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Implementation and Test of Auction Methods for Solving Generalized Network Flow Problems with Separable Convex Cost

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  • F. Guerriero

    (Università della Calabria)

  • P. Tseng

    (University of Washington)

Abstract

We describe the implementation and testing of two methods, based on the auction approach, for solving the problem of minimizing a separable convex cost subject to generalized network flow conservation constraints. The first method is the ∈-relaxation method of Ref. 1; the second is an extension of the auction sequential/shortest path algorithm for ordinary network flow to generalized network flow. We report test results on a large set of randomly generated problems with varying topology, arc gains, and cost function. Comparison with the commercial code CPLEX on linear/quadratic cost problems and with the public-domain code PPRN on nonlinear cost ordinary network problems are also made. The test results show that the auction sequential/shortest path algorithm is generally fastest for solving quadratic cost problems and mixed linear/nonlinear cost problems with arc gain range near 1. The ∈-relaxation method is generally fastest for solving nonlinear cost ordinary network problems and mixed linear/nonlinear cost problems with arc gain range away from 1. CPLEX is generally fastest for solving linear cost and mixed linear/quadratic cost problems with arc gain range near 1.

Suggested Citation

  • F. Guerriero & P. Tseng, 2002. "Implementation and Test of Auction Methods for Solving Generalized Network Flow Problems with Separable Convex Cost," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 113-144, October.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:1:d:10.1023_a:1019629113986
    DOI: 10.1023/A:1019629113986
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    1. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    2. Ron S. Dembo & John M. Mulvey & Stavros A. Zenios, 1989. "OR Practice—Large-Scale Nonlinear Network Models and Their Application," Operations Research, INFORMS, vol. 37(3), pages 353-372, June.
    3. Castro, J. & Nabona, N., 1996. "An implementation of linear and nonlinear multicommodity network flows," European Journal of Operational Research, Elsevier, vol. 92(1), pages 37-53, July.
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    Cited by:

    1. Christensen, Tue Rauff Lind & Klose, Andreas, 2021. "A fast exact method for the capacitated facility location problem with differentiable convex production costs," European Journal of Operational Research, Elsevier, vol. 292(3), pages 855-868.

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