Optimization method for location selection of battery swap cabinets for electric bicycles in food delivery scenarios

Abstract

The present invention discloses a method for optimizing the location path of a battery swap cabinet for electric bicycles in a takeaway delivery scenario, including S11, determining the problem objectives and constraints; S12, determining the symbolic representation of parameters and variables; S13, establishing a mathematical model; S21, determining the main problem; S22, determining the pricing sub-problem; S31, encoding and evaluating the solution; S32, initialization phase design; S33, branch and bound method phase design; S34, column generation method phase design; S35, label algorithm phase design. When optimizing the location path of a battery swap cabinet, the present invention considers the impact of multiple parking lots and battery swap cabinet capacity design on the location path strategy from the perspective of practical applications, constructs a battery swap cabinet location path optimization model with the goal of minimizing total cost, and uses an improved branch pricing algorithm to solve the optimization model.

Description

Technical Field

[0001] The present invention belongs to the technical field of logistics optimization and relates to a method for optimizing the site selection path of a battery swap cabinet for electric bicycles in a takeout delivery scenario. Background Art

[0002] The delivery optimization problems of express delivery, take-out, fresh food, etc. in urban logistics can be collectively referred to as the vehicle routing problem. The vehicle routing problem is a typical NP-hard problem. At present, the research on solution methods mainly focuses on meta-heuristic methods and exact algorithms. Among them, the branch-and-price algorithm, as a classic exact algorithm, was first formally proposed by Desrosiers. This algorithm combines the column generation method with the branch-and-bound method to solve the vehicle routing problem, which is an integer programming problem. Summary of the invention

[0003] The purpose of the present invention is to provide a method for optimizing the location path of a battery swap cabinet in a takeaway delivery scenario with multiple parking lots, which specifically considers the impact of the location and capacity allocation of the battery swap cabinet on the operating cost. The method uses an improved branch pricing algorithm to solve this problem.

[0004] The technical solution includes the following steps:

[0005] S10, establishing a battery swap cabinet location path optimization model;

[0006] S20, establishing a set partitioning model;

[0007] S30, solution algorithm for the design model;

[0008] Wherein, S10 specifically includes the following steps:

[0009] S11, determine the problem objectives and constraints;

[0010] S12, determine the symbolic representation of parameters and variables;

[0011] S13, establishing a mathematical model;

[0012] S20 specifically includes the following steps:

[0013] S21, determine the main problem;

[0014] S22, determine the pricing sub-problem;

[0015] S30 specifically includes the following steps:

[0016] S31, solution coding and evaluation;

[0017] S32, initialization phase design;

[0018] S33, branch and bound stage design;

[0019] S34, column generation method stage design;

[0020] S35, labeling algorithm stage design.

[0021] Preferably, S11 determines the problem objective and constraints, wherein the objective is to minimize the total cost. The specific problem description is as follows: a multi-distribution center and directed network G = (V, A), V represents a set of logistics nodes in the network, including multiple distribution centers, a group of customer nodes and a group of candidate battery swap cabinet nodes, and A represents an arc set of the distribution network; wherein the customer's demand, location, and the location of the candidate battery swap cabinet are all known, and each distribution center has an equal-sized takeaway delivery fleet equipped with the same model of electric mopeds; based on actual conditions, it is assumed that the distribution center is equipped with a battery swap cabinet and has a sufficient number of batteries in reserve, the driver starts from the distribution center with a full charge, and returns to the distribution center of departure after serving a group of customers; each electric vehicle has a maximum loading capacity, so the total demand for a vehicle to serve customers shall not exceed its maximum loading capacity; during the delivery process, each electric vehicle has an average Balance the use of electricity and keep the remaining level of electricity within the preset range. Therefore, electric vehicles need to go to the battery swap cabinet to swap batteries. Regarding the setting of the battery swap cabinet, two operational issues are involved, namely the location in terms of candidate node selection and the design capacity in terms of available battery swapping. The integration of delivery route arrangement, the location of battery swap stations and the battery distribution between multiple sites ensures the operational performance of the delivery system. It is assumed that the replaced battery cannot be used on the same day after being charged in the battery swap cabinet. Therefore, in order to meet the battery swap needs of all food delivery drivers within a day, the scale of the battery swap station, that is, the number of batteries configured for the battery swap cabinet, should be greater than the number of battery swaps of electric vehicles in the battery swap cabinet. The total cost consists of two parts, the cost of deploying the battery swap cabinet at the candidate battery swap cabinet node, and the transportation cost incurred by all electric vehicles. The problem aims to make decisions on vehicle routes, the location of the battery swap cabinet and the amount of battery storage at the same time to minimize the total cost.

