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Volumn 34, Issue 1, 2007, Pages 70-90

Neural network and regression spline value function approximations for stochastic dynamic programming

Author keywords

Design of experiments; Inventory forecasting; Latin hypercube; Markov decision process; Orthogonal array; Statistical modeling; Water reservoir management

Indexed keywords

APPROXIMATION THEORY; DECISION MAKING; DYNAMIC PROGRAMMING; NEURAL NETWORKS; RANDOM PROCESSES; REGRESSION ANALYSIS; RESERVOIRS (WATER); VALUE ENGINEERING;

EID: 33746257756     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2005.02.043     Document Type: Article
Times cited : (45)

References (64)
  • 1
    • 0003787146 scopus 로고
    • Princeton University Press, Princeton
    • Bellman R.E. Dynamic programming (1957), Princeton University Press, Princeton
    • (1957) Dynamic programming
    • Bellman, R.E.1
  • 4
    • 0018501971 scopus 로고
    • Optimal management of a multireservoir water supply system
    • Gal S. Optimal management of a multireservoir water supply system. Water Resources Research 15 (1979) 737-748
    • (1979) Water Resources Research , vol.15 , pp. 737-748
    • Gal, S.1
  • 5
    • 0019896959 scopus 로고
    • Optimal integrated control of univoltine pest populations with age structure
    • Shoemaker C.A. Optimal integrated control of univoltine pest populations with age structure. Operations Research 30 (1982) 40-61
    • (1982) Operations Research , vol.30 , pp. 40-61
    • Shoemaker, C.A.1
  • 6
    • 0022153573 scopus 로고
    • Real applications of Markov decision processes
    • White D.J. Real applications of Markov decision processes. Interfaces 15 6 (1985) 73-83
    • (1985) Interfaces , vol.15 , Issue.6 , pp. 73-83
    • White, D.J.1
  • 7
    • 0002075766 scopus 로고
    • Further real applications of Markov decision processes
    • White D.J. Further real applications of Markov decision processes. Interfaces 18 5 (1988) 55-61
    • (1988) Interfaces , vol.18 , Issue.5 , pp. 55-61
    • White, D.J.1
  • 8
    • 0024158874 scopus 로고
    • Gradient dynamic programming for stochastic optimal control of multidimensional water resources systems
    • Foufoula-Georgiou E., and Kitanidis P.K. Gradient dynamic programming for stochastic optimal control of multidimensional water resources systems. Water Resources Research 24 (1988) 1345-1359
    • (1988) Water Resources Research , vol.24 , pp. 1345-1359
    • Foufoula-Georgiou, E.1    Kitanidis, P.K.2
  • 10
    • 0141575686 scopus 로고    scopus 로고
    • Chen VCP, Günther D, Johnson EL. Solving for an optimal airline yield management policy via statistical learning. Journal of the Royal Statistical Society, Series C 2003; 52(1):1-12.
  • 13
    • 0344873950 scopus 로고
    • Parallel processing of stochastic dynamic programming for continuous state systems with linear interpolation
    • Eschenbach E.A., Shoemaker C.A., and Caffey H. Parallel processing of stochastic dynamic programming for continuous state systems with linear interpolation. ORSA Journal on Computing 7 (1995) 386-401
    • (1995) ORSA Journal on Computing , vol.7 , pp. 386-401
    • Eschenbach, E.A.1    Shoemaker, C.A.2    Caffey, H.3
  • 15
    • 0001820934 scopus 로고    scopus 로고
    • Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming
    • Chen V.C.P., Ruppert D., and Shoemaker C.A. Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming. Operations Research 47 (1999) 38-53
    • (1999) Operations Research , vol.47 , pp. 38-53
    • Chen, V.C.P.1    Ruppert, D.2    Shoemaker, C.A.3
  • 16
    • 0033612096 scopus 로고    scopus 로고
    • Application of MARS and orthogonal arrays to inventory forecasting stochastic dynamic programs
    • Chen V.C.P. Application of MARS and orthogonal arrays to inventory forecasting stochastic dynamic programs. Computational Statistics and Data Analysis 30 (1999) 317-341
    • (1999) Computational Statistics and Data Analysis , vol.30 , pp. 317-341
    • Chen, V.C.P.1
  • 17
    • 0036013020 scopus 로고    scopus 로고
    • Measuring the goodness of orthogonal array discretizations for stochastic programming and stochastic dynamic programming
    • Chen V.C.P. Measuring the goodness of orthogonal array discretizations for stochastic programming and stochastic dynamic programming. SIAM Journal of Optimizations 12 (2001) 322-344
    • (2001) SIAM Journal of Optimizations , vol.12 , pp. 322-344
    • Chen, V.C.P.1
  • 18
    • 0002432565 scopus 로고
    • Multivariate adaptive regression splines (with discussion)
    • Friedman J.H. Multivariate adaptive regression splines (with discussion). Annals of Statistics 19 (1991) 1-141
    • (1991) Annals of Statistics , vol.19 , pp. 1-141
    • Friedman, J.H.1
  • 19
    • 0026900479 scopus 로고
    • Calibration of nonlinear solid-state sensor arrays using multivariate regression techniques
    • Carey W.P., and Yee S.S. Calibration of nonlinear solid-state sensor arrays using multivariate regression techniques. Sensors and Actuators, B. Chemical B9 2 (1992) 113-122
    • (1992) Sensors and Actuators, B. Chemical , vol.B9 , Issue.2 , pp. 113-122
    • Carey, W.P.1    Yee, S.S.2
  • 20
    • 0031224956 scopus 로고    scopus 로고
    • Statistical techniques for the classification of chromites in diamond exploration samples
    • Griffin W.L., Fisher N.I., Friedman J.H., and Ryan C.G. Statistical techniques for the classification of chromites in diamond exploration samples. Journal of Geochemical Exploration 59 3 (1997) 233-249
    • (1997) Journal of Geochemical Exploration , vol.59 , Issue.3 , pp. 233-249
    • Griffin, W.L.1    Fisher, N.I.2    Friedman, J.H.3    Ryan, C.G.4
  • 21
    • 0034282783 scopus 로고    scopus 로고
    • Combining non-parametric models with logistic regression. an application to motor vehicle injury data
    • Kuhnert P.M., Do K.-A., and McClure R. Combining non-parametric models with logistic regression. an application to motor vehicle injury data. Computational Statistics and Data Analysis 34 3 (2000) 371-386
    • (2000) Computational Statistics and Data Analysis , vol.34 , Issue.3 , pp. 371-386
    • Kuhnert, P.M.1    Do, K.-A.2    McClure, R.3
  • 22
    • 0036242834 scopus 로고    scopus 로고
    • Development of reflectance spectral libraries for characterization of soil properties
    • Shepherd K.D., and Walsh M.G. Development of reflectance spectral libraries for characterization of soil properties. Soil Science Society of America Journal 66 3 (2002) 988-998
    • (2002) Soil Science Society of America Journal , vol.66 , Issue.3 , pp. 988-998
    • Shepherd, K.D.1    Walsh, M.G.2
  • 23
    • 0027010219 scopus 로고
    • Deriving corrosion knowledge from case histories: the neural network approach
    • Smets H.M.G., and Bogaerts W.F.L. Deriving corrosion knowledge from case histories: the neural network approach. Materials & Design 13 3 (1992) 149-153
    • (1992) Materials & Design , vol.13 , Issue.3 , pp. 149-153
    • Smets, H.M.G.1    Bogaerts, W.F.L.2
  • 24
    • 0027883618 scopus 로고
    • Failure prediction of fibre-reinforced materials with neural networks
    • Labossiere P., and Turkkan N. Failure prediction of fibre-reinforced materials with neural networks. Journal of Reinforced Plastics and Composites 12 12 (1993) 1270-1280
    • (1993) Journal of Reinforced Plastics and Composites , vol.12 , Issue.12 , pp. 1270-1280
    • Labossiere, P.1    Turkkan, N.2
  • 26
    • 0033951434 scopus 로고    scopus 로고
    • Issues regarding artificial beural network modeling for reactors and fermenters
    • Chen V.C.P., and Rollins D.K. Issues regarding artificial beural network modeling for reactors and fermenters. Bioprocess Engineering 22 (2000) 85-93
