The green vehicle routing problem is a variation of the classic vehicle routing problem in which the transportation fleet is composed of electric vehicles with limited autonomy in need of recharge during their duties. As an NP-hard problem, this problem is very difficult to solve. In this paper, we first propose a memetic algorithm (MA)—a population-based algorithm—to tackle this problem. To be more specific, we incorporate an adaptive local search procedure based on a reward and punishment mechanism inspired by reinforcement learning to effectively manage the multiple neighborhood moves and guide the search, an effective backbone-based crossover operator to generate the feasible child solutions to obtain a better trade-off between intensification and diversification of the search, and a longest common subsequence-based population updating strategy to effectively manage the population. The purpose of this research is to propose a highly effective heuristic for solving the green vehicle routing problem and bring new ideas for this type of problem. Experimental results show that our algorithm is highly effective in comparison with the current state-of-the-art algorithms. In particular, our algorithm is able to find the best solutions for 84 out of the 92 instances. Key component of the approach is analyzed to evaluate its impact on the proposed algorithm and to identify the appropriate search mechanism for this type of problem.

The growing concerns about human pollution has motivated practitioners and researchers to focus on the environmental and social impacts of logistics and supply chains. In this paper, we consider the environmental impact of carbon dioxide emission on a vehicle routing problem with multiple depots. We present a hybrid evolutionary algorithm (HEA) to tackle it by combining a variable neighborhood search and an evolutionary algorithm. The proposed hybrid evolutionary algorithm includes several distinct features such as multiple neighborhood operators, a route-based crossover operator, and a distance- and quality-based population updating strategy. The results from our numerical experiments confirm the effectiveness and superiority of the proposed HEA in comparison with the best-performing methods in the literature and the public exact optimization solver CPLEX. Furthermore, an important aspect of the HEA is studied to assess its effect on the performance of the HEA.

We prove that a cyclic coordinate fixed point algorithm for nonexpansive mappings when the underlying Hilbert space is decomposed into a Cartesian product of finitely many block spaces is weakly convergent to a fixed point of the mapping under investigation. Our result relaxes a condition imposed on the stepsizes of Theorem 3.4 of Chow, et al [Chow, Y. T., Wu, T. and Yin, W., Cyclic coordinate-update algorithms for fixed-point problems: analysis and applcations, SIAM J. Sci. Comput., 39 (2017), No. 4, A1280–A1300].