Towards Comparative Analysis Of Branch - And - Bound And Nearest Neighbour Algorithms

The branch - and - bound strategy has been used successfully in solving certain categories of combinatorial optimization problems. It has also been viewed as a tool for solving Travelling Salesman Problem (TSP) of moderate size. In this paper a TSP of moderate size is designed, both the brute-force and branch- and - bound approaches are implemented in solving it. The goal is to find out which of those two approaches is more efficient and to further find out how the branch- and- bound method could be refined either as a distinct method or by combining it with some heuristic, with a view to increasing the space of problems it can solve, and the implication of that on its complexity. This paper contains partial results of an on-going research. Hence, only the results of implementation of branch - and -bound, and brute force algorithms are presented. It is hoped that the refinement that is envisioned of the branch - and - bound strategy would be discussed in another paper in the future.