Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
A Meta-heuristic Algorithm for the Multidimensional 0-1 Knapsack Problem
A Multi-point Local Search in Permutation Space Using Partially Enumerative Continuous Relaxations
Kazumiti NUMATAYuichiro HIDEKATA
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2007 Volume 20 Issue 1 Pages 21-30


In this paper, we propose a new meta-heuristic algorithm for the multidimensional 0-1 knapsack problem (MKP). The proposed method is based on the following four steps. First, a local search is performed in permutation space, where each permutation gives an order of project selection. Second, an initial point (permutation) is determined for the local search by using the information obtained from the solution of a continuously relaxed MKP. Third, a reduction by selection bias (RSB) meta-strategy is applied. Fourth, multi-start points (permutations) are generated by solving the continuously relaxed MKPs with the enumeratively assumed values of some of the variables.
To evaluate the proposed method, we used it to solved 60 benchmark problems in the OR-Library and 8 problems in the HCES (Hearin Center for Enterprise Science) resources, and compared the objective values and execution times to those obtained by using existing methods. The results show that the proposed algorithm competes well with the existing ones that are known to be effective.

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