Fitness Landscape Analysis of NK Landscapes and Vehicle Routing Problems by Expanded Barrier Trees

  • Bas van Stein
  • Michael Emmerich
  • Zhiwei Yang
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 227)


Combinatorial landscape analysis (CLA) is an essential tool for understanding problem difficulty in combinatorial optimization and to get a more fundamental understanding for the behavior of search heuristics. Within CLA, Barrier trees are an efficient tool to visualize essential topographical features of a landscape. They capture the fitness of local optima and how they are separated by fitness barriers from other local optima. The contribution of this study is two-fold: Firstly, the Barrier tree will be extended by a visualization of the size of fitness basins (valleys below saddle points) using expandable node sizes for saddle points and a graded dual-color scheme will be used to distinguish between penalized infeasible and non-penalized feasible solutions of different fitness. Secondly, fitness landscapes of two important NP hard problems with practical relevance will be studied: These are the NK landscapes and Vehicle Routing Problems (with time window constraints). Here the goal is to use EBT to study the influence of problem parameters on the landscape structure: for NK landscapes the number of interacting genes K and for Vehicle Routing Problems the influence of the number of vehicles, the capacity and time window constraints.


Search Space Saddle Point Local Optimum Vehicle Route Problem Infeasible Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.LIACSLeiden UniversityLeidenThe Netherlands

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