[0022] Preferably, the step S12, determining symbolic representations of parameters and variables, comprises:

[0023]

[0024] Preferably, the step S13 is to establish a mathematical model; specifically, to establish a mathematical model for vehicle path optimization:

[0025]

[0026] Objective function (1) aims to calculate the total cost, with the goal of minimizing the sum of the cost of building a battery swap station and the transportation cost of the electric vehicle fleet, and finding the path with the lowest cost, the location of the battery swap station and the capacity allocation; constraint (2) ensures that each customer node that needs to be served during each delivery process has a vehicle visiting it and that the vehicle leaves after the service is completed; constraint (3) ensures that electric vehicles only replace batteries at locations where battery swap stations have been built; constraint (4) ensures that the flow of each vehicle at all nodes is balanced, that is, a vehicle must leave after visiting a node; constraint (5) indicates that vehicles departing from a distribution center must return to the distribution center and cannot go to other distribution centers; constraint (6) indicates that electric vehicles leaving the distribution center can be assigned to a route at most once to serve the corresponding customers; constraint (7) indicates a vehicle quantity limit, which means that the number of vehicles participating in the delivery of each distribution center should be less than the predetermined fleet size, because some vehicles may be arranged as standby; constraint (8) specifies the number of vehicles that should be configured in the battery swap station. The number of batteries is limited, and it needs to meet the battery replacement needs of all electric vehicles visiting the battery swap station. Constraint (8) tracks the remaining load of the electric vehicle at each node based on the driving path sequence of the electric vehicle; constraint (9) limits the range of the remaining load of the electric vehicle at each node; constraint (10) tracks the time when the electric vehicle arrives at each node based on the driving path sequence of the electric vehicle; constraint (11) ensures that the time when the delivery person starts to serve the customer meets the customer's time window; constraint (12) tracks the remaining power of the electric vehicle at each node based on the driving path sequence of the electric vehicle; constraint (13) indicates that the electric vehicles all start from the distribution center in a fully charged state; constraint (14) indicates that the battery power level of the electric vehicle is reset to Q after visiting the battery swap station; constraint (15) ensures that the electric vehicle does not consume battery power when serving the customer point; constraint (16) ensures that the battery power of the electric vehicle remains above the safety line during delivery; constraint (17) represents the binary nature of the decision variable.

[0027] Preferably, the step S21, determining the main problem, specifically includes:

[0028] Let R be the set of all feasible paths that satisfy the constraints of the pricing subproblem, c r is the total cost of the path r∈R; let the symbol pair (r,s) be used to represent the correspondence between the route and the distribution center, s represents the distribution center to which the route belongs; let the binary variable The symbol pair (r, s) represents the specific information of the path; if the vehicle goes from node i to node j in path r, then Otherwise, it is 0; if the path represented by (r, s) is adopted in the final solution, the binary decision variable Otherwise it is 0; if path r passes through node i, then the binary variable Otherwise, 0;

[0029]

[0030] Therefore, the specific formula of the main problem is as follows:

[0031]

[0032] The objective function (20) aims to find a set of feasible paths containing BSS construction planning with the minimum cost as the goal; constraint (21) ensures that each customer is visited once; constraint (22) ensures that the number of vehicles used by each distribution center does not exceed the actual number; constraint (23) defines the binary decision variables;

[0033] The number of feasible paths contained in R of the master problem is very large. One column represents a feasible path. It is difficult to solve the master problem containing all columns. Therefore, we simplify the master problem into a restricted master problem based on the column generation method. Let Ω represent the set of all feasible paths generated in the current restricted master problem.

