Sampling Local Optima Networks of Large Combinatorial Search Spaces: The QAP Case

Local Optima Networks (LON) model combinatorial landscapes as graphs, where nodes are local optima and edges transitions among them according to given move operators. Modelling landscapes as networks brings a new rich set of metrics to characterize them. Most of the previous works on LONs fully enumerate the underlying landscapes to extract all local optima, which limits their use to small instances. This article proposes a sound sampling procedure to extract LONs of larger instances and estimate their metrics. The results obtained on two classes of Quadratic Assignment Problem (QAP) benchmark instances show that the method produces reliable results.

[1]  Alessandro Vespignani,et al.  Characterization and modeling of weighted networks , 2005 .

[2]  Sébastien Vérel,et al.  Local Optima Networks of NK Landscapes With Neutrality , 2011, IEEE Transactions on Evolutionary Computation.

[3]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[4]  É. Taillard.  COMPARISON OF ITERATIVE SEARCHES FOR THE QUADRATIC ASSIGNMENT PROBLEM. , 1995 .

[5]  Sébastien Vérel,et al.  Local Optima Networks with Escape Edges , 2011, Artificial Evolution.

[6]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[7]  S. Kauffman,et al.  Towards a general theory of adaptive walks on rugged landscapes. , 1987, Journal of theoretical biology.

[8]  Enrique Alba,et al.  Local Optima Networks, Landscape Autocorrelation and Heuristic Search Performance , 2012, PPSN.

[9]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[10]  Sébastien Vérel,et al.  Complex-network analysis of combinatorial spaces: The NK landscape case , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Sébastien Vérel,et al.  Local Optima Networks of the Permutation Flow-Shop Problem , 2013, Artificial Evolution.

[12]  Christian M. Reidys,et al.  Combinatorial Landscapes , 2002, SIAM Rev..

[13]  Sébastien Vérel,et al.  Local optima networks and the performance of iterated local search , 2012, GECCO '12.

[14]  Enrique Alba,et al.  Autocorrelation measures for the quadratic assignment problem , 2012, Appl. Math. Lett..

[15]  Sébastien Vérel,et al.  First-Improvement vs. Best-Improvement Local Optima Networks of NK Landscapes , 2010, PPSN.

[16]  Sébastien Vérel,et al.  A study of NK landscapes' basins and local optima networks , 2008, GECCO '08.

[17]  S. Berg.  Snowball Sampling—I , 2006 .

[18]  Andries P. Engelbrecht,et al.  Recent Advances in the Theory and Application of Fitness Landscapes , 2013 .

[19]  David W. Corne,et al.  Instance Generators and Test Suites for the Multiobjective Quadratic Assignment Problem , 2003, EMO.