Talk Abstract:

Optimization of Uncertain Dynamic Systems: Algorithms and Applications to Hydropower Reservoirs, Inventory Problems

Christine Shoemaker
School of Civil and Environmental Engineering and Center for Applied Mathematics
Cornell University
cas12@cornell.edu

This talk will discuss methods the author has developed with her students and co-workers to incorporate statistical procedures (splines, experimental design and regression) into a Stochastic Dynamic Programming (SDP) algorithm to greatly increase the efficiency of SDP for nonlinear systems with greater than three continuous state variables. This talk will discuss the use of tensor product cubic splines and stochastic dynamic programming applied to a system of n=5 hydropower reservoirs (Johnson et al, Oper. Res.), 1993 , which showed that highly accurate SDP results could be obtained 400 times faster using tensor product cubic splines than the conventional interpolation methods. A more recent application using orthogonal arrays and Mars regression (Chen et al, Oper. Res. 1999) is shown to be even more efficient (for both CPU time and memory) for larger systems (i.e. n>7). In this case a nine dimensional stochastic dynamic programming model is solved for an inventory problem on a single processor of a computer that is slower than current PC's. Current research is focused on improvements in this method and application to systems of hydropower reservoirs.

Part I of the talk

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