Stochastic Optimization on Computational Grids

Steve Wright
Senior Computer Scientist
Argonne National Laboratory

Stochastic optimization problems arise in many applications, especially those involving planning under uncertainty. When the huge (possibly infinite) number of scenarios is accounted for in the model, the dimensions of these problems may become extremely large. The challenge is not only to solve the problem, but also to estimate the quality of a candidate solution. We describe an asynchronous algorithm for solving two-stage linear programming problems with recourse and its implementation on the computational grid provided by the Condor system. Software tools developed in the metaNEOS and Condor projects are key to the implementation, which has been used to solve instances of unprecedented size. We also describe use of the code to verify recent results concerning convergence of sampled approximations to problems in which the underlying distributions are discrete, and to verify the optimality of candidate solutions. This talk represents joint work with Jeff Linderoth and Alex Shapiro.