Robust optimization approach for a chance-constrained binary knapsack problem
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We consider a certain class of chance-constrained binary knapsack problem where each item has a normally distributed random weight that is independent of the other items. For this problem we propose an efficient pseudo-polynomial time algorithm based on the robust optimization approach for finding a solution with a theoretical bound on the probability of satisfying the knapsack constraint. Our algorithm is tested on a wide range of random instances, and the results demonstrate that it provides qualified solutions quickly. In contrast, a state-of-the-art MIP solver is only applicable for instances of the problem with a restricted number of items.
KeywordsKnapsack problem Combinatorial optimization Chance-constrained programming Robust optimization
Mathematics Subject Classification90C15 90C27 90C59
This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant 2011-0027301).
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