Abstract
In modelling and managing complex environmental systems, inherent uncertainties of all relevant natural processes are to be taken into consideration. In the present paper diverse stochastic modelling and optimization approaches for handling such problems (primarily in the field of water quality analysis and control) are highlighted, drawing on the findings of case studies and real-world applications.
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References
J. Alcamo, L. Hordijk, J. Kamari, P. Kauppi, M. Posch and E. Runca, Integrated analysis of acidification in Europe, J. Envir. Manag. 21 (1985) 47–61.
V.I. Arkin, A.N. Shiriaev and R.J.-B. Wets (eds.),Stochastic Optimization (Springer, Berlin/Heidelberg/New York, 1986).
G.F. Bayley and J.M. Hammersley, The effective number of independent observations in an autocorrelated time series, J. Roy. Statist. Soc., Series 1B, 8 (1946) 184–197.
M.B. Beck, Water quality modelling: A review of the analysis of uncertainty, Water Resources Res. 23 (1987) 1393–1442.
M.B. Beck and G. van Straten (eds.),Uncertainty and Forecasting in Water Quality (Springer, Berlin/Heidelberg/New York, 1983).
J.O. Berger,Statistical Decision Theory and Bayesian Analysis (Springer, Berlin/Heidelberg/New York, 1985).
J.R. Birge and R.J.-B. Wets, Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse, Math. Progr. Study 27 (1986) 54–102.
J.G. Boon, J. Pintér and L. Somlyódy, A new stochastic approach for controlling point source river pollution, in.Closing the Gap between Theory and Practice (Proc. Baltimore Symp.), Publications of the International Association of Hydrologic Societies No. 180 (1989) pp. 141–149.
D. Braess,Nonlinear Approximation Theory (Springer, Berlin/Heidelberg/New York, 1986).
D.H. Burn and E.A. McBean, Optimization modeling of water quality in an uncertain environment, Water Resources Res. 21 (1985) 934–940.
K.-W. Chen and A.S. Papadopoulos, A nonparametric method for estimating the joint probability density of BOD and DO, Ecological Modelling 41 (1988) 183–191.
W.G. Cochran,Sampling Techniques (Wiley, New York, 1962).
R. Cooke and J. Pintér, Optimization in risk management, Civil. Eng. Sys. 6 (1989) 122–128.
M.H. De Groot,Optimal Statistical Decisions (McGraw-Hill, New York, 1970).
R. Dorfman, H.D. Jacoby and H.A. Thomas, (eds.),Models for Managing Regional Water Quality (Harvard University Press, Cambridge, 1972).
M.A.H. Dempster (ed.),Stochastic Programming (Academic Press, London, 1980).
J. Dupačová, The minimax approach to stochastic programming and an illustrative application, Stochastics 20 (1987) 73–88.
J.H. Ellis, Stochastic water quality optimization using imbedded chance constraints, Water Resources Res. 23 (1987) 2227–2238.
J.H. Ellis, E.A. McBean and G.J. Farquhar, Chance constrained/stochastic linear programing model for acid rain abatement I. Complete colinearity and noncolinearity, Atmospheric Environment 19 (1985) 925–937.
J.H. Ellis, E.A. McBean and G.J. Farquhar, Chance constrained/stochastic linear programing model for acid rain abatement II. Limited colinearity, Atmospheric Environment 20 (1986) 501–511.
Yu.M. Ermoliev,Stochastic Programming Methods (Nauka, Moscow (1976) (in Russian).
Yu.M. Ermoliev and R.J.-B. Wets (eds.),Numerical Techniques for Stochastic Optimization (Springer, Berlin/Heidelberg/New York, 1988).
J. Fehér and J. Pintér, Analysis and management of non-point source pollution: The Rakaca Creek watershed case study, Research Report, VITUKI, Budapest (1986) (in Hungarian).
S.D. Flåm and J. Pintér, Selecting oil exploration strategies: Some stochastic problem formulations and solution methods, Research Report CMI 852611-1, Christian Michelsen Institute, Fantoft, Bergen, Norway (1985).
O. Fujiwara, S.K. Gnanendran and S. Ohgaki, Chance constrained model for river water quality management, J. Env. Eng. Div. ASCE 113 (1987) 1018–1031.
D.A. Haith,Environmental Systems Optimization (Wiley, New York, 1982).
J.D. Hendrickson, S. Sorooshian and L.E. Brazil, Comparison of Newton-type and direct search algorithms for calibration of conceptual rainfall-runoff models, Water Resources Res. 24 (1988) 691–700.
E. Henley and H. Kumamoto,Reliability Engineering and Risk Assesment (Prentice-Hall, Englewood Cliffs, 1981).
C.L. Hwang and A.S.M. Masud,Multiple Objective Decision Making-Methods and Applications (Springer, Berlin/Heidelberg/New York, 1980).
G. Jolánkai and J. Pintér, Water quality and management modelling of non-point source pollution — a case study, in:Monitoring to Detect Changes in Water Quality (Proc. Budapest Symp.) Publications of the International Association of Hydrologic Societies No. 157 (1986) pp. 197–206.
P. Kall,Stochastic Linear Programming (Springer, Berlin/Heidelberg/New York, 1976).
P. Kall, Stochastic programming with recourse: upper bounds and moment problems, Research Report, Institute for Operations Research, University of Zürich (1987).
P. Kall and A. Prékopa (eds.),Recent Results in Stochastic Programming (Springer, Berlin/Heidelberg/New York, 1980).
W.K. Klein Haneveld,Duality in Stochastic Linear and Dynamic Programming (Springer, Berlin/Heidelberg/New York, 1986).
P.R. Kleindorfer and H.C. Kunreuther, (eds.),Insuring and Managing Hazardous Risks: From Seveso to Bhopal and Beyond (Springer, Berlin/Heidelberg/New York, 1987).
L. Koncsos and J. Pintér, Optimal real-time operation of reservoirs, Research Report, VITUKI, Budapest (1988) (in Hungarian).
C. Loehle, Robust parameter estimation for nonlinear models, Ecological Modelling 41 (1988) 41–54.
D.P. Loucks, J.R. Stedinger and D.A. Haith,Water Resources Systems Planning and Analysis (Prentice-Hall, Englewood Cliffs, 1981).
W. Novotny and G. Chesters,Handbook of Nonpoint Pollution (Van Nostrand Reinhold, New York, 1982).
G.T. Orlob (ed.),Mathematical Modeling of Water Quality: Streams, Lakes and Reservoirs (Wiley, New York, 1983).
P.M. Pardalos and J.B. Rosen,Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science 268 (Springer, Berlin/Heidelberg, 1987).
J. Pintér, Globally convergent methods forn-dimensional multiextremal optimization, Optimization 17 (1986) 187–202.
J. Pintér, Extended univariate algorithms forn-dimensional global optimization, Computing 36 (1986) 91–103.
J. Pintér, A conceptual optimization framework for regional acidification control, Sys. Anal., Modelling, Simulation 4 (1987) 213–226.
J. Pintér, Branch-and-bound methods for solving global optimization problems with Lipschitzian structure, Optimization 19 (1988) 101–110.
J. Pintér, Solving nonlinear equation systems via global partition and search: Some experimental results, Computing 43 (1990) 309–323.
J. Pintér, Deterministic approximations of probability inequalities, ZOR—Methods and Models of Operations Research, Series Theory 33 (1989) 219–239.
J. Pintér, Lipschitzian global optimization: Theory and applications, Research Report 90.020, RIZA, Lelystad (1990).
J. Pintér, P. Benedek and A. Darázas, Risk management of accidental water pollution: An illustrative application, Water Sci. Technol. 22 (1990) 265–274.
J. Pintér and G. Pesti, Set partition by globally optimized cluster seed points, Eur. J. Oper. Res. 51 (1991) to appear.
J. Pintér and L. Somlyódy, A stochastic lake eutrophication management model, in: Stochastic Optimization, eds. Arkin, Shiriaev and Wets (Springer, Berlin/Heidelberg/New York, 1986) pp. 501–512.
J. Pintér and L. Somlyódy, Optimization of regional water quality monitoring strategies, Water Sci. Technol. 19 (1987) 721–727.
J. Pintér, J. Szabó and L. Somlyódy, Multiextremal optimization for calibrating water resources models, Env. Software 1 (1986) 98–105.
B.T. Poljak, Nonlinear programming methods in the presence of noise, Math. Progr. 14 (1978) 87–97.
A. Prékopa, Contributions to the theory of stochastic programming, Math. Progr. 4 (1973) 202–221.
A. Prékopa and R.J.-B. Wets (eds.),Stochastic Programming, Mathematical Programming Study, vols. 27–28 (1986).
M.L. Richardson (ed.),Risk Assessment of Chemicals in the Environment (The Royal Society of Chemistry, London, 1988).
T.G. Sanders (ed.),Design of Water Quality Monitoring Networks (Colorado State University Press, Fort Collins, CO, 1979).
T. Schilperoort and S. Groot, Design and optimization of water quality monitoring networks, Research Report 268, Delft Hydraulics Laboratory, Delft, The Netherlands (1983).
L. Somlyódy, Modeling a complex environmental system: The Lake Balaton case study, Math. Modelling 3 (1982) 481–502.
L. Somlyódy and G. van Straten (eds.),Modeling and Managing Shallow Lake Eutrophication (Springer, Berlin/Heidelberg/New York, 1986).
L. Somlyódy and R.J.-B. Wets, Stochastic optimization models for lake eutrophication management, CP-85-16, IIASA, Laxenburg, Austria (1985) (Appeared also in Oper. Res. (1988).)
I. Takács and J. Pintér, Optimization of biological waste-water treatment processes, Research Report, VITUKI, Budapest (1988) (in Hungarian).
A.A. Törn and A. Žilinskas,Global Optimization (Springer, Berlin/Heidelberg/New York, 1989).
Y.-K. Tung and W.E. Hathhorn, Probability distribution for critical DO location in streams, Ecological Modelling 42 (1988) 61–74.
R.J.-B. Wets, Stochastic programming: Solution techniques and approximation schemes, in:Mathematical Programming: The State of the Art, eds. A. Bachem, M. Grötschel and B. Korte (Springer, Berlin/Heidelberg/New York, 1983) pp. 566–603.
D.B. Yudin,Problems and Methods of Stochastic Programming (Sovietskoye Radio, Moscow, 1980) (in Russian).
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Pintér, J. Stochastic modelling and optimization for environmental management. Ann Oper Res 31, 527–544 (1991). https://doi.org/10.1007/BF02204868
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DOI: https://doi.org/10.1007/BF02204868