A scatter search method for the multidimensional knapsack problem with generalized upper bound constraints

In this article, a scatter search (SS) heuristic is proposed to solve the multidimensional knapsack problem with generalized upper bound constraints (GUBMKP). The method is organized according to the general structure of SS. We discuss the design and implementation for each of the components of SS. A greedy randomized adaptive search procedure is applied in order to diversify the initial solutions. In order to select diversified solutions to enter the reference set, we propose an algorithm based on the structure of generalized upper bound constraints. Several approaches of combining solutions are proposed to solve the problem. The computational results show the heuristic is competitive compared to the former leading method for the GUBMKP.