Scalable parallel Benders decomposition for stochastic linear programming

Abstract

We develop a scalable parallel implementation of the classical Benders decomposition algorithm for two-stage stochastic linear programs. Using a primal-dual, path-following algorithm for solving the scenario subproblems we develop a parallel implementation that alleviates the difficulties of load balancing. Furthermore, the dual and primal step calculations can be implemented using a data-parallel programming paradigm. With this approach the code effectively utilizes both the multiple, independent processors and the vector units of the target architecture, the Connection Machine CM-5. The, usually limiting, master program is solved very efficiently using the interior point code LoQo on the front-end workstation. The implementation scales almost perfectly with problem and machine size. Extensive computational testing is reported with several large problems with up to 2 million constraints and 13.8 million variables.