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A Circuit Constraint for Multiple Tours Problems

  • Philippe VismaraEmail author
  • Nicolas Briot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)

Abstract

Routing problems appear in many practical applications. In the context of Constraint Programming, circuit constraints have been successfully developed to handle problems like the well-known Traveling Salesman Problem or the Vehicle Routing Problem. These kind of constraints are linked to the search for a Hamiltonian circuit in a graph. In this paper we consider a more general multiple tour problem that consists in covering a part of the graph with a set of minimal cost circuits. We define a new global constraint WeightedSubCircuits that generalizes the WeightedCircuit constraint by releasing the need to obtain a Hamiltonian circuit. It enforces multiple disjoint circuits of bounded total cost to partially cover a weighted graph, the subsets of vertices to be covered being induced by external constraints. We show that enforcing Bounds Consistency for WeightedSubCircuits is NP-hard. We propose an incomplete but polynomial filtering method based on the search for a lower bound of a weighted Steiner circuit.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.LIRMMUniv Montpellier, CNRSMontpellierFrance
  2. 2.MISTEA, Montpellier SupAgro, INRAUniv MontpellierMontpellierFrance

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