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An empirical evaluation of a walk-relax-round heuristic for mixed integer convex programs

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  • Kuo-Ling Huang
  • Sanjay Mehrotra

Abstract

Recently, a walk-and-round heuristic was proposed by Huang and Mehrotra (Comput Optim Appl, 2012 ) for generating high quality feasible solutions of mixed integer linear programs. This approach uses geometric random walks on a polyhedral set to sample points in this set. It subsequently rounds these random points using a heuristic, such as the feasibility pump. In this paper, the walk-and-round heuristic is further developed for the mixed integer convex programs (MICPs). Specifically, an outer approximation relaxation step is incorporated. The resulting approach is called a walk-relax-round heuristic. Computational results on problems from the CMU-IBM library show that the points generated from the random walk steps bring additional value. Specifically, the walk-relax-round heuristic using a long step Dikin walk found an optimal solution for 51 out of the 58 MICP test problems. In comparison, the feasibility pump heuristic starting at a continuous relaxation optimum found an optimal solution for 45 test problems. Computational comparisons with a commercial software Cplex 12.1 on mixed integer convex quadratic programs are also given. Our results show that the walk-relax-round heuristic is promising. This may be because the random walk points provide an improved outer approximation of the convex region. Copyright Springer Science+Business Media New York 2015

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  • Kuo-Ling Huang & Sanjay Mehrotra, 2015. "An empirical evaluation of a walk-relax-round heuristic for mixed integer convex programs," Computational Optimization and Applications, Springer, vol. 60(3), pages 559-585, April.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:3:p:559-585
    DOI: 10.1007/s10589-014-9693-5
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    References listed on IDEAS

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    1. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    2. Kuo-Ling Huang & Sanjay Mehrotra, 2013. "An empirical evaluation of walk-and-round heuristics for mixed integer linear programs," Computational Optimization and Applications, Springer, vol. 55(3), pages 545-570, July.
    3. Stephen Baumert & Archis Ghate & Seksan Kiatsupaibul & Yanfang Shen & Robert L. Smith & Zelda B. Zabinsky, 2009. "Discrete Hit-and-Run for Sampling Points from Arbitrary Distributions Over Subsets of Integer Hyperrectangles," Operations Research, INFORMS, vol. 57(3), pages 727-739, June.
    4. Pierre Bonami & João Gonçalves, 2012. "Heuristics for convex mixed integer nonlinear programs," Computational Optimization and Applications, Springer, vol. 51(2), pages 729-747, March.
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