A Distributed Implementation of Asynchronous Parallel Branch and Bound

Abstract

Branch-and-bound is a popular method for searching an optimal solution in the scope of discrete optimization. It consists of a heuristic iterative tree search and its principle lies in successive decompositions of the original problem in smaller disjoint subproblems until an optimal solution is found. In this paper, we propose new models to implement branch-and-bound in parallel, where several subproblems are concurrently decomposed at each iteration. In our shared data-object model processors communicate through a distributed shared memory that allows subproblems to be totally or partially ordered. We show that a variation from the synchronous to asynchronous parallel branch-and-bound allows optimizations of the operations over the data structure that improve their performance and, possibly, the overall performance as well. Finally, some experiments are described that corroborate our theoretical previsions.

This work was partially supported by DRET and the project Stratagème of the French CNRS. It was done in relation to the ESPRIT III — HCM project SCOOP — Solving Combinatorial Optimization Problems in Parallel.