The pollution traveling salesman problem with refueling

Abstract

This study presents the Pollution Traveling Salesman Problem with Refueling, a novel optimization problem which integrates two recently proposed variants of the Traveling Salesman Problem: the Pollution Traveling Salesman Problem and the Traveling Salesman Problem with Refueling. The proposed problem captures the operational dynamics of a real-world routing scenario involving a single vehicle originating from a central depot and delivering products to end customers. When considering the vehicle’s fuel tank capacity and fuel consumption during the routing process, the need to visit fuel stations for refueling arises. To address this complex problem, a new mixed integer linear programming model was developed, and the Gurobi solver was employed to solve smaller instances. For the effective resolution of larger practical problem cases, a two-stage double adaptive general variable neighborhood search method was proposed. The proposed methodology exhibits comparable efficiency to a commercial solver, demonstrating notably low execution time requirements. To further assess its performance, a comparative study was conducted on TSPLib instances. In comparison to various solution approaches documented in the open literature, encompassing both Variable Neighborhood Search-based and alternative methods, our proposed approach consistently yields highly competitive results within low execution times.