Hybrid Variable Neighbourhood Decomposition Search for 0-1 Mixed Integer Programming Problem

In this paper we propose new hybrid heuristics for the 0-1 mixed integer programming problem, based on the variable neighbourhood decomposition search principle and on exploiting information obtained from a series of relaxations. In the case of a maximization problem, we add iteratively pseudo-cuts to the problem in order to produce a sequence of lower and upper bounds of the problem, so that integrality gap is reduced. We validate our approaches on the well-known 0-1 multidimensional knapsack problem, in which the general-purpose CPLEX MIP solver is used as a black box for solving subproblems generated during the search process. The results obtained with these methods are comparable with the current state-of-the-art heuristics on a set of large scale instances.