Abstract
Local optima networks are a valuable tool used to analyse and visualise the global structure of combinatorial search spaces; in particular, the existence and distribution of multiple funnels in the landscape. We extract and analyse the networks induced by Chained-LK, a powerful iterated local search for the TSP, on a large set of randomly generated (Uniform and Clustered) instances. Results indicate that increasing the perturbation strength employed by Chained-LK modifies the landscape’s global structure, with the effect being markedly different for the two classes of instances. Our quantitative analysis shows that several funnel metrics have stronger correlations with Chained-LK success rate than the number of local optima, indicating that global structure clearly impacts search performance.
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Acknowledgements
This work was supported by the Leverhulme Trust [award number RPG-2015-395] and by the UK’s Engineering and Physical Sciences Research Council [grant number EP/J017515/1]. Results were obtained using the EPSRC-funded ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk, EPSRC grant EP/K000586/1).
Data Access. All data generated for this research are openly available from the Stirling Online Repository for Research Data (http://hdl.handle.net/11667/104).
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McMenemy, P., Veerapen, N., Ochoa, G. (2018). How Perturbation Strength Shapes the Global Structure of TSP Fitness Landscapes. In: Liefooghe, A., López-Ibáñez, M. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2018. Lecture Notes in Computer Science(), vol 10782. Springer, Cham. https://doi.org/10.1007/978-3-319-77449-7_3
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