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Dual‐ascent methods for large‐scale multicommodity flow problems

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  • Cynthia Barnhart

Abstract

The capacitated multicommodity network flow problem presents itself in a number of problem contexts including transportation, communication, and production. To solve the large‐scale multicommodity flow problems encountered in these fields, we develop dual‐ascent heuristics and a primal solution generator. The dual‐ascent solutions, in addition to determining lower bounds on the optimal objective function value, provide advanced starting solutions for use with primal‐based solution techniques. The primal solution generator uses the dual‐ascent solution to obtain heuristically primal solutions to the multicommodity flow problems. Computational experiments performed on three test problem sets show that the dual‐ascent and primal heuristic procedures typically determine nearoptimal solutions quickly. In addition, by using the dual‐ascent procedure to obtain advanced starting solutions, run times for optimal multicommodity flow procedures are reduced significantly and greatly improved solutions are obtained by the new primal solution generator. © 1993 John Wiley & Sons, Inc.

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  • Cynthia Barnhart, 1993. "Dual‐ascent methods for large‐scale multicommodity flow problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 305-324, April.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:3:p:305-324
    DOI: 10.1002/1520-6750(199304)40:33.0.CO;2-4
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    1. Rina R. Schneur & James B. Orlin, 1998. "A Scaling Algorithm for Multicommodity Flow Problems," Operations Research, INFORMS, vol. 46(2), pages 231-246, April.
    2. Antonio Frangioni, 2005. "About Lagrangian Methods in Integer Optimization," Annals of Operations Research, Springer, vol. 139(1), pages 163-193, October.
    3. Hongbin Liu & Guopeng Song & Tianyu Liu & Bo Guo, 2022. "Multitask Emergency Logistics Planning under Multimodal Transportation," Mathematics, MDPI, vol. 10(19), pages 1-25, October.

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