Implementation and test of auction methods for solving generalized network flow problems with separable convex cost

  • Authors:

  • F. Guerriero;P. Tseng

  • Affiliations:

  • Assistant Professor, Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria, Rende, Italy;Professor, Department of Mathematics, University of Washington, Seattle, Washington

  • Venue:
  • Journal of Optimization Theory and Applications
  • Year:
  • 2002

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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 ε-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 ε-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.