On Minimum Reload Cost Cycle Cover

  • Authors:

  • Giulia Galbiati;Stefano Gualandi;Francesco Maffioli

  • Affiliations:

  • Dipartimento di Informatica e Sistemistica, Universití degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy;Dipartimento di Matematica, Universití degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy;Politecnico di Milano, Dipartimento di Elettronica e Informazione, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2014

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Abstract

We consider the problem of spanning the nodes of a given colored graph G=(N,A) by a set of node-disjoint cycles at minimum reload cost, where a non-negative reload cost is paid whenever passing through a node where the two consecutive arcs have different colors. We call this problem Minimum Reload Cost Cycle Cover (MinRC3 for short). We prove that it is strongly NP-hard and not approximable within 1@e for any @e0 even when the number of colors is 2, the reload costs are symmetric and satisfy the triangle inequality. Some IP models for MinRC3 are then presented, one well suited for a Column Generation approach. The corresponding pricing subproblem is also proved strongly NP-hard. Primal bounds for MinRC3 are obtained via local search based heuristics exploiting 2-opt and 3-opt neighborhoods. Computational results are presented comparing lower and upper bounds obtained by the above mentioned approaches.