Computational Optimization and Applications

, Volume 60, Issue 3, pp 559–585 | Cite as

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

  • Kuo-Ling Huang
  • Sanjay Mehrotra


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.


Mixed integer convex programs Geometric random walk  Feasibility pump Primal heuristic 



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

Supplementary material

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Supplementary material 1 (pdf 111 KB)
10589_2014_9693_MOESM2_ESM.pdf (114 kb)
Supplementary material 2 (pdf 114 KB)
10589_2014_9693_MOESM3_ESM.pdf (113 kb)
Supplementary material 3 (pdf 113 KB)


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanstonUSA

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