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