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On Minimum Changeover Cost Arborescences

  • Giulia Galbiati
  • Stefano Gualandi
  • Francesco Maffioli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)

Abstract

We are given a digraph G = (N,A), where each arc is colored with one among k given colors. We look for a spanning arborescence T of G rooted (wlog) at node 1 and having minimum changeover cost. We call this the Minimum Changeover Cost Arborescence problem. To the authors’ knowledge, it is a new problem. The concept of changeover costs is similar to the one, already considered in the literature, of reload costs, but the latter depend also on the amount of commodity flowing in the arcs and through the nodes, whereas this is not the case for the changeover costs. Here, given any node j ≠ 1, if a is the color of the single arc entering node j in arborescence T, and b is the color of an arc (if any) leaving node j, then these two arcs contribute to the total changeover cost of T by the quantity d ab , an entry of a k-dimensional square matrix D. We first prove that our problem is NPO-complete and very hard to approximate. Then we present Integer Programming formulations together with a combinatorial lower bound, a greedy heuristic and an exact solution approach. Finally, we report extensive computational results and exhibit a set of challenging instances.

Keywords

Span Tree Greedy Heuristic Quadratic Assignment Problem Steiner Tree Problem Integer Program Formulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Giulia Galbiati
    • 1
  • Stefano Gualandi
    • 2
  • Francesco Maffioli
    • 3
  1. 1.Dipartimento di Informatica e SistemisticaUniversità degli Studi di PaviaItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di PaviaItaly
  3. 3.Dipartimento di Elettronica e InformazionePolitecnico di MilanoItaly

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