    • (2000) Bioprocess Engineering , vol.22 , pp. 85-93
    • Chen, V.C.P.1    Rollins, D.K.2
  • 27
  • 28
    • 0035965535 scopus 로고    scopus 로고
    • Prediction of the molecular weight for a vinylidene chloride/vinyl chloride resin during shear-related thermal degradation in air by using a back-propagation artificial neural network
    • Liu J. Prediction of the molecular weight for a vinylidene chloride/vinyl chloride resin during shear-related thermal degradation in air by using a back-propagation artificial neural network. Industrial and Engineering Chemistry Research 40 24 (2001) 5719-5723
    • (2001) Industrial and Engineering Chemistry Research , vol.40 , Issue.24 , pp. 5719-5723
    • Liu, J.1
  • 29
    • 0035166839 scopus 로고    scopus 로고
    • Use of neural network models to predict industrial bioreactor effluent quality
    • Pigram G.M., and Macdonald T.R. Use of neural network models to predict industrial bioreactor effluent quality. Environmental Science and Technology 35 1 (2001) 157-162
    • (2001) Environmental Science and Technology , vol.35 , Issue.1 , pp. 157-162
    • Pigram, G.M.1    Macdonald, T.R.2
  • 30
    • 0036172679 scopus 로고    scopus 로고
    • Neural network based representation of UH-60A pilot and hub accelerations
    • Kottapalli S. Neural network based representation of UH-60A pilot and hub accelerations. Journal of the American Helicopter Society 47 1 (2002) 33-41
    • (2002) Journal of the American Helicopter Society , vol.47 , Issue.1 , pp. 33-41
    • Kottapalli, S.1
  • 32
    • 67649635624 scopus 로고    scopus 로고
    • A review of design and modeling in computer experiments
    • Khattree R., and Rao C.R. (Eds), Elsevier Science, Amsterdam
    • Chen V.C.P., Tsui K.-L., Barton R.R., and Allen J.K. A review of design and modeling in computer experiments. In: Khattree R., and Rao C.R. (Eds). Handbook of statistics. statistics in industry vol. 22 (2003), Elsevier Science, Amsterdam 231-261
    • (2003) Handbook of statistics. statistics in industry , vol.22 , pp. 231-261
    • Chen, V.C.P.1    Tsui, K.-L.2    Barton, R.R.3    Allen, J.K.4
  • 34
    • 0027642557 scopus 로고
    • Comparison of two nonparametric estimation schemes. MARS and neural networks
    • De Veaux R.D., Psichogios D.C., and Ungar L.H. Comparison of two nonparametric estimation schemes. MARS and neural networks. Computers & Chemical Engineering 17 8 (1993) 819-837
    • (1993) Computers & Chemical Engineering , vol.17 , Issue.8 , pp. 819-837
    • De Veaux, R.D.1    Psichogios, D.C.2    Ungar, L.H.3
  • 35
    • 0033348590 scopus 로고    scopus 로고
    • Automatic learning using neural networks and adaptive regression
    • Pham D.T., and Peat B.J. Automatic learning using neural networks and adaptive regression. Measurement and Control 32 9 (1999) 270-274
    • (1999) Measurement and Control , vol.32 , Issue.9 , pp. 270-274
    • Pham, D.T.1    Peat, B.J.2
  • 36
    • 33746255710 scopus 로고    scopus 로고
    • Palmer KD. Data collection plans and meta models for chemical process flowsheet simulators. PhD dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA, 1998.
  • 40
    • 33746211643 scopus 로고    scopus 로고
    • Baglietto M, Cervellera C, Sanguineti M, Zoppoli R. Water reservoirs management under uncertainty by approximating networks and learning from data. In: Topics on participatory planning and managing water systems. Amsterdam: Elsevier Science Ltd., 2005, to appear.
  • 42
    • 33746211649 scopus 로고    scopus 로고
    • Heath DC, Jackson PL. Modelling the evolution of demand forecasts with application to safety stock analysis in production/distribution systems. Technical report #989, School of Operations Research & Industrial Engineering, Cornell University, Ithaca, NY, 1991.
  • 43
    • 0030618794 scopus 로고    scopus 로고
