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In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem

Author

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  • Claudia Bode

    (Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, D-55128 Mainz, Germany)

  • Stefan Irnich

    (Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, D-55128 Mainz, Germany)

Abstract

Recently, Bode and Irnich [Bode C, Irnich S (2012) Cut-first branch-and-price-second for the capacitated arc-routing problem. Oper. Res. 60(5):1167–1182] presented a cut-first branch-and-price-second algorithm for solving the capacitated arc-routing problem (CARP). The fundamental difference to other approaches for exactly solving the CARP is that the entire algorithm works directly on the typically sparse underlying graph representing the street network. This enables the use of highly efficient dynamic programming-based pricing algorithms to solve the column-generation subproblem also known as the pricing problem. The contribution of this paper is the in-depth analysis of the CARP pricing problem and its possible relaxations, including the construction of new labeling algorithms for their solution and comprehensive computational tests on standard benchmark problems. We show that a systematic variation of different relaxations provides a powerful approach to solve knowingly hard instances of the CARP to proven optimality.

Suggested Citation

  • Claudia Bode & Stefan Irnich, 2015. "In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem," Transportation Science, INFORMS, vol. 49(2), pages 369-383, May.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:2:p:369-383
    DOI: 10.1287/trsc.2013.0507
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    References listed on IDEAS

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    1. Beullens, Patrick & Muyldermans, Luc & Cattrysse, Dirk & Van Oudheusden, Dirk, 2003. "A guided local search heuristic for the capacitated arc routing problem," European Journal of Operational Research, Elsevier, vol. 147(3), pages 629-643, June.
    2. Villeneuve, Daniel & Desaulniers, Guy, 2005. "The shortest path problem with forbidden paths," European Journal of Operational Research, Elsevier, vol. 165(1), pages 97-107, August.
    3. Hatem Ben Amor & Jacques Desrosiers & José Manuel Valério de Carvalho, 2006. "Dual-Optimal Inequalities for Stabilized Column Generation," Operations Research, INFORMS, vol. 54(3), pages 454-463, June.
    4. Stefan Irnich & Daniel Villeneuve, 2006. "The Shortest-Path Problem with Resource Constraints and k -Cycle Elimination for k (ge) 3," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 391-406, August.
    5. Claudia Bode & Stefan Irnich, 2012. "Cut-First Branch-and-Price-Second for the Capacitated Arc-Routing Problem," Operations Research, INFORMS, vol. 60(5), pages 1167-1182, October.
    6. Santos, Luís & Coutinho-Rodrigues, João & Current, John R., 2010. "An improved ant colony optimization based algorithm for the capacitated arc routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 246-266, February.
    7. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
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    Citations

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    Cited by:

    1. Diego Pecin & Eduardo Uchoa, 2019. "Comparative Analysis of Capacitated Arc Routing Formulations for Designing a New Branch-Cut-and-Price Algorithm," Transportation Science, INFORMS, vol. 53(6), pages 1673-1694, November.
    2. Christian Tilk, 2016. "Branch-and-Price-and-Cut for the Vehicle Routing and Truck Driver Scheduling Problem," Working Papers 1616, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    3. Lee, Chungmok, 2022. "A robust optimization approach with probe-able uncertainty," European Journal of Operational Research, Elsevier, vol. 296(1), pages 218-239.
    4. Guy Desaulniers & Fausto Errico & Stefan Irnich & Michael Schneider, 2016. "Exact Algorithms for Electric Vehicle-Routing Problems with Time Windows," Operations Research, INFORMS, vol. 64(6), pages 1388-1405, December.
    5. Jesica Armas & Peter Keenan & Angel A. Juan & Seán McGarraghy, 2019. "Solving large-scale time capacitated arc routing problems: from real-time heuristics to metaheuristics," Annals of Operations Research, Springer, vol. 273(1), pages 135-162, February.
    6. Timo Hintsch & Stefan Irnich & Lone Kiilerich, 2021. "Branch-Price-and-Cut for the Soft-Clustered Capacitated Arc-Routing Problem," Transportation Science, INFORMS, vol. 55(3), pages 687-705, May.
    7. Ann-Kathrin Rothenbächer, 2019. "Branch-and-Price-and-Cut for the Periodic Vehicle Routing Problem with Flexible Schedule Structures," Transportation Science, INFORMS, vol. 53(3), pages 850-866, May.
    8. Christian Tilk & Stefan Irnich, 2017. "Dynamic Programming for the Minimum Tour Duration Problem," Transportation Science, INFORMS, vol. 51(2), pages 549-565, May.

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