# Electric-Vehicle Routing Planning Based on the Law of Electric Energy Consumption
## 1 Introduction  
As a result of rapid economic development and the continuous growth in the population, human demand for fossil fuels is also increasing, which is leading to a situation of environmental pollution and energy crises. A major cause of air pollution is the large quantity of emissions from fuel combustion vehicles, which rely on fossil fuels for energy. According to statistics, the total emissions from automobiles in China have shown a trend of continuous growth, increasing over the last decade from 37.706 million tons to 39.393 million tons at an average annual growth rate of 0.9%, which has placed tremendous pressure on the environment [1]. In addition, China has now become the world's largest energy consumer, and nearly 70% of its oil is consumed by fuel combustion vehicles [2]. As a result of this growth trend, the shortage of energy may become a major obstacle to China's economic development in the future. Therefore, China has announced research to meet the schedule of banning fuel combustion vehicles to reach carbon neutralization in the next 50 years. New energy vehicles, especially pure electric vehicles, have become the main strategic direction of auto industry transformation. Urban logistics account for a significant proportion of the use of fuel combustion vehicles. In addition, the need for frequent and efficient cargo delivery has continuously grown as a result of the fast development of the e-commerce industry in recent years. In response to national policies, the urban logistics industry has considered pure electric vehicles (EVs) as a major alternative to fuel combustion vehicles (CVs), as EVsproduce no greenhouse gas emissions during operation. However, the operation of EVs has been challenged by their special characteristics: (1) compared to CVs, EVs have shorter driving mileage, which causes the problem of \"the anxiety of mileage\"; (2) EVs cannot complete a long-distance task without recharging; (3) under current technology, EVs take more time to refuel than CVs; and (4) there is a complex nonlinear relationship between the energy consumption of electric vehicles and many factors such as vehicle parameters, driving distance, vehicle load, driving conditions, and the external environment. Because of these features, the traditional vehicle routing problem (VRP) is no longer applicable for EVs. Therefore, it is of great necessity to formulate an appropriate EV routing model to plan reasonable routes and improve delivery efficiency, and extra attention should be given to the energy consumption process of EVs in realistic operations. In this work, we first analyze the main factors affecting the energy consumption of EVs and generate two typical driving conditions of EVs in suburban and urban areas. Then, we construct a nonlinear electric battery consumption model based on EVs' driving cycles to mimic real-life energy consumption. Furthermore, we propose our Electric Vehicle Routing Problem with Time Windows Based on Driving Cycles (EVRPTW-DC) to determine minimum-cost routes for a fleet of EVs to serve a given set of customers from a distribution center. To solve EVRPTW-DC, we design an adaptive particle swarm optimization algorithm. In the case studies, instances of different scales are set up with realistic operational data. Experiments are conducted for both EVRPTW-DC and EVRPTW under the linear energy consumption law (L-EVRPTW). Optimal routes from both models are compared and we find that delivery paths of L-EVRPTW are usually inferior to those of EVRPTW-DC due to battery capacity violation. We further explore the applicability of EVPRTW-DC and discuss the conditions of using a linear electric energy consumption coefficient. The paper is organized as follows. In Section 2, a review of EVRPTW-DC-related literature is presented. In Section 3, we analyze the driving cycles of EVs and construct the nonlinear energy consumption model, which is then incorporated into the EVRPTW-DC model in Section 4. Section 5 describes the particle swarm algorithm.