A three-phase algorithm for the pollution traveling Salesman problem

Abstract

This paper studies a variant of the Pollution Traveling Salesman Problem (PTSP) focused on fuel consumption and pollution emissions (PTSPC). The PTSPC generalizes the well-known Traveling Salesman Problem (TSP), classified as NP-Hard. In the PTSPC, a vehicle must deliver a load to each customer through a Hamiltonian cycle, minimizing an objective function that considers the speed of each edge, the mass of the truck, the mass of the load pending delivery, and the distance traveled. We have proposed a three-phase algorithm for the PTSPC. The first phase solves the Traveling Salesman Problem (TSP) exactly with a time limit and heuristically using a Nearest Neighborhood Search approach. This phase considers the constraints associated with the PTSPC by using commercial software. In the second phase, both the obtained solutions and their inverse sequences from the initial phase undergo enhancement utilizing metaheuristic algorithms tailored for the PTSPC. These algorithms include Variable Neighborhood Search (VNS), Tabu Search (TS), and Simulated Annealing (SA). Subsequently, for the third phase, the best solution identified in the second phase—determined by having the minimum value by the PTSPC objective function—is subjected to resolution by a mathematical model designed for the PTSPC, considering the heuristic emphasis of commercial software. The efficiency of the former algorithm has been validated through experimentation involving the adaptation of instances from the Pollution Routing Problem (PRP) to the PTSPC. This approach demonstrates the capacity to yield high-quality solutions within acceptable computing times.