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Adaptive CP-Based Lagrangian Relaxation for TSP Solving

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12296))

Abstract

M. Sellmann showed that CP-based Lagrangian relaxation gave good results but the interactions between the filtering algorithms and the Lagrangian multipliers were quite difficult to understand. In other words, it is difficult to determine when filtering algorithms should be triggered. There are two main reasons for this: the best multipliers do not lead to the best filtering and each filtering disrupts the solving of the Lagrangian multiplier problem. In this paper, we study these interactions for the Traveling Salesman Problem (TSP) because the resolution of the TSP in CP is mainly based on a Lagrangian relaxation. We propose to match the calls to the filtering algorithms with the strong variations of the objective value. In addition, we try to avoid oscillations of the objective function. We introduce Scope Sizing Subgradient algorithm, denoted by SSSA, which is an adaptive algorithm, that implements this idea. We experimentally show the advantage of this approach by considering different search strategies or additional constraints. A gain of a factor of two in time is observed compared to the state of the art.

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Notes

  1. 1.

    Normally, in CP, when \(F_2\), a FA, is added to \(F_1\), another FA, all values eliminated by \(F_1\) are also eliminated by the combination of \(F_1\) and \(F_2\).

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Authors and Affiliations

  1. Université Côte d’Azur, CNRS, I3S, Nice, France

    Nicolas Isoart & Jean-Charles Régin

Authors
  1. Nicolas Isoart
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  2. Jean-Charles Régin
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Corresponding author

Correspondence to Nicolas Isoart .

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Editors and Affiliations

  1. LAAS - CNRS, Toulouse, France

    Emmanuel Hebrard

  2. TU Wien, Vienna, Wien, Austria

    Nysret Musliu

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Isoart, N., Régin, JC. (2020). Adaptive CP-Based Lagrangian Relaxation for TSP Solving. In: Hebrard, E., Musliu, N. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2020. Lecture Notes in Computer Science(), vol 12296. Springer, Cham. https://doi.org/10.1007/978-3-030-58942-4_20

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  • DOI: https://doi.org/10.1007/978-3-030-58942-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58941-7

  • Online ISBN: 978-3-030-58942-4

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