The travelling salesperson problem with hotel selection

In this paper, we present the travelling salesperson problem with hotel selection (TSPHS), an extension of the TSP with a number of interesting applications. We present a mathematical formulation, explain the difference with related optimization problems and indicate what makes this problem inherently more difficult. We develop a simple but efficient heuristic that uses two constructive initialization procedures and an improvement procedure consisting of several neighbourhood search operators designed specifically for this problem, as well as some typical neighbourhoods from the literature. We generate several benchmark instances of varying sizes and compare the performance of our heuristic with CPLEX (10.0). We also generate some problems with known optimal solutions and use these to further demonstrate that our heuristic achieves good results in very limited computation times.