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

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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.

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Acknowledgments

The research of both authors was partially supported by Grant ONR N00014-09-10518, N00014-210051.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 60208, USA

    Kuo-Ling Huang & Sanjay Mehrotra

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  1. Kuo-Ling Huang
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  2. Sanjay Mehrotra
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Correspondence to Sanjay Mehrotra.

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Huang, KL., Mehrotra, S. An empirical evaluation of a walk-relax-round heuristic for mixed integer convex programs. Comput Optim Appl 60, 559–585 (2015). https://doi.org/10.1007/s10589-014-9693-5

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