Heuristic and exact reduction procedures to solve the discounted 0–1 knapsack problem

In this paper we consider the discounted 0–1 knapsack problem (DKP), which is an extension of classical where a set items decomposed into groups three items. At most one item can be chosen from each group and aim to maximize total profit selected while respecting capacity constraint. The DKP relatively recent in literature. It was considered several works metaheuristics are implemented solve instances propose two-phase approach reduced by applying exact / or heuristic fixation rules first phase that viewed as preprocessing phase. remaining then solved dynamic programming. Experiments performed on available literature show techniques very useful these instances. Indeed, greatly reduces size instances, leading significant reduction time required for programming provide optimal solution. Then, generate new more difficult methods. hardness confirmed experimentally considering both use CPLEX solver our approach.