[0034]

[0035] Preferably, the S22, determining the pricing sub-problem, is specifically:

[0036] The purpose of this pricing subproblem is to find a feasible path with a negative test number attached to the restricted main problem. The pricing subproblem is essentially a shortest path problem with resource constraints. Its objective function is closely related to the dual information of the restricted main problem. The constraint is to ensure that a vehicle completes a delivery task under the premise of satisfying the resource constraints. The specific formula of the pricing subproblem is as follows:

[0037]

[0038] Constraints(4)-(6)and(8)-(16) (26)

[0039] The objective function (25) represents the number of tests of a feasible path, where is the modified cost of arc (i,j), λ b is the fixed unit capacity and operating cost of the battery swap cabinet, π i and σ s They correspond to the dual variables of constraints (21) and (22) of the restricted main problem respectively. Constraint (26) includes the vehicle flow balance constraint in the context of multiple distribution centers, vehicle load constraint, power constraint and time window constraint. Only when the objective function value is less than 0, the new column obtained from the pricing subproblem can be added to the restricted main problem for iteration to make the objective function of the main problem better.

[0040] Preferably, the encoding and evaluation of the solution in S31 is as follows: the solution to the site selection path optimization problem is composed of the driving paths of all vehicles, and the solution to the problem is represented by natural number encoding.

[0041] Preferably, the S32 initialization phase is designed;

[0042] Specifically, the generation of the initial solution is divided into two stages. In the first stage, the distance greedy heuristic is used to determine the vehicle path. First, a vehicle is enabled. The vehicle starts from the distribution center and inserts the unserved customer points closest to the current vehicle in sequence without considering the electric vehicle mileage limit and the battery swap cabinet selection strategy. When the load constraint is not met, the vehicle returns to the distribution center. Then another vehicle is enabled to repeat the above operation until all customer points are inserted into the vehicle path. In the second stage, based on the path generated in the first stage and the electric vehicle mileage constraint, the greedy heuristic battery swap cabinet selection method is used to locate and allocate the battery swap cabinet. This method is to insert the battery swap station node into the solution so that all sub-paths meet the battery power constraint and obtain a complete battery swap station selection and allocation decision. The set of sub-paths in the solution is defined as R = {r 1 ,r 2 ,r 3 ,…,r |K|}, the subpath is represented by r k ={o,v 1 ,…,v n ,o′}, for each non-empty subpath r k , each node in the path must determine in turn whether the vehicle violates the battery power constraint when visiting; create a list This list is used to store the nodes that currently have the potential to affect the insertion decision of the swap station. If a node v that violates the constraint is encountered * , v * Previously, nodes at the battery swap station or distribution center were added in sequence. Then, from Starting from the first node in , generate a feasible battery swap station set F v , that is, the vehicle satisfies the battery power constraint when arriving at any battery swap station in the set. If the feasible battery swap station set is empty, the next node is calculated until the feasible battery swap station set of a node is not empty. Define F v The insertion cost of the swap station i after being inserted into the node v is: ΔC iv =β 1 (d v,i +d v+1,i -d v,v+1 )+β 2 d v+1,i +β 3 ρλ f , where β 1 , β2 and β 3 is a weight coefficient between 0 and 1, β 1 +β 2 +β 3 =1; v+1 is the next node after node v in the solution, ρ is a binary variable, which takes the value of 1 when the battery swap station i is in the selected state in the solution, otherwise it takes the value of 0. The insertion cost of the battery swap station is considered to be d v+1,i The purpose is to avoid the vehicle from going to the built battery swap station far away from node v+1 as much as possible, so that the vehicle has a higher remaining power when it arrives at node v+1, which improves the utilization efficiency of the battery and may reduce the subsequent demand for battery swapping. v Select the battery swap station with the lowest insertion cost i * Insert into the solution node v, then clear Then, starting from the inserted battery swap station node, continue to determine whether the subsequent nodes violate the battery power constraint; repeat the above operation until the nodes of all sub-paths meet the battery power constraint.

[0043] Preferably, in the design of the S33 branch and bound method stage, an arc-based branching strategy is adopted.

[0044] Preferably, the method of solving the integer solution by combining the branch strategy with the column generation algorithm comprises the following steps:

[0045] Step 1: Initialize the valid feasible path set, generate the initial restricted relaxed master problem, and record it in the root node;

[0046] Step 2: Initialize the search tree and add the root node;

[0047] Step 3: Use the depth-first search strategy to select node N from the search tree, and use the information of node N to generate the restricted relaxed master problem;

[0048] Step 4: Use the column generation algorithm to solve the restricted relaxed master problem and obtain the solution X;

[0049] Step 5: If the solution X is an integer solution, go to Step 6; otherwise, go to Step 7;

[0050] Step 6: Compare the objective function value of solution X with the current upper bound. If it is less than the upper bound, update the upper bound value. Otherwise, perform pruning and go to Step 8.

[0051] Step 7: If the objective function value of the floating point solution X is less than the current upper bound, select an arc for branching according to the arc branching strategy, generate two left and right child nodes to add to the search tree, and delete the current node. Otherwise, perform pruning;

[0052] Step8: If the search tree is not empty, go to Step3; otherwise, go to Step9;

[0053] Step9: The current upper bound is the optimal integer solution.

[0054] The beneficial effects of the present invention are as follows:

[0055] When optimizing the site selection path of a battery swap cabinet, the present invention considers the impact of multiple parking lots and battery swap cabinet capacity design on the site selection path strategy from the perspective of practical applications, constructs a battery swap cabinet site selection path optimization model with the goal of minimizing total cost, and uses an improved branch pricing algorithm to solve the optimization model.

[0056] The present invention can not only enable logistics companies to plan drivers' delivery routes more reasonably under limited resources, help companies improve delivery efficiency and save delivery costs, but also enable the route planning process to take into account the site selection and capacity allocation strategy of the battery swap station, and reasonably reduce the investment cost of the company in infrastructure. Both aspects are of great significance to improving the competitiveness of enterprises. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of a method for optimizing the location path of a battery swap cabinet for electric bicycles in a takeaway delivery scenario according to an embodiment of the present invention;

[0058] Figure 2 This is a problem example diagram of a method for optimizing the location path of a battery swap cabinet for electric bicycles in a takeaway delivery scenario according to an embodiment of the present invention;

[0059] Figure 3 This is a comparison chart of the solution time of the improved branch pricing algorithm and the standard branch pricing algorithm for the battery swap cabinet site selection path optimization method for electric bicycles in the food delivery scenario of an embodiment of the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0061] On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims. Further, in order to make the public have a better understanding of the present invention, some specific details are described in detail in the detailed description of the present invention below. Those skilled in the art can fully understand the present invention without the description of these details.

