Reoptimization techniques for MIP solvers

Abstract

Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixedinteger programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-andbound algorithms employed by general MIP solvers based on the idea to “warmstart” using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach.