Interval-parameter robust quadratic programming for water quality management under uncertainty

Engineering Optimization

Volumn 40, Issue 7, 2008, Pages 613-635

  Li, Y P ^a   Huang, G H ^b   Nie, S L ^c   Mo, D W ^a  

^a PEKING UNIVERSITY   (China)

^b UNIVERSITY OF REGINA   (Canada)

^c HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Decision making; Environment; Fuzzy sets; Interval analysis; Quadratic optimization; Robust programming; Uncertainty; Water quality

Indexed keywords

COMPUTER SOFTWARE SELECTION AND EVALUATION; CONSERVATION; ECONOMICS; FUZZY SETS; MANAGEMENT; MATHEMATICAL PROGRAMMING; NONLINEAR PROGRAMMING; OFFSHORE OIL WELL PRODUCTION; PLANNING; QUALITY CONTROL; QUALITY MANAGEMENT; SET THEORY; WATER CONSERVATION; WATER MANAGEMENT; WATER QUALITY; WATER SUPPLY;

(001) PARAMETER; (I ,J) CONDITIONS; APPLIED (CO); CASE STUDIES; ECONOMIC REVENUE; ECONOMIES OF SCALE; EFFECTIVE PLANNING; GENERAL (CO); INTERVAL NUMBERS; NON-LINEARITIES; OBJECTIVE FUNCTION (OF); OPTIMIZATION FRAMEWORK; QUALITY REQUIREMENTS; SOCIO ECONOMIC DEVELOPMENTS; WATER QUALITY MANAGEMENT;

QUADRATIC PROGRAMMING;

EID: 46149096497     PISSN: 0305215X     EISSN: 10290273     Source Type: Journal    
DOI: 10.1080/03052150801918347     Document Type: Article

References (52)

