An Analysis of Problem Difficulty for a Class of Optimisation Heuristics

  • Enda Ridge
  • Daniel Kudenko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4446)


This paper investigates the effect of the cost matrix standard deviation of Travelling Salesman Problem (TSP) instances on the performance of a class of combinatorial optimisation heuristics. Ant Colony Optimisation (ACO) is the class of heuristic investigated. Results demonstrate that for a given instance size, an increase in the standard deviation of the cost matrix of instances results in an increase in the difficulty of the instances. This implies that for ACO, it is insufficient to report results on problems classified only by problem size, as has been commonly done in most ACO research to date. Some description of the cost matrix distribution is also required when attempting to explain and predict the performance of these algorithms on the TSP.


Problem Instance Travelling Salesperson Problem Cost Matrix Optimisation Heuristic Instance Size 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Enda Ridge
    • 1
  • Daniel Kudenko
    • 1
  1. 1.Department of Computer Science, The University of York, York YO10 5DDEngland

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