Abstract
A new nonlinear programming algorithm is proposed for stochastic programming problems. This method relies on sampling to estimate the probabilistic objective function and constraints. The computational burden of excessive model calculations for determining the search direction is bypassed through a reweighting method using Kernel Density Estimation. The improvements accomplished by this algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS) are presented through two real world case studies involving parameter design for off-line quality control of a chemical reactor, and optimal capacity expansion for electric utilities in uncertain markets.
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References
Birge, J.R. and F. Louveaux. (1997). Introduction to Stochastic Programming. New York: Springer.
Charnes, A. and W.W. Cooper. (1959). “Chance-Constrained Programming.” Management Science 5, 73–79.
Dantzig, G.B. and G. Infanger. (1991). “Large Scale Stochastic Linear Programs-Importance Sampling and Bender Decomposition.” In Brezinski and U. Kulisch (eds.), Computational and Applied Mathematics, pp. 111–119.
Davidon, W.C. (1991). “Variable Metric Method for Minimization.” SIAM Journal of Optimization 1, 1–17.
Dempster, M.A.H. (1988). “On Stochastic Programming II: Dynamic Problems under Risk.” Stochastics 25, 15–22.
Hesterberg, T. (1995). “Weighted Average Importance Sampling Defensive Mixture Distributions.” Technometrics 37, 185–194.
Hesterberg, T. (1996). “Estimate and Confidence Intervals for Importance Sampling Sensitivity Analysis.” Mathematical and Computer Modeling 23(8-9), 79–86.
Higle, J.L. and S. Sen. (1991). “Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse.” Mathematics of Operations Research 16, 650–669.
Kalagnanam, J.R. and U.M. Diwekar. (1997). “An Efficient Sampling Technique for Off-Line Quality Control.” Technometrics 39, 308–319.
Ku, A. (1995). “Modelling Uncertainty in Electricity Capacity Planning.” Ph.D. Thesis, University of Lon-don, London Business School, 445 p.
Louveaux, F. and Y. Smeers. (1988). “Optimal Investments for Electricity Generation: A Stochastic Model and Test-Problem.” In Numerical Techniques for Stochastic Optimization.Springer Series in Computational Mathematics, Vol. 445, pp. 33–64. Berlin: Springer.
Rockafellar, R.T. and R.J.-B. Wets. (1976). “Stochastic Convex Programming: Basic Duality.” Pacific Journal of Mathematics 63, 173–195.
Rockafellar, R.T. and R.J.-B. Wets. (1991). “Scenarios and Policy Aggregation in Optimization under Uncertainty.” Mathematics of Operations Research 16, 119–147.
Rubin, E.S., J.R. Kalagnanam, H.C. Frey and M.B. Berkenpas. (1997). “Integrated Environmental Control Modeling (IECM) of Coal-Fired Power Systems.” Journal of Air and Waste Management Association 47, 1180–1191.
Ruszczynski, A. (1986). “A Regularized Decomposition for Minimizing a Sum of Polyhedral Functions.” Mathematical Programming 35, 309–333.
Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. Boca Raton: Chapman & Hall (CRC Reprint, 1998).
Taguchi, G. (1986). Introduction to Quality Engineering. Tokyo: Asian Productivity Center.
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Sahin, K.H., Diwekar, U.M. Better Optimization of Nonlinear Uncertain Systems (BONUS): A New Algorithm for Stochastic Programming Using Reweighting through Kernel Density Estimation. Ann Oper Res 132, 47–68 (2004). https://doi.org/10.1023/B:ANOR.0000045276.18995.c8
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DOI: https://doi.org/10.1023/B:ANOR.0000045276.18995.c8