1. Ben-Tal, A. and Nemirovski, A., 1999. Robust solutions to uncertain linear programs. Operational Research Letters, 25 (1), 1-13.
2. Ben-Tal,A. and Nemirovski, A., 2002. Robust optimization - methodology and applications. Mathematic Program Search B, 92, 453-480.
3. Canestrelli,E.and Giove, S., 1991. Optimizingaquadraticfunction with fuzzy linear coefficients.Control and Cybernetics, 20 (1), 25-44.
4. Chang, N.B., Chen, H.W. and Ning, S.K., 2001. Identification of river water quality using the fuzzy synthetic evaluation approach. Journal of Environmental Management, 63 (3), 293-305.
5. Chen, H.W. and Chang, N.B., 1998. Water pollution control in the river basin by genetic algorithm-based fuzzy multi-objective programming modelling. Water Science and Technology, 37 (8), 55-63.
6. Chen, M.J. and Huang, G.H., 2001. A derivative algorithm for inexact quadratic program-application to environmental decision-making under uncertainty. European Journal of Operational Research, 128 (3), 570-586.
7. Cui, W. and Blockley, D.I., 1990. Decision making with fuzzy quadratic programming. Civil Engineering Systems, 7 (3), 140-146.
8. Dubois, D. and Prade, H., 1978. Operations on fuzzy number. International Journal of Systems Science, 9 (6), 613-626.
9. Dubois, D. and Prade, H., 1988. Possibility Theory - An Approach to the Computerized Processing of Uncertainty. New York: Plenum Press.
10. Dubois, D. and Prade, H., 1999. On fuzzy interpolation. International Journal of General Systems, 28 (2), 103-112.
11. Dubois, D., Prade, H. and Sabbadin, R., 2001. Decision-theoretic foundations of qualitative possibility theory. European Journal of Operational Research, 128 (3), 459-478.
12. Eckenfelder, Jr., W.W., 2000. Industrial Water Pollution Control. 3rd edn. New York: McGraw-Hill.
13. Grigg, N.S., 1985. Water Resources Planning. New York: McGraw-Hill.
14. Haith, A.D., 1982. Environmental Systems Optimiztion. New York: Wiley.
15. Han, D., Cluckie, I. D., Karbassioun, D., Lawry, J. and Krauskop, B., 2002. River flow modelling using fuzzy decision trees. Water Resources Management, 16 (6), 431-445.
16. Hillier, F.S. and Lieberman, G.J., 1986. Introduction to Operations Research. 4th edn. Oakland, CA: Holden-Day.
17. Huang, G.H., 1996. IPWM: an interval parameter water quality management model. Engineering Optimization, 26 (2), 79-103.
18. Huang, G.H., 1998. A hybrid inexact-stochastic water management model. European Journal of Operational Research, 107 (1), 137-158.
19. Huang, G.H. and Chang, N.B., 2003. The perspectives of environmental informatics and systems analysis. Journal of Environmental Informatics, 1 (1), 1-6.
20. Huang, G.H., Baetz, B.W. and Patry, G.G., 1994. Waste flow allocation planning through a grey fuzzy quadratic programming approach. Civil Engineering Systems, 11 (3), 209-243.
21. Huang, G.H., Baetz, B.W. and Patry, G.G., 1995. Grey quadratic programming and its application to municipal waste management planning under uncertainty. Engineering Optimization, 23 (1), 210-223.
22. Inuiguchi, M. and Sakawa, 1994. Possible and necessary optimality tests in possibilistic linear programming problems. Fuzzy Sets and Systems, 67 (1), 29-46.
23. Inuiguchi, M. and Sakawa, M., 1998. Robust optimization under softness in a fuzzy linear programming problem. International Journal of Approximate Reasoning, 18 (1-2), 21-34.
24. Inuiguchi, M. and Tanino, T., 2000. Portfolio selection under independent possibilistic information. Fuzzy Sets and Systems, 115 (1), 83-92.
25. Jairaj, P.G. and Vedula, S., 2000. Multireservoir system optimization using fuzzy mathematical programming. Water Resources Management, 14 (6), 457-472.
26. Kuhn, H.W. and Tucker, A.W., 1951. Nonlinear programming. In: J. Neyman, ed. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, CA: University of California Press, 481-492.
27. Lau, K.K. and Womersley, R.S., 2001. Multistage quadratic stochastic programming. Journal of Computational and Applied Mathematics, 129 (1-2), 105-138.
28. Lee, C.S. and Chang S.P., 2005. Interactive fuzzy optimization for an economic and environmental balance in a river system. Water Research, 39 (1), 221-231.
29. Leung, Y., 1988. Spatial Analysis and Planning Under Imprecision (Studies in Regional Science and Urban Economics). Amsterdam, The Netherlands: Elsevier.
30. Li, Y.P. and Huang, G.H., 2007a. An inexact multistage stochastic quadratic programming method for planning water resources systems under uncertainty. Environmental Engineering Science, 24 (10), 1377-1393.
31. Li, Y.P. and Huang, G.H., 2007b. Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty. International Journal of Systems Science, 38 (5), 219-233.
32. Li, Y.P., Huang, G.H. and Nie, S.L., 2006a. An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty. Advances in Water Resources, 29 (5), 776-789.
33. Li, Y.P., Huang, G.H. and Nie, S.L., 2007. Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning. Engineering Optimization, 39 (2), 163-183
34. Li, Y.P., Huang, G.H., Nie, S.L., Nie, X.H. and Maqsood, I., 2006b. An interval-parameter two-stage stochastic integer programming model for environmental systems planning under uncertainty. Engineering Optimization, 38 (4), 461-483.
35. Liu, L.Z. and Li, Y.Z., 2006. The fuzzy quadratic assignment problem with penalty: new models and genetic algorithm. Applied Mathematics and Computation, 174 (2), 1229-1244.
36. Loucks, D.P., Stedinger, J.R. and Haith, D.A., 1981. Water Resource Systems Planning and Analysis. Englewood Cliffs, NJ: Prentice-Hall.
37. Luhandjula, M.K. and Gupta, M.M., 1996. On fuzzy stochastic optimization. Fuzzy Sets and Systems, 81 (1), 47-55.
38. Luhandjula, M.K., Ichihashi, H. and Inuiguchi, M., 1992. Fuzzy and semi-infinite mathematical programming. Information Science, 61 (3), 233-250.
39. Morgan, D.R., Eheart, J.W. and Valocchi, A.J., 1993. Aquifer remediation design under uncertainty using a new chance constrained programming technique. Water Resources Research, 29 (3), 551-568.
40. Negoita, C.V., Minoiu, S. and Stan, E., 1976. On considering imprecision in dynamic linear programming. Economic Computation and Economic Cybernetics Studies and Research, 3 (1), 83-96.
41. Rockafellar, R.T. and Wets, R.J.-B., 1986.A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming. Mathematic Programming Study, 28, 63-93.
42. Shil'man, S.V., 1992. Stochastic quasigradient method for quadratic optimization under dependent observations. Automation and Remote Control, 53, 1881-1896.
43. Slowinski, R., 1986. A multicriteria fuzzy linear programming method for water supply system development planning. Fuzzy Sets and Systems, 19 (3), 217-237.
44. Soyster, A.L., 1973. Convex programming with set-inclusive constraints: applications to inexact linear programming. Operations Research, 21, 1154-1157.
45. Tang, J. and Wang, D. 1997. An interactive approach based on a genetic algorithm for a type of quadratic programming problems with fuzzy objective and resources. Computers and Operations Research, 24 (5), 413-429.
46. Thomann, R.V. and Mueller, J.A. 1987. Principles of Surface Water Quality Modeling and Control. New York: Harper & Row.
47. Thuesen, H.G., Fabrycky, W.J. and Thuesen, G.J., 1977. Engineering Economy. Englewood Cliffs, NJ: Prentice-Hall.
48. USEPA, 1981. Quality Criteria for Water. Washington, DC: US Environmental Protection Agency.
49. Viessman, Jr., W. and Hammer, M.J., 1998. Water Supply and Pollution Control. 6th edn. Reading, MA: Addison-Wesley.
50. Wu, S.M., Huang, G.H. and Guo, H.C., 1997. An interactive inexact-fuzzy approach for multiobjective planning of water resource systems. Water Science and Technology, 36, 235-242.
51. Zhu, Z.P. and ReVelle, C., 1988. A siting model for regional wastewater treatment systems: the chain configuration case. Water Resources Research, 24 (1), 137-145.
52. Zhu, Z.P. and ReVelle, C., 1990. A cost allocation method for facilities siting with fixed change cost functions. Civil Engineering Systems, 7 (1), 29-38.