A Quantum-Levy and variable neighborhood-enhanced metaheuristic for supply hub-based green pickup heterogeneous vehicle routing problem

Abstract

Abstract Due to the growing interest in green logistics and the challenge of just-in-time part logistics, as well as considering the current popularity of supply hub, this paper focuses on a supply hub-based green pickup heterogeneous vehicle routing problem with capacity constraints (CGPHVRP) in the automobile industry. An integer programming model is therefore established, aiming to minimize the total energy consumption for executing all pickup tasks and the total penalty costs imposed on early and late deliveries. The epsilon constraint method is utilized to verify the validity of the proposed model. To solve this problem which is inherently NP-hard, a Quantum-Levy and variable neighborhood-enhanced multi-objective honey badger algorithm (QLVNMHBA) is proposed. Taking advantages of both Quantum behavior and Levy flight, the Quantum-Levy strategy is presented to enhance the exploration. Simultaneously, the adaptive variable neighborhood search including three innovative neighborhood operators is designed to enhance the exploitation and fasten the convergence speed. Furthermore, the convex lens imaging opposition-based learning is applied to initialize the population. Finally, computational experiments reveal that the QLVNMHBA outperforms the other four state-of-the-art algorithms in both solution quality and convergence speed, and the use of heterogeneous fleet could achieve significant reductions in energy consumption over a homogeneous one. Moreover, a specific case is applied to demonstrate the practicality of the proposed model and algorithm.