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Application of graph-theoretic approaches to the random landscapes of the three-dimensional assignment problem

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Abstract

We study local optima of combinatorial optimization problems. We show that a local search algorithm can be represented as a digraph and apply recent results for spanning forests of a diagraph. We establish a correspondence between the number of local optima and the algebraic multiplicities of eigenvalues of digraph laplacians. We apply our finding to the three-dimensional assignment problem.

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Authors and Affiliations

  1. Department of Industrial Engineering, New Mexico State University, Las Cruces, NM, 88003, USA

    Alla Kammerdiner

  2. Air Force Research Laboratory, Munitions Directorate, Eglin AFB, FL, 32542, USA

    Eduardo Pasiliao

Authors
  1. Alla Kammerdiner
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  2. Eduardo Pasiliao
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Correspondence to Alla Kammerdiner.

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Kammerdiner, A., Pasiliao, E. Application of graph-theoretic approaches to the random landscapes of the three-dimensional assignment problem. Optim Lett 7, 79–87 (2013). https://doi.org/10.1007/s11590-011-0396-x

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  • DOI: https://doi.org/10.1007/s11590-011-0396-x

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