Approximate and exact algorithms for an energy minimization traveling salesman problem

Shijin Wang (1) , Ming Liu (2) , Feng Chu (3, 4)

1 School of Economics & Management
2 School of Economics and Management
3 IBISC - Informatique, BioInformatique, Systèmes Complexes
4 School of Economics and Management

Energy saving is a great challenge for clean transportation. In this paper, we study the Energy Minimization Traveling Salesman Problem (EMTSP), which is a generation of the classical Traveling Salesman Problem (TSP), and an important theoretical basis and a special case of the Energy Minimization Vehicle Routing Problem (EMVRP). The objective of the studied problem is to minimize the sum of the product of load (including curb weight of the vehicle) and traveled distances. An approximation algorithm based on the Christofides's Heuristic is proposed and its worst-case ratio bound is proven. A branch and bound (B&B) algorithm integrated with a fast 1-tree based lower bound is developed to obtain optimal solutions. The results of computational experiments show the efficiency and the effectiveness of the B&B algorithm, as well as the heuristic methods.

Keywords: Energy minimization; Approximation algorithm; Branch and bound; Traveling salesman problem; Christofides's heuristic

Domains: Operations Research [math.OC]

Shijin Wang, Ming Liu, Feng Chu. Approximate and exact algorithms for an energy minimization traveling salesman problem. Journal of Cleaner Production, 2020, 249, pp.119433. ⟨10.1016/j.jclepro.2019.119433⟩. ⟨hal-02427206⟩