## 1 Introduction  
Logistics distribution in cities has the characteristics of multi-variety [1], small-batch and multi-frequency [2]. The transportation and distribution of related products require more costs and vehicles, consume more energy and emit more carbon dioxide. Take waste management as an example. Traditional waste management generally leads to unnecessary waste collection or collection delay, thus increasing the annual collection cost by about 70%. Inefficient route planning also leads to an increase in the number of collection vehicles sent, road traffic volume and fuel volume of vehicles [3], which directly lead to an increase in carbon emissions. The use of multi-compartment vehicles (MCVs) is increasing in actual logistics [4], which can meet the logistics service needs of separate loading and joint distribution of different kinds of products. The application of these MCVs facilitates the joint distribution of multi-variety, small-batch and multi-frequency products in the city, such as the collection of solid waste [3], the distribution of perishable products [5] and the transportation of medical waste [6]. Compared with ordinary single-compartment vehicles(SCVs), MCVs have obvious advantages in cost reduction [4] and energy conservation and emission reduction [3]. Continuing to take waste management as an example, the application of ordinary SCVs will increase the number of vehicles and increase the fuel burden. But the application of MCVs can reduce cross-infection between wastes and carbon emissions [3]. In an experiment of source-separated waste collection in Shanghai, China, the joint collection of MCVs (multiple wastes collected by one type of MCV) reduced carbon dioxide emissions by 24.54 kg and costs by 5720.73 CNY compared with the separate collection of SCVs (multiple wastes collected by multiple types of SCVs) [7]. The broad application prospect of MCVs in many fields of urban traffic lays a realistic foundation for the multi-compartment vehicle routing problem (MCVRP) [4]. The corresponding multi-compartment vehicle routing planning has become a research hotspot in the field [8]. Therefore, compared with the capacitated vehicle routing problem (CVRP) model (based on SCVs), it is more appropriate to use the MCVRP model (based on MCVs) to study the problem. However, with the development of cities, environmental pollution and traffic congestion problems have appeared in many cities [9], which make urban traffic unsustainable. The application of MCVs in urban logistics has to face traffic congestion problems and be constrained by carbon emission reduction policies. Correspondingly, the study of MCVRP also needs to consider the impact of traffic congestion and the constraint of emission reduction policies. On the one hand, the problem of urban traffic congestion is increasingly serious [10], which prolongs the travel time of vehicles, increases the energy consumption of vehicles and ultimately increases the carbon emissions of urban traffic [11; 12; 13]. For example, the operation of urban traffic has a great impact on the carbon emissions of motor vehicles, and the carbon emissions under mild traffic congestion are 4.51 times that under smooth traffic [14]. On the other hand, the transportation industry, as one of the three major carbon emission industries, is the main implementation and constraint field of energy conservation and emission reduction policies. Carbon emissions from the transport sector (from energy consumption) account for 16.2-25% of global carbon emissions. Among them, path planning is the main content of transportation, and inefficient path planning will increase energy consumption and carbon emissions [3]. In China, green and low-carbon action in transportation has been listed as one of the ten actions in the Carbon Peak Action Plan by 2030 [15]. Internationally, the combined application of carbon tax policy and carbon trading policy has gradually become the choice of energy conservation and emission reduction for relevant industries with high carbon emissions [16].