[0062] The specific technical solution of the present invention includes: S10, establishing a vehicle path optimization model;

[0063] S11, determine the problem objectives and constraints;

[0064] The optimization goal of the present invention is to minimize the total cost. The specific problem is described as follows: a multi-distribution center and directed network G = (V, A), V represents a set of logistics nodes in the network, including multiple distribution centers, a group of customer nodes and a group of candidate battery exchange cabinet nodes, and A represents an arc set in the network. Among them, the customer's needs, location, and the location of the candidate battery exchange cabinet are all known, and each distribution center has an equal-sized takeaway delivery fleet equipped with the same model of electric mopeds. According to the actual situation, it is assumed that the distribution center is equipped with a battery exchange cabinet and reserves a sufficient number of batteries. The driver starts from the distribution center with a full charge and returns to the distribution center at the time of departure after serving a group of customers. Each electric vehicle has a maximum loading capacity, so the total demand for a vehicle to serve customers shall not exceed its maximum loading capacity. During the distribution process, each electric vehicle needs to balance the use of electricity and maintain a relatively safe level of remaining electricity. Therefore, in order to improve the distribution efficiency, electric vehicles need to go to some battery exchange cabinets for battery exchange. Regarding the setting of the battery exchange cabinet, two operational issues are generally involved, namely the position in the selection of candidate nodes and the design capability in the exchange of available batteries. The integration of delivery route scheduling, battery swap station locations, and battery allocation between multiple sites ensures the operational performance of the delivery system. Assuming that the replaced battery cannot be used on the same day after being charged in the battery swap cabinet, in order to meet the battery swap needs of all food delivery drivers within a day, the scale of the battery swap station, that is, the number of batteries configured for the battery swap cabinet, should be greater than the number of battery swaps of electric vehicles in the battery swap cabinet. The total cost consists of two parts: the cost of deploying the battery swap cabinet at the candidate battery swap cabinet node, and the transportation cost incurred by all electric vehicles. The problem aims to make decisions on vehicle routes, the location of the battery swap cabinet, and the amount of battery storage at the same time to minimize the total cost and meet the needs of all customers.

[0065] S12, determine the symbolic representation of parameters and variables;

[0066] In order to facilitate the establishment of the subsequent mathematical model, it is necessary to first explain the parameters and variables involved in the model.

[0067]

[0068]

[0069] S13, establish a mathematical model.

[0070] Based on the above problem objectives, constraints and symbolic representation, the present invention finally establishes a mathematical model for vehicle path optimization:

[0071]

[0072]

[0073] Objective function (1) aims to calculate the total cost, with the goal of minimizing the sum of the cost of building a battery swap station and the transportation cost of the electric vehicle fleet, and finding the path with the lowest cost, the location of the battery swap station, and the capacity allocation. Constraint (2) ensures that each customer node that needs to be served during the delivery process has a vehicle visiting it, and the vehicle leaves after the service is completed. Constraint (3) ensures that electric vehicles only replace batteries at the location where a battery swap station has been built. Constraint (4) ensures that the flow of each vehicle at all nodes is balanced, that is, a vehicle must leave after visiting a node. Constraint (5) indicates that vehicles departing from a distribution center must return to the distribution center and cannot go to other distribution centers. Constraint (6) indicates that electric vehicles leaving the distribution center can be assigned to a route at most once to serve the corresponding customers. Constraint (7) represents a vehicle quantity restriction, which means that the number of vehicles participating in the delivery of each distribution center should be less than the predetermined fleet size, because some vehicles may be arranged as spares. Constraint (8) limits the number of batteries that should be configured in the battery swap station, which needs to meet the battery swap needs of all electric vehicles visiting the battery swap station. Constraint (8) tracks the remaining load of electric vehicles at each node based on the driving path sequence of electric vehicles. Constraint (9) limits the range of the remaining load of the electric vehicle at each node. Constraint (10) tracks the time when the electric vehicle arrives at each node based on the order of the electric vehicle's driving path. Constraint (11) ensures that the time when the delivery person starts serving the customer meets the customer's time window. Constraint (12) tracks the remaining power of the electric vehicle at each node based on the order of the electric vehicle's driving path. Constraint (13) indicates that the electric vehicles all depart from the distribution center in a fully charged state. Constraint (14) indicates that the battery power level of the electric vehicle is reset to Q after visiting the battery swap station. Constraint (15) ensures that the electric vehicle does not consume battery power when serving the customer point. Constraint (16) ensures that the battery power of the electric vehicle remains above the safety line during delivery. Constraint (17) represents the binary nature of the decision variable.

