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Dynamic programming and strong bounds for the $0$-$1$ knapsack problem. (English) Zbl 1231.90338
Summary: Two new algorithms recently proved to outperform all previous methods for the exact solution of the $0$-$1$ knapsack problem. This paper presents a combination of such approaches, where, in addition, valid inequalities are generated and surrogate relaxed, and a new initial core problem is adopted. The algorithm is able to solve all classical test instances, with up to 10,000 variables, in less than 0.2 seconds on a HP9000-735/99 computer. The {\tt C} language implementation of the algorithm is available on the internet.

MSC:
90C29Multi-objective programming; goal programming
90C27Combinatorial optimization
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut
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