An algorithm for the disjunctively constrained knapsack problem

This paper proposes an adaptation of the scatter search (SS) meta‐heuristic for approximately solving the disjunctively constrained knapsack problem (DCKP). The DCKP can be viewed as a variant of the standard knapsack problem with special disjunctive constraints. Two versions of SS are presented which are organised following the usual structure of SS. The method is analysed computationally on a set of problem instances of the literature and compared to the results provided by the Cplex solver and other algorithms of the literature. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the proposed method provides results of high quality within reasonable computational time.