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Benders decomposition: an integer-programming extension with further computational enhancements
Tarvin, David Antony
Tarvin, David Antony
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2014
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2014
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We extend Benders decomposition in two ways. We begin by introducing a new integer Benders decomposition algorithm (IBDA) that solves pure integer programs (IPs). IBDA solves a mixed-integer relaxation of the IP by Benders decomposition and then conducts a type of local search to identify promising solutions to the original problem. IBDA's key contributions are the local-search technique and a novel use of solution-elimination constraints. We prove IBDA's correctness and demonstrate that the algorithm solves certain IPs faster than other available techniques. Slow Benders master-problem solution times can limit IBDA's effectiveness, however. To ameliorate this problem, we therefore develop a "Benders decomposition algorithm using enumeration to solve master problems" (BDEA). BDEA stores objective-function values for all master-problem solutions, and then solves the subsequent master problem by comparing the incumbent value to the value of the most recent Benders cut for every feasible solution. Using enumeration, master-problem solution times remain constant even as the number of Benders cuts increases. We demonstrate BDEA's performance using a stochastic capacitated facility-location problem. Computational tests show that BDEA can reduce average solution times by up to 74% compared to a standard BDA implementation.
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