A matheuristic for the 0-1 generalized quadratic multiple knapsack problem

In this study, we address the 0-1 generalized quadratic multiple Knapsack problem. We use a linearization technique of the existing mathematical model and we propose a new matheuristic that we called Matheuristic Variable Neighborhood Search combining variable neighborhood search with integer programing to solve the large sized instances. The matheuristic considers a local search technique with an adaptive perturbation mechanism to assign the classes to different knapsacks, and then once the assignment is identified, applies the IP to select the items to allocate to each knapsack. Experimental results obtained on a wide set of benchmark instances clearly show the competitiveness of the proposed approach compared to the best state-of-the-art solving techniques.