The asymmetric M-travelling salesmen problem: A duality based branch-and-bound algorithm

Abstract This paper presents a new model and branch-and-bound algorithm for the asymmetric m-travelling salesmen problem. The algorithm uses a Lagrangean relaxation, a subgradient algorithm to solve the Lagrangean dual, a greedy algorthim for obtaining minimal m-trees, penalties to strengthen the lower bounds on candidate problems, and a new concept known as staged optimization. Computational experience for problems having up to 100 cities is presented.