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A generator and a simplex solver for network piecewise linear programs

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Abstract

This is a brief report on our recent work in network piecewise linear programming (NPLP), and it consists of two parts. In the first park, we describe a generator for NPLP problems which is derived from the classical network linear program generator NETGEN. The generator creates networks of the same topological structures as NETGEN, but each arc is associated with a convex piecewise linear cost. The purpose of this program is to provide a set of standard test problems which can be used to compare the performance of various algorithms for NPLP. In the second part, we introduce a network simplex method that directly solves a network piecewise linear program without reformulating it as a network linear program of higher dimension. Forty benchmark NPLP problems are solved by this method and a reformulation method. The computational results are in favor of the direct method and show that solving an NPLP problem is not much harder than solving a network linear program of the same dimension.

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Authors and Affiliations

  1. Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080, Beijing, China

    Sun Jie

  2. Department of IEMS, Northwestern University, 60208, Evanston, IL, USA

    Sun Jie

  3. Department of EECS, Northwestern University, 60208, Evanston, IL, USA

    K. Tsai

Authors
  1. Sun Jie
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  2. K. Tsai
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Additional information

This research is supported in part by National Science Foundation of USA under Grant DDM-8721709.

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Sun, J., Tsai, K. A generator and a simplex solver for network piecewise linear programs. Acta Mathematicae Applicatae Sinica 10, 177–185 (1994). https://doi.org/10.1007/BF02006117

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  • DOI: https://doi.org/10.1007/BF02006117

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