An interface design for general parallel branch-and-bound algorithms

Abstract

Abstract. Branch-and-Bound algorithms are general methods applicable to various combinatorial optimization problems. There are two hopeful methods to improve the algorithms. One is development of the algorithms which exploit the structure of each problem. The other is parallelization of the algorithms. These two methods have been studied by different research communities independently. If a well-designed interface separating the two kinds of implementation of the methods clearly could be constructed, it would enable us to adapt latest algorithms or technology easily. In this paper, we propose a small and simple interface design of a generalized system for parallel branch-and-bound algorithms.Key words: parallel processing, combinatorial optimization problem, branchand-bound algorithms. IntroductionBranch-and-bound algorithms are general methods applicable to various combinatorial optimization problems. These algorithms are search-based techniques that enumerate the entire solution space implicitly. In order to perform this enumeration efficiently, it is necessary to limit the number of feasible solutions that need to be explicitly produced. This process can be accomplished by clever algorithms, which exploit the structure of each problem, and many complicated algorithms have been proposed for each problem. We call implementations of such algorithms problem depending implementation. Unfortunately, even if such procedures are applied, some instances of the problems cannot be solved in a reasonable amount of time. Parallelization is one of the most hopeful methods to accelerate the enumeration speed. We consider high-level parallelism of such algorithms. In such kinds of applications of parallelism, generality of the branch-and-bound algorithm framework should be maintained. Therefore, it is reasonable to develop a generalized system that provides the general framework of the parallel branch-and-bound algorithms and some facilities to make use of it. There are several architectures of parallel computers and several ways to map the framework on a architecture of them. Therefore, many implementations of high-level parallelism should be considered. We call an implementation of the parallelism parallelization architecture depending implementation.