Effect of the selection of branch variables in parallel branch and bound method

Abstract

SUMMARYThe branch and bound method is a solution method which is used in deriving the optimal solution for combinatorial optimization problems. The parallel implementation of the branch and bound method is considered, aiming at expansion of the range of applicable problems. With recent advances in PCs and network technology, there have been studies of the parallel branch and bound method in a metacomputing environment, which differs from conventional parallel computers. It is difficult in the branch and bound method to identify the effective strategy for each sample problem beforehand, since the behavior of the program is different in each case. In this study, the following method is considered in order to determine whether it is possible to foresee the effective strategy. Some feasible problems in the meta-computing environment are first solved by several different strategies, and the effective strategy is identified. Then, the identified strategy is used to reduce the later processing time. As a real sample problem, a program for the parallel branch and bound method was prepared to solve the traveling salesman problem. The scheme for branch variable selection was varied. The method that derives an optimal solution, and the method that searches all optimal solutions with the same evaluation value are compared in terms of computation time and acceleration.