Electric vehicles are environmental transportation modes that are widely applied in green logistics systems. To guarantee the energy efficiency, the impacts of customer service modes and recharging strategies need to be integrated into the optimization of electric logistics resource. This paper proposes an electric vehicle routing problem with mixed backhauls, time windows, and recharging strategies (EVRPMBTW-RS), minimizing the total travel cost with sophisticated constraints on the time-dependent pickup and delivery requests, limited recharging station capacity, and battery remaining capacity of electric vehicles. Mixed service sequences of linehaul and backhaul customers is allocated for the routing planning, with the synchronous optimization of recharging strategies including the selection of recharging stations and determination of recharging time. A time-discretized multi-commodity network flow model is constructed based on an extended space-time-state modeling framework, which is formulated as a quadratic 0-1 programming model by using the augmented Lagrangian relaxation technique. After the dualization and linearized transformation, we decompose the model into a sequence of least-cost path subproblems based on the alternating direction multiplier method (ADMM). The subproblems are alternately minimized and solved using the time-dependent forward dynamic programming algorithm. The solution quality can be guaranteed through calculating the optimality gap between the best lower bound and upper bound for each iteration. The proposed solution approach is examined on examples of a simple 7-node network and real-world Yizhuang road network. This paper provides a theoretical foundation for the route optimization method of electric logistics vehicles, and contributes to improve the operational efficiency of electric logistics systems.

电动汽车是广泛应用于绿色物流系统的环境运输方式。为了保证能源效率，需要将客户服务模式和充电策略的影响整合到电力物流资源的优化中。本文提出了一种具有混合回程，时间窗和充电策略（EVRPMBTW-RS）的电动汽车路由问题，该方法通过在与时间有关的取货和交付请求，有限的充电站容量和电池剩余量等复杂约束条件下最大程度地降低了总行驶成本电动汽车的容量。将线路回程和回程客户的混合服务序列分配给路由规划，同步优化充电策略，包括选择充电站和确定充电时间。基于扩展的时空建模框架，建立了时间离散的多商品网络流模型，利用扩展的拉格朗日松弛技术将其建模为二次0-1规划模型。经过对偶化和线性化变换后，我们基于交替方向乘数法（ADMM）将模型分解为一系列成本最低的路径子问题。使用与时间有关的前向动态规划算法，可以将子问题交替最小化和求解。通过为每次迭代计算最佳下限和上限之间的最佳差距，可以保证解决方案的质量。本文以简单的7节点网络和真实世界的亦庄公路网为例，研究了提出的解决方案方法。本文为电力物流车辆的路径优化方法提供了理论基础，为提高电力物流系统的运行效率做出了贡献。