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Heuristics for the 0-1 multidimensional knapsack problem. (English) Zbl 1176.90657
Summary: Two heuristics for the 0-1 multidimensional knapsack problem (MKP) are presented. The first one uses surrogate relaxation, and the relaxed problem is solved via a modified dynamic-programming algorithm. The heuristics provides a feasible solution for (MKP). The second one combines a limited-branch-and-cut-procedure with the previous approach, and tries to improve the bound obtained by exploring some nodes that have been rejected by the modified dynamic-programming algorithm. Computational experiences show that our approaches give better results than the existing heuristics, and thus permit one to obtain a smaller gap between the solution provided and an optimal solution.
MSC:
90C59Approximation methods and heuristics
90C39Dynamic programming
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut