Best-first branch-and bound on a hypercube

Abstract

The branch-and-bound technique is a common method for finding exact solutions to difficult problems in combinatorial optimization. This paper will discuss issues surrounding implementation of a particular branch-and-bound algorithm for the traveling-salesman problem on a hypercube multi-computer. The natural parallel algorithm is based on a number of asynchronous processes which interact through a globally shared list of unfinished work. In a distributed-memory environment we must find a non-centralized version of this shared data structure. In addition, detecting termination of the computation is tricky; an algorithm will be presented which ensures proper termination. Finally, issues affecting performance will be discussed.