[0074] S20, establishing a set partitioning model.

[0075] The above-mentioned mixed integer programming model contains a large number of variables and complex structures, which is computationally very challenging. In order to obtain the optimal solution of the above-mentioned mixed integer programming model, the present invention rewrites the model into a set partitioning model based on the principle of column generation method, and decomposes it into a main problem and a pricing sub-problem. The main problem has a simple structure but contains an increasing number of column variables, which are used to deal with the constraints of connecting vehicles together and the constraints of battery swap cabinet site selection and capacity allocation. Therefore, the main problem is defined by the objective function and constraints (2)-(4), (7). The pricing sub-problem is a shortest path problem with resource constraints, which is defined by the modified objective function and other constraints to obtain a feasible path.

[0076] S21, determine the main problem.

[0077] Let R be the set of all feasible paths that satisfy the constraints of the pricing subproblem, c r is the total cost of the path r∈R. Let the symbol pair (r,s) be used to represent the correspondence between the route and the distribution center, and s represents the distribution center to which the route belongs. Let the binary variable The symbol pair (r, s) represents the specific information of the path. If the vehicle goes from node i to node j in path r, then Otherwise, it is 0. If the path represented by (r, s) is adopted in the final solution, the binary decision variable Otherwise it is 0. If path r passes through node i, then the binary variable Otherwise 0.

[0078]

[0079] Therefore, the specific formula of the main problem is as follows:

[0080]

[0081] Objective function (20) aims to find a set of feasible paths containing BSS construction planning with minimum cost. Constraint (21) ensures that each customer is visited once. Constraint (22) ensures that the number of vehicles used by each distribution center does not exceed the actual number. Constraint (23) defines the binary decision variables.

[0082] The number of feasible paths contained in the master problem R is very large. One column represents a feasible path. It is difficult to solve the master problem containing all columns. Therefore, we simplify the master problem into a restricted master problem based on the column generation method, and let Ω represent the set of all feasible paths generated in the current restricted master problem.

[0083]

[0084] S22, determine the pricing sub-problem.

[0085] The purpose of this pricing subproblem is to find a feasible path with a negative test number attached to the constrained main problem. The pricing subproblem is essentially a shortest path problem with resource constraints. Its objective function is closely related to the dual information of the constrained main problem. The constraint is to ensure that a vehicle completes a delivery task under the premise of satisfying the resource constraints. The specific formula of the pricing subproblem is as follows:

[0086]

[0087] Constraints(4)-(6)and(8)-(16) (26)

[0088] The objective function (25) represents the number of tests of a feasible path. is the modified cost of arc (i,j), π i and σ s They correspond to the dual variables of constraints (21) and (22) of the restricted master problem. Constraint (26) includes the flow balance constraint of vehicles in the context of multiple distribution centers, vehicle load constraint, power constraint and time window constraint. Only when the objective function value is less than 0, the new column obtained by the pricing subproblem can be added to the restricted master problem for iteration to make the objective function of the master problem better.

[0089] S30, design a solution algorithm for the model.

[0090] Desrosiers et al. proposed a branch-and-price algorithm, which combines the column generation method with the branch-and-bound method to solve the vehicle routing problem, which is an integer programming problem. In recent years, many scholars have used the branch-and-price method to effectively solve the extension problem of EVRP. The present invention explores a new ELRP in the context of takeout delivery, taking into account the battery reserves of multiple distribution centers and battery swap stations. Therefore, based on the new problem characteristics, we improve the branch-and-price algorithm to effectively solve the problem. The present invention starts with a restricted main problem containing an initial feasible column, constructs a pricing subproblem based on the optimal dual variable of the restricted relaxed main problem, uses a labeling algorithm that mixes exact rules and heuristic rules to obtