Solving Large Nonconvex Water Resources Management Models Using Generalized Benders Decomposition

Ximing Cai (), Daene C. McKinney (), Leon S. Lasdon () and David W. Watkins ()
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Ximing Cai: International Food Policy Research Institute, 2033 K. Washington D.C., 20006
Daene C. McKinney: Department of Civil Engineering, College of Engineering, The University of Texas at Austin, Austin, Texas 78712
Leon S. Lasdon: Department of Management Science and Information Systems, Graduate School of Business, The University of Texas at Austin, Austin, Texas 78712
David W. Watkins: Department of Civil and Environmental Engineering, Michigan Technological University, Houghton, Michigan 49931

Operations Research, 2001, vol. 49, issue 2, 235-245

Abstract: 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.

Keywords: Natural Resources: water resources management modeling; Nonlinear Programming: nonconvexivity in large nonlinear models; Algorithm: Generalized Benders Decomposition (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (10)

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