A survey on benders decomposition applied to fixed-charge network design problems
Computers and Operations Research
Benders decomposition for the uncapacitated multiple allocation hub location problem
Computers and Operations Research
Environmental Modelling & Software
Benders Decomposition for Hub Location Problems with Economies of Scale
Transportation Science
Multiple allocation hub-and-spoke network design under hub congestion
Computers and Operations Research
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Nonconvex nonlinear programming (NLP) problems arise frequently in water resources management, e.g., reservoir operations, groundwater remediation, and integrated water quantity and quality management. Such problems are usually large and sparse. Existing software for global optimization cannot cope with problems of this size, while current local sparse NLP solvers, e.g., MINOS (Murtagh and Saunders 1987), or CONOPT (Drud 1994) cannot guarantee a global solution. In this paper, we apply the Generalized Benders Decomposition (GBD) algorithm to two large nonconvex water resources models involving reservoir operations and water allocation in a river basin, using an approximation to the GBD cuts proposed by Floudas et al. (1989) and Floudas (1995). To ensure feasibility of the GBD subproblem, we relax its constraints by introducing elastic slack variables, penalizing these slacks in the objective function. This approach leads to solutions with excellent objective values in run times much less than the GAMS NLP solvers MINOS5 and CONOPT2, if the complicating variables are carefully selected. Using these solutions as initial points for MINOS5 or CONOPT2 often leads to further improvements.