PySP: modeling and solving stochastic programs in Python

Although stochastic programming is a powerful tool for modeling decisionmaking under uncertainty, various impediments have historically prevented its widespread use. One key factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of deterministic models, which are often formulated first. A second key factor relates to the difficulty of solving stochastic programming models, particularly the general mixed-integer, multi-stage case. Intricate, configurable, and parallel decomposition strategies are frequently required to achieve tractable run-times. We simultaneously address both of these factors in our PySP software package, which is part of the COIN-OR Coopr open-source Python project for optimization. To formulate a stochastic program in PySP, the user specifies both the deterministic base model and the scenario tree with associated uncertain parameters in the Pyomo open-source algebraic modeling language. Given these two models, PySP provides two paths for solution of the corresponding stochastic program. The first alternative involves writing the extensive form and invoking a standard deterministic (mixed-integer) solver. For more complex stochastic programs, we provide an implementation of Rockafellar and Wets’ Progressive Hedging algorithm. Our particular focus is on the use of Progressive Hedging as an effective heuristic for approximating Jean-Paul Watson Sandia National Laboratories Discrete Math and Complex Systems Department PO Box 5800, MS 1318 Albuquerque, NM 87185-1318 E-mail: [email protected] David L. Woodruff Graduate School of Management University of California Davis Davis, CA 95616-8609 E-mail: [email protected] William E. Hart Sandia National Laboratories Computer Science and Informatics Department PO Box 5800, MS 1318 Albuquerque, NM 87185-1318 E-mail: [email protected]