Solving 0-1 mixed integer programs with variable neighbourhood decomposition search

Abstract

In this paper we propose a new heuristic for solving 0-1 mixed integer programs based on the variable neighbourhood decomposition search principle. It combines variable neighbourhood search with general-purpose CPLEX MIP solver. We perform systematic hard variables fixing (or diving) following the variable neighbourhood search rules. variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that by exploiting boundary effects in this way, solution quality can be considerably improved. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very difficult MIP problems. Moreover, computational results show that our method outperforms CPLEX MIP solver, as well as three other recent most successful MIP solution methods.