Decomposition methods for water resources optimization models with fixed costs

Advances in Water Resources

Volumn 21, Issue 4, 1998, Pages 283-295

  Watkins Jr , David W ^a   McKinney, Daene C ^a  

^a The University of Texas at Austin   (United States)

Author keywords

Benders decomposition; Capacity expansion; Conjunctive use; Mixed integer nonlinear programming; Outer approximation

Indexed keywords

CAPACITY EXPANSION; GENERALIZED BENDERS DECOMPOSITION (GBD) ALGORITHM; MIXED INTEGER LINEAR PROGRAMMING; OUTER APPROXIMATION (OA) ALGORITHM;

ALGORITHMS; APPROXIMATION THEORY; GROUNDWATER RESOURCES; INTEGER PROGRAMMING; ITERATIVE METHODS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; NONLINEAR PROGRAMMING; PROBLEM SOLVING; SURFACE WATER RESOURCES;

WATER RESOURCES;

ALGORITHM; OPTIMIZATION; WATER RESOURCE;

DECOMPOSITION ALGORITHM; DECOMPOSITION ANALYSIS; METHODOLOGY; OPTIMIZATION MODEL; PLANNING METHOD; WATER MANAGEMENT; WATER RESOURCES;

EID: 0032054538     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0309-1708(96)00061-9     Document Type: Article

References (35)

1. Aguado, E. & Remson, I., Ground-water management with fixed charges. J. Water Resour. Plan. Manage., 106(WR2) (1980) 375-382.
2. Basagaoglu, H. & Yazicigil, H., Optimal capacity-expansion planning in multiaquifer systems. J. Water Resour. Plan. Manage., 120(6) (1994) 836-856.
3. Beale, E. M. L., Integer programming. In The State of the Art in Numerical Analysis, ed. D. Jacobs. Academic Press, 1977, p. 409.
4. Benders, J. F., Partitioning procedures for solving mixed variables programming problems. Numerische Mathematik, 4 (1962) 238-252.
5. Brooke, A., Kendrick, D. & Meeraus, A., GAMS: A User's Guide, Release 2.25. The Scientific Press, San Fran., Calif., 1992.
6. Dantzig, G. B., Glynn, P. W., Avriel, M., Stone, J. C., Entriken, R. & Nakayama, M., Decomposition techniques for multi-area generation and transmission planning under uncertainty. Final Rept. for EPRI Project 2940-1, EPRI, Palo Alto, Calif., 1989.
7. Dougherty, D. E. & Marryott, R. A., Optimal groundwater management 1. Simulated annealing. Water Resour. Res., 27(10) (1991) 2493-2508.
8. Duran, M. A. & Grossman, I. E., An outer approximation algorithm for a class of mixed-integer nonlinear programs. Math. Prog., 36 (1986) 307-339.
9. Fletcher, R. & Leyffer, S., Solving mixed integer nonlinear programs by outer approximation. Math. Prog., 66(3) (1994) 327.
10. Floudas, C. A., Nonlinear and Mixed-Integer and Optimization: Fundamentals and Applications. Oxford University Press, New York, 1995.
11. Floudas, C. A., Aggarwal, A. & Ciric, A. R., Global optimum search for nonconvex NLP and MINLP problems. Comput. Chem. Engng, 13(10) (1989) 1117-1132.
12. Floudas, C. A. & Paules, IV, G. E., A mixed-integer nonlinear programming formulation for the synthesis of heat-integrated distillation sequences. Comput. Chem. Engng, 12(6) (1988) 531-546.
13. Geoffrion, A. M., Generalized Benders decomposition. J. Opt. Theory and Appl., 10(4) (1972) 237-260.
14. Graves, G. W., Water pollution control. In Techniques of Optimization, ed. A. V. Balakrishnan. Academic Press, New York, 1972, pp. 499-509.
15. Grossman, I. E. & Sargeant, R. W. H., Optimum design of multipurpose chemical plants. Ind. Eng. Chem. Process Des. Dev., 18(2) (1979) 343-348.
16. Horst, R. & Tuy, H., Global Optimization. Springer-Verlag, New York, 1993.
17. Karatzas, G. P. & Pinder, G. F., Groundwater management using the outer approximation method. Water Resour. Res., 29(10) (1993) 3371-3378.
18. Karatzas, G. P. & Pinder, G. F., The solution of groundwater quality management problems with a nonconvex feasible region using a cutting plane optimization technique. Water Resour. Res., 32(4) (1996) 3091-3100.
19. Kim, J. H. & Mays, L. W., Optimal rehabilitation model for water-distribution systems. J. Water Resour. Plan. Manage., 120(6) (1994) 674-692.
20. Kocis, G. R. & Grossman, I. E., Relaxation strategy for the structural optimization of process flow sheets. I&EC Res., 26 (1987) 1869-1881.
21. Lall, U. & Santini, M. D., An optimization model for unconfined stratified aquifer systems. J. Hydrol., 111 (1989) 145-162.
22. Loucks, D. P., Stedinger, J. R. & Haith, D. A., Water Resources Systems Planning and Analysis. Prentice Hall, 1981.
23. Maddock, III, T., Algebraic technological function from a simulation model. Water Resour. Res., 18(1) (1972) 129-134.
24. Manousiouthakis, V. & Sourlas, D., A global optimization approach to rationally constrained rational programming. Chem. Eng. Comm., 115 (1992) 127-147.
25. McKinney, D. C. & Lin, M.-D., Genetic algorithm solution of groundwater management models. Water Resour. Res., 30(6) (1994) 1897-1906.
26. McKinney, D. C. & Lin, M.-D., Approximate mixed-integer nonlinear programming methods for optimal aquifer remediation design. Water Resour. Res., 31(3) (1995) 731-740.
27. Paules, IV, G. E. & Floudas, C. A., APROS: Algorithmic development methodology for discrete-continuous optimization problems. Ops. Res., 37(6) (1989) 902-915.
28. Ritzel, B. J., Eheart, J. W. & Ranjithan, S., Using genetic algorithms to solve a multiple objective groundwater pollution containment problem. Water Resour. Res., 30(5) (1994) 1589-1603.
29. Rouhani, R., Lasdon, L., Leboe, W. & Waren, A. D., A generalized Benders decomposition approach to reactive source planning in power systems. In Mathematical Programming Essays in Honor of George B. Dantzig, Part II, ed. R. W. Cottle. North-Holland, New York, 1985, pp. 62-75.
30. Siddiqi, S. N., Reliability differentiated pricing and optimal planning for electrical power systems, PhD. Dissertation, Dept. of Electrical and Computer Engineering, The University of Texas, Austin, 1993.
31. Viswanathan, J. & Grossman, I. E., A combined penalty function and outer approximation method for MINLP optimization. Comp. Chem. Engng, 14 (1990) 769-782.
32. Wagner, H. M., Principles of Operations Research, 2nd Edn. Prentice-Hall, Englewood Cliffs, NJ, 1975.
33. Watkins, Jr, D. W. & McKinney, D. C., Robust optimization for incorporating risk and uncertainty in the planning of sustainable water resources systems. Modelling and Management of Sustainable Basin-Scale Water Resource Systems, Proc. IAHS XXI General Assembly of IUGG, Boulder, CO, July 2-12, 1995, pp. 225-232.
34. Yuan, X., Zhang, S., Pibileau, L. & Domenech, S., Une methode d'optimisation non lineare en variables mixtes pour la conception de procedes. Partie I: presentation de l'algorithme. RAIRO Rech Opera (1987).
35. Ziari, H. A., McCarl, B. A. & Stockle, C., A nonlinear mixed integer program model for evaluating runoff impoundments for supplemental irrigation. Water Resour. Res., 31(6) (1995) 1585-1594.