Parallel Branch and Bound Algorithm - A comparison between serial, OpenMP and MPI implementations

This paper presents a comparison of an extended version of the regular Branch and Bound algorithm previously implemented in serial with a new parallel implementation, using both MPI (distributed memory parallel model) and OpenMP (shared memory parallel model). The branch-and-bound algorithm is an enumerative optimization technique, where finding a solution to a mixed integer programming (MIP) problem is based on the construction of a tree where nodes represent candidate problems and branches represent the new restrictions to be considered. Through this tree all integer solutions of the feasible region of the problem are listed explicitly or implicitly ensuring that all the optimal solutions will be found. A common approach to solve such problems is to convert sub-problems of the mixed integer problem to linear programming problems, thereby eliminating some of the integer constraints, and then trying to solve that problem using an existing linear program approach. The paper describes the general branch and bound algorithm used and provides details on the implementation and the results of the comparison.