Adaptive Kernel Search: A heuristic for solving Mixed Integer linear Programs

We introduce Adaptive Kernel Search (AKS), a heuristic framework for the solution of (general) Mixed Integer linear Programs (MIPs). AKS extends and enhances Kernel Search, a heuristic framework that has been shown to produce high-quality solutions for a number of specific (combinatorial) optimization problems in a short amount of time. AKS solves a sequence of carefully constructed restricted MIPs (using a commercial MIP solver). The computational effort required to solve the first restricted MIP guides the construction of the subsequent MIPs. The restricted MIPs are constructed around a kernel, which contains the variables that are presumably non-zero in an optimal solution. Computational results, for a set of 137 instances, show that AKS significantly outperforms other state-of-the-art heuristics for solving MIPs. AKS also compares favorably to CPLEX and offers more flexibility to trade-off solution quality and computing time.