Abstract: With the continuous development of logistics industry, the number of logistics transportation vehicles is increasing, and the use of traditional fuel vehicle caused a certain pressure to the environment. In recent years, because of the characteristics of energy conservation and environmental protection, logistics electric vehicles have been widely used. However, due to the electric vehicle has to charging for a long time and the development present situation of transportation industry, the electric vehicle is currently not completely replace the traditional fuel vehicle, the two kinds of vehicles will exist in the field of logistics distribution. The open multi-depot distribution vehicle routing problem with fuel vehicle and electric vehicle as distribution vehicles is research topic of this paper. The goal is to minimize total distribution costs, which including carbon emission cost, transportation cost and time window penalty cost. A linear programming mathematical model is established. For the NP-hard characteristic, an improved particle swarm optimization algorithm is designed. The theory of good-point set is employed in the particle swarm optimization algorithm for generating initial population to increase the diversity of particle swarm optimization algorithm. In iteration phase of the particle swarm optimization, in order to achieve the global optimal, the random neighborhood strategy is provided to avoid the particle swarm into local optimum. Finally, a numerical example is designed to test. The results show that the improved particle swarm optimization algorithm is superior to the standard particle swarm optimization algorithm. By analyzing the costs obtained by the two algorithms, it is concluded that the ratio of the total cost obtained by the improved particle swarm optimization algorithm is 5.69% lower than that obtained by the standard particle swarm optimization algorithm, which proves the effectiveness of the improved particle swarm optimization algorithm designed in this paper. The number of traditional fuel vehicle used considering the carbon cost is declined compared to without considering the cost of carbon emissions, and the total cost of open hybrid VRP is less than the cost of closed-loop hybrid VRP.

Key words: Decision optimization and control technology; Vehicle routing optimization; Particle swarm optimization; The mixed fleet; Multi-depot distribution; Joint optimization

摘要： 随着物流行业的迅速发展，物流运输车辆不断增加，而传统燃油汽车的使用对环境造成了 一定的压力，近年来，物流电动汽车由于其节能环保的特性，得到了广泛的应用。然而由于电动 汽车的充电时间较长以及运输行业的发展现状，电动汽车目前无法完全取代传统燃油汽车，两种 车型同时存在于物流配送领域。文章针对半开放式多配送中心的燃油汽车和电动汽车混合车型的 车辆路径优化问题进行研究，同时考虑了客户需求量、车辆载重量以及电动汽车的充电需求等约 束条件，以碳排放成本、运输成本以及时间窗惩罚成本之和最小为目标建立线性整数规划数学模 型，针对该问题的 NP 难特性，设计了改进的粒子群算法进行求解。应用佳点集理论产生初始种群， 增加粒子群算法的多样性，在迭代过程中，增加局部搜索策略，避免粒子群算法陷入局部最优。 实验结果表明：改进的粒子群算法获得的总成本相比标准粒子群算法获得的总成本降低 5.69%，证 明了该设计的改进粒子群算法在求解开放式混合车型车辆路径优化问题时的有效性；相比于不考 虑碳排放的情况，考虑碳排放时传统燃油车的使用数量有所下降；相比于单一配送中心路径优化 情况，开放式的多配送中心路径优化，更有利于降低物流成本。

关键词: 决策优化与控制技术；车辆路径优化；粒子群算法；混合车型；多配送中心；联合优化