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The integration of an interior-point cutting plane method within a branch-and-price algorithm

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Abstract.

This paper presents a novel integration of interior point cutting plane methods within branch-and-price algorithms. Unlike the classical method, columns are generated at a ‘‘central’’ dual solution by applying the analytic centre cutting plane method (ACCPM) on the dual of the full master problem. First, we introduce some modifications to ACCPM. We propose a new procedure to recover primal feasibility after adding cuts and use, for the first time, a dual Newton’s method to calculate the new analytic centre after branching. Second, we discuss the integration of ACCPM within the branch-and-price algorithm. We detail the use of ACCPM as the search goes deep in the branch and bound tree, making full utilization of past information as a warm start. We exploit dual information from ACCPM to generate incumbent feasible solutions and to guide branching. Finally, the overall approach is implemented and tested for the bin-packing problem and the capacitated facility location problem with single sourcing. We compare against Cplex-MIP 7.5 as well as a classical branch-and-price algorithm.

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Authors and Affiliations

  1. Department of Management Sciences, University of Waterloo, 200 University Ave., W. Waterloo, ON, Ca N2L 3G1

    Samir Elhedhli

  2. GERAD/Faculty of Management, McGill university, 1001 Sherbrooke, W. Montreal, Qc, Ca H3A 1G5

    Jean-Louis Goffin

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  1. Samir Elhedhli
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  2. Jean-Louis Goffin
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Correspondence to Samir Elhedhli.

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Mathematics Subject Classification (1991): 20E28, 20G40, 20C20

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Elhedhli, S., Goffin, JL. The integration of an interior-point cutting plane method within a branch-and-price algorithm. Math. Program., Ser. A 100, 267–294 (2004). https://doi.org/10.1007/s10107-003-0469-4

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  • DOI: https://doi.org/10.1007/s10107-003-0469-4

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