A non-assignment problem-based formulation for the asymmetric travelling salesman problem and its variation

In this paper, an exact formulation for the asymmetric travelling salesman problem (ATSP) is presented by approaching it as a single commodity flow problem. This approach is different from existing exact formulations in the literature which are based on the assignment problem (AP), thus, it resolves issues that the AP-based formulations pose for solving certain real world instances by standard integer programming methods such as branch and bound. Moreover, in our computational experiments, half of the total computational time is expended to find the first feasible solution, then it is converged quickly to optimality. In contrast, the AP-based models rapidly computed an initial feasible solution but showed slow convergence to the optimum. Moreover, it is extendable to other variations of the travelling salesman problem (TSP) such as the multiple TSP and the selective TSP.