A New Hybrid Algorithm for the Multiple-Choice Multi-Dimensional Knapsack Problem

In this paper, we approximately solve the multiple-choice multi-dimensional knapsack problem. We propose a hybrid algorithm based on branch and bound method and Pareto-algebraic operations. The algorithm starts by an initial solution and then combines one-by-one groups of the problem instance to generate partial solutions in each iteration. Most of these partial solutions are discarded by Pareto dominance and bounding process leading at the end to optimality or near optimality in the case when only a subset of partial solutions is maintained at each step. Furthermore, a rounding procedure is introduced to improve the bounding process by generating high quality feasible solutions during algorithm execution. The performance of the proposed heuristic has been evaluated on several problem instances. Encouraging results have been obtained. Key-Words: combinatorial optimization, heuristics, knapsacks, branch and bound.