    • An aggregate stochastic dynamic programming model of multireservoir Systems
    • Archibald T.W., McKinnon K.I.M., and Thomas L.C. An aggregate stochastic dynamic programming model of multireservoir Systems. Water Resources Research 33 (1997) 333-340
    • (1997) Water Resources Research , vol.33 , pp. 333-340
    • Archibald, T.W.1    McKinnon, K.I.M.2    Thomas, L.C.3
  • 44
    • 0042744948 scopus 로고
    • Exact and approximate solutions of affine reservoirs models
    • Lamond B.F., and Sobel M.J. Exact and approximate solutions of affine reservoirs models. Operations Research 43 (1995) 771-780
    • (1995) Operations Research , vol.43 , pp. 771-780
    • Lamond, B.F.1    Sobel, M.J.2
  • 45
    • 0019716203 scopus 로고
    • A decomposition method for the long-term scheduling of reservoirs in series
    • Turgeon A. A decomposition method for the long-term scheduling of reservoirs in series. Water Resources Research 17 (1981) 1565-1570
    • (1981) Water Resources Research , vol.17 , pp. 1565-1570
    • Turgeon, A.1
  • 46
    • 0020335699 scopus 로고
    • Dynamic programming applications in water resources
    • Yakowitz S. Dynamic programming applications in water resources. Water Resources Research 18 (1982) 673-696
    • (1982) Water Resources Research , vol.18 , pp. 673-696
    • Yakowitz, S.1
  • 48
    • 0011458175 scopus 로고
    • Hypercubes of strength 'd' leading to confounded designs in factorial experiments
    • Rao C.R. Hypercubes of strength 'd' leading to confounded designs in factorial experiments. Bulletin of the Calcutta Mathematical Society 38 (1946) 67-78
    • (1946) Bulletin of the Calcutta Mathematical Society , vol.38 , pp. 67-78
    • Rao, C.R.1
  • 51
    • 0001290271 scopus 로고
    • Hadamard matrices and their applications
    • Hedayat A.S., and Wallis W.D. Hadamard matrices and their applications. Annals of Statistics 6 (1978) 1184-1238
    • (1978) Annals of Statistics , vol.6 , pp. 1184-1238
    • Hedayat, A.S.1    Wallis, W.D.2
  • 54
    • 0023331258 scopus 로고    scopus 로고
    • Lippmann RP. An introduction to computing with neural nets. IEEE ASSP Magazine (1987) 4-22.
  • 57
    • 0000243355 scopus 로고
    • Learning in neural networks. a statistical perspective
    • White H. Learning in neural networks. a statistical perspective. Neural Computation 1 (1989) 425-464
    • (1989) Neural Computation , vol.1 , pp. 425-464
    • White, H.1
  • 59
    • 0002983776 scopus 로고
    • Statistical aspects of neural networks
    • Barndorff-Nielsen O.E., Jensen J.L., and Kendall W.S. (Eds), Chapman & Hall, New York
    • Ripley B.D. Statistical aspects of neural networks. In: Barndorff-Nielsen O.E., Jensen J.L., and Kendall W.S. (Eds). Networks and chaos-statistical and probabilistic aspects (1993), Chapman & Hall, New York 40-123
    • (1993) Networks and chaos-statistical and probabilistic aspects , pp. 40-123
    • Ripley, B.D.1
  • 60
    • 84972539015 scopus 로고
    • Neural networks. a review from a statistical perspective (with discussion)
    • Cheng B., and Titterington D.M. Neural networks. a review from a statistical perspective (with discussion). Statistical science 9 (1994) 2-54
    • (1994) Statistical science , vol.9 , pp. 2-54
    • Cheng, B.1    Titterington, D.M.2
  • 61
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory 39 (1993) 930-945
    • (1993) IEEE Transactions on Information Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 64
    • 0028543366 scopus 로고
    • Training feedforward networks with the Marquardt algorithm
    • Hagan M.T., and Menhaj M. Training feedforward networks with the Marquardt algorithm. IEEE Transaction on Neural Networks 5 (1994) 989-993
    • (1994) IEEE Transaction on Neural Networks , vol.5 , pp. 989-993
    • Hagan, M.T.1    Menhaj, M.2


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