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

Author

Listed:
  • Claudia Bode

    (Johannes Gutenberg University Mainz)

  • Stefan Irnich

    (Johannes Gutenberg University Mainz)

Abstract

Recently, Bode and Irnich (‘Cut-First Branch-and-Price-Second for the Capacitated Arc-Routing Problem’, Operations Research, 2012, doi: 10.1287/opre.1120.1079) presented a cut-first branch-and-price-second algorithm for solving the capacitated arc-routing problem (CARP). The fundamental difference to other approaches from the literature 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 for solving 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, theoretical complexity results, and comprehensive computational tests on standard benchmark problems. We will 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, 2012. "In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem," Working Papers 1212, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    • Handle: RePEc:jgu:wpaper:1212
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    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1212.pdf
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    References listed on IDEAS

    as
    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.
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    3. 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.
    4. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2011. "New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem," Operations Research, INFORMS, vol. 59(5), pages 1269-1283, October.
    5. 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.
    6. 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.
    7. Aristide Mingozzi & Lucio Bianco & Salvatore Ricciardelli, 1997. "Dynamic Programming Strategies for the Traveling Salesman Problem with Time Window and Precedence Constraints," Operations Research, INFORMS, vol. 45(3), pages 365-377, June.
    8. 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.
    9. 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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    Full references (including those not matched with items on IDEAS)

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