Methodology of mining massive data sets for improving manufacturing quality/efficiency
Data mining for design and manufacturing
Approximating networks and extended Ritz method for the solution of functional optimization problems
Journal of Optimization Theory and Applications
Proceedings of the 38th conference on Winter simulation
Approximate Solutions of a Dynamic Forecast-Inventory Model
Manufacturing & Service Operations Management
Efficient sampling in approximate dynamic programming algorithms
Computational Optimization and Applications
A Decision-Making Framework for Ozone Pollution Control
Operations Research
Computational Optimization and Applications
Functional Optimization Through Semilocal Approximate Minimization
Operations Research
Adaptive value function approximation for continuous-state stochastic dynamic programming
Computers and Operations Research
Low-discrepancy sampling for approximate dynamic programming with local approximators
Computers and Operations Research
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In stochastic dynamic programming (SDP) with continuous state and decision variables, the future value function is computed at discrete points in the state spac e. Interpolation can be used to approximate the values of the future value function between these discrete points. However, for large dimensional problems the number of discrete points required to obtain a good approximation of the future value function can be prohibitively large. Statistical methods of experimental design and function estimation may be employed to overcome this "curse of dimensionality." In this paper, we describe a method for estimating the future value function by multivariate adaptive regression splines (MARS) fit over a discretization scheme based on orthogonal array (OA) experimental designs. Because orthogonal arrays only grow polynomially in the state-space dimension, our OA/MARS method is accurately able to solve higher dimensional SDP problems than previously possible. To our knowledge, the most efficient method published prior to this work employs tensor-product cubic splines to approximate the future value function (Johnson et al. 1993). The computational advantages of OA/MA RS are demonstrated in comparisons with the method using tensor-product cubic splines for applications of an inventory forecasting SDP with up to nine state variables computed on a small workstation. In particular, the storage of an adequate tensor-product cubic spline for six dimensions exceeds the memory of our workstation, and the run time for an accurate OA/MARS SDP solution would be at least an order of magnitude faster than using tensor-product cubic splines for higher than six dimensions.