Solution of Traveling Salesman Problem with Hotel Selection in the framework of MILP-tropical optimization

In this paper, Traveling Salesman Problem with Hotel Selection (TSPHS), an extension of the Traveling Salesman Problem (TSP) has been considered. A mathematical formulation has been presented in the framework of Mixed Integer Linear Programming (MILP). Subsequently, the problem has been formulated in the novel framework of tropical mathematics and a strategy to obtain exact solution has been proposed. The performance of the proposed solution, in terms of the optimality and computational time requirement, has been compared with the solution strategies available in literature including traditional MILP. The results indicate that the proposed solution strategy not only leads to optimal results but also is computationally much more efficient.