The Quadratic Multiknapsack Problem with Conflicts and Balance Constraints

Abstract

The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem that includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. Summary of Contribution: The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities -- with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem which includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. The problem we address is clearly in the core of the operations research applications in which subsets have to be built and, in particular, we add the concept of fairness to the modeling and solution process by computationally evaluating techniques to take fairness into account. This is clearly at the core of computational evaluation of algorithms.