Comparison of Parallel Implementations of the Branch-and-Bound Method for Shared Memory Systems

Abstract

Four parallel algorithms are considered that implement the branch-and-bound method (BnB) for solving problems of finding a global minimum. The algorithms are designed for computing systems with shared memory. The BnB is based on two basic operations: branching and eliminating. To implement the elimination operation, interval arithmetic is used, which for real intervals defines operations similar to ordinary arithmetic. The main difference between the algorithms lies in the different implementation of storing the list of subproblems. In the process of testing on a representative set of test problems, the speed of the algorithms, their scalability, and their resistance to search anomalies are investigated.