal a much richer global structure than the suggestion of a 'big-valley' structure. Most landscapes of the tested instances have multiple valleys or funnels; and the number, disposition and interaction of these funnels seem to relate to search difficulty on the studied landscapes. We also find that the structured TSP instances feature high levels of neutrality, an observation not previously reported in the literature. We then propose ways of analysing and visualising these neutral landscapes.
DOI Link: 10.1007/s10732-017-9334-0
Rights: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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