Selective clustered traveling salesman problem

In this study, we introduce the Selective Clustered Travelling Salesman Problem, an extension of the well-known Travelling Salesman Problem where customers are grouped in clusters, and a profit is associated with each customer. The purpose of this problem is to find the most beneficial tour within a certain time budget, which consists of a subset of clusters and all nodes in each cluster visited on the tour. We formulate the problem as a mixed integer linear programming odel and develop a metaheuristic, using three constructive algorithms, by proposing a problem-specific neighbourhood structures to solve the problem effectively. The proposed algorithm has a sort of large variable neighbourhood search structure. Computational tests are made on benchmark instances with up to 400 vertices. Results show that the mathematical formulation is able to find the optimal solutions of all instances up to 358 vertices. Also, it is found that the proposed algorithm in spite of one parameter unlike the metaheuristics have several, significantly reduces the solution time, and besides, it gives high quality solutions especially for large-size problems.