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Partial polyhedral description and generation of discrete optimization problems with known optima

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  • Martha G. Pilcher
  • Ronald L. Rardin

Abstract

We detail a random cut concept for generating instances of discrete optimization problems based on a partial description of the polytope of solutions. We show how implementations of this approach have the useful properties that an optimal solution and the form of valid equalities required to solve the problem by cutting methods are both known at the completion of generation. The former makes possible large‐scale testing of heuristics, and the latter facilitates cutting algorithm research. The random cut concept of problem generation is first discussed in general and then details are provided on its implementation for symmetric traveling salesman problems.

Suggested Citation

  • Martha G. Pilcher & Ronald L. Rardin, 1992. "Partial polyhedral description and generation of discrete optimization problems with known optima," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 839-858, October.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:6:p:839-858
    DOI: 10.1002/1520-6750(199210)39:63.0.CO;2-C
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    1. M. Grötschel & W. R. Pulleyblank, 1986. "Clique Tree Inequalities and the Symmetric Travelling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 537-569, November.
    2. Harlan Crowder & Manfred W. Padberg, 1980. "Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality," Management Science, INFORMS, vol. 26(5), pages 495-509, May.
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