On a distributed implementation of a decomposition method for multistage linear stochastic programs

Abstract

Implementation of a parallel decomposition method for solving linear multistage stochastic programming problems in Sun Network is described. The problem is decomposed into a system of subproblems connected in a tree-like structure. The subproblems can execute independently in parallel generating proposals for their predecessors and some backward information for their successors. Information is exchanged asynchronously through special buffers. This is the first truly parallel implementation of the method which was previously tested in multitasking environment. It is shown how the environment for parallel, distributed computations is constructed from the standard tools available in Sun Network and Unix operating system. Issues of communication, distribution of code and distributed semaphores are discussed. The main concepts of implementation are described in detail. The subproblems and the buffers are implemented as Unix processes performing their tasks on the client-server basis. The buffers are the servers ofexchanged information and subproblems may access this information making requests to the server. Numerical tests were performed which show that the method allows substantial reduction of the solution time. The tradeoffs between decomposition and aggregation of the problem are discussed and some alternative methods of allocation of tasks to machines are compared.