Parallel search in discrete optimization problems

Abstract

We present two generic schemes for heuristic depth-first search on highly parallel MIMD systems. The first one employs a task attraction scheme, where the work packets are generated by splitting the donor's node stack. This stack-splitting scheme works efficiently on architectures with a small communication diameter and/or a moderate number of processing elements. The second scheme, named search-frontier splitting, also employs a task attraction technique, but uses pre-computed work packets that are taken from one level of the state space tree. In a first phase, the nodes of a search-frontier are generated and stored in the processors' local memories. Then, each processor expands its “own” frontier nodes, communicating only when there is no more work on its local stack or when a solution has been found. Our empirical results obtained on a 1024-node MIMD system indicate, that the search-frontier splitting incurs fewer overheads and scales better than stack-splitting — especially on the highly parallel systems. Both schemes are easily portable. They use common PVM message passing primitives and can be applied to a variety of application domains in operations research and artificial intelligence.