How Perturbation Strength Shapes the Global Structure of TSP Fitness Landscapes

  • Paul McMenemyEmail author
  • Nadarajen Veerapen
  • Gabriela Ochoa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10782)


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.


Local optima network Travelling salesman problem Chained-LK Perturbation strength Combinatorial fitness landscape 



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 (, EPSRC grant EP/K000586/1).

Data Access. All data generated for this research are openly available from the Stirling Online Repository for Research Data (


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computing Science and MathematicsUniversity of StirlingStirlingUK

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