## 2 Literature Review  
The concept of the location-routing problem (LRP) can be traced back to 1961. [PERSON] first discussed the relationship between location selection and transportation cost in transportation problems [15]. LRP and its variants have been studied extensively in the past. [PERSON] and [PERSON] proposed a multi-vehicle and multi-facility warehouse location-routing problem model with vehicle capacity constraints [16]. [PERSON] et al. [17] studied a three-tier distribution system with suppliers, warehouses, and multiple geographically dispersed retailers, where retailers could replenish goods from warehouses and suppliers. A model was established to minimize the long-term average cost within the system while meeting the demand of each retailer. [PERSON] [18] put forward a linear programming model for multi-plan periodic location paths by reasonably defining variables and designed a hybrid evolutionary algorithm to solve it. [PERSON] [19] introduced the damage cost of goods incurred in transit and established a location-route optimisation model considering two-stage transportation cost, damage cost, and penalty cost, and service level. A Genetic Algorithm-Particle Swarm Optimization algorithm was designed to solve the problem. However, the energy consumption cost was not considered in the model. [PERSON] et al. [20] studied the LRP of a multi-journey vehicle path, i.e., considering that the vehicle runs multiple routes within the travel constraint time, and a three-stage heuristic algorithm was designed to solve the problem. [PERSON] et al. [21] build a heterogeneous fleet two-echelon capacitated location-routing model for joint delivery in city logistics. [PERSON] et al. [22] proposed a bi-objective model, and designed an improved algorithm. The effectiveness of the improved algorithm was demonstrated through a comparison. [PERSON] et al. [23] established a location-routing problem model considering a heterogeneous fleet and time windows. A hybrid evolutionary algorithm combining multiple heuristics was designed to solve the problem. [PERSON] et al. [24] considered multiple conditions in the regional low-carbon location-routing problem, such as simultaneous pickup and delivery, time windows. [PERSON] et al. [25] and [PERSON] et al. [26] studied location-routing problem with simultaneous pick-up and delivery. To solve the problem, a simulated annealing (SA) heuristic algorithm was designed and a hyper-heuristic approach based on iterated local search was proposed, respectively. For the cold-chain logistics problems, [PERSON] et al. [27] studied a location model for perishable products in two-tier distribution centers, introduced the cost of goods damage into the objective function, designed an improved genetic algorithm to solve the model, and demonstrated the effectiveness of the model and algorithm through an example. However, the distance studied was calculated using the radial shape of the location and demand points. [PERSON] et al. [28] designed a satisfaction degree function according to service time windows and introduced a minimum envelope clustering analysis method and tabu search algorithm to solve the problem. [PERSON] et al. [29] constructed location inventory routing problem under a demand environment in a cold-chain logistics network, and non-dominatedsorting introduced a multi-objective genetic algorithm (GA). [PERSON] et al. [30] studied a cold-chain logistics distribution network considering carbon footprint, the model of minimum total cost including carbon emission cost was constructed, and a hybrid algorithm was designed to solve the model. Most of the existing LRP research focused on a general logistics distribution network and single-stage location-routing problems.