A tree search based combination heuristic for the knapsack problem with setup

We propose a tree search heuristic to the Knapsack Problem with Setup (KPS).We demonstrate the benefit of a new technique to avoid solutions duplication.Computational experiments show the efficiency of the proposed heuristic. Knapsack Problems with Setups (KPS) have received increasing attention in recent research for their potential use in the modeling of various concrete industrial and financial problems, such as order acceptance and production scheduling. The KPS problem consists in selecting appropriate items, from a set of disjoint families of items, to enter a knapsack while maximizing its value. An individual item can be selected only if a setup is incurred for the family to which it belongs. In this paper, we propose a tree search heuristic to the KPS that generates compound moves by a strategically truncated form of tree search. We adopt a new avoid duplication technique that consists in converting a KPS solution to an integer index. The efficiency of the proposed method is evaluated by computational experiments involving a set of randomly generated instances. The results demonstrate the impact of the avoiding duplication technique in terms of enhancing solution quality and computation time. The efficiency of the proposed method was confirmed by its ability to produce optimal and near optimal solutions in a short computation time.