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In and out forests on combinatorial landscapes

Author

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  • Kammerdiner, A.R.
  • Pasiliao, E.L.

Abstract

Fitness landscape theory is a mathematical framework for numerical analysis of search algorithms on combinatorial optimization problems. We study a representation of fitness landscape as a weighted directed graph. We consider out forest and in forest structures in this graph and establish important relationships among the forest structures of a directed graph, the spectral properties of the Laplacian matrices, and the numbers of local optima of the landscape. These relationships provide a new approach for computing the numbers of local optima for various problem instances and neighborhood structures.

Suggested Citation

  • Kammerdiner, A.R. & Pasiliao, E.L., 2014. "In and out forests on combinatorial landscapes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 78-84.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:78-84
    DOI: 10.1016/j.ejor.2013.11.025
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    References listed on IDEAS

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    1. Pedamallu, Chandra Sekhar & Ozdamar, Linet, 2008. "Investigating a hybrid simulated annealing and local search algorithm for constrained optimization," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1230-1245, March.
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    5. Don A. Grundel & Pavlo A. Krokhmal & Carlos A. S. Oliveira & Panos M. Pardalos, 2007. "On the number of local minima for the multidimensional assignment problem," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 1-18, January.
    6. Stutzle, Thomas, 2006. "Iterated local search for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1519-1539, November.
    7. Hvattum, Lars Magnus & Glover, Fred, 2009. "Finding local optima of high-dimensional functions using direct search methods," European Journal of Operational Research, Elsevier, vol. 195(1), pages 31-45, May.
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