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A two-level metaheuristic for the all colors shortest path problem

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Abstract

Given an undirected weighted graph, in which each vertex is assigned to a color and one of them is identified as source, in the all-colors shortest path problem we look for a minimum cost shortest path that starts from the source and spans all different colors. The problem is known to be NP-Hard and hard to approximate. In this work we propose a variant of the problem in which the source is unspecified and show the two problems to be computationally equivalent. Furthermore, we propose a mathematical formulation, a compact representation for feasible solutions and a VNS metaheuristic that is based on it. Computational results show the effectiveness of the proposed approach for the two problems.

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Notes

  1. http://www.dipmat2.unisa.it/people/carrabs/www/DataSet/ACSP_Instances.zip.

  2. https://setiathome.berkeley.edu/cpu_list.php.

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Acknowledgements

The authors wish to thank H. Akcan, who provided the set of benchmark instances proposed in [4].

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Authors and Affiliations

  1. Department of Mathematics, University of Salerno, Fisciano, Italy

    F. Carrabs, R. Cerulli, R. Pentangelo & A. Raiconi

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  1. F. Carrabs
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  2. R. Cerulli
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  3. R. Pentangelo
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  4. A. Raiconi
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Correspondence to A. Raiconi.

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Carrabs, F., Cerulli, R., Pentangelo, R. et al. A two-level metaheuristic for the all colors shortest path problem. Comput Optim Appl 71, 525–551 (2018). https://doi.org/10.1007/s10589-018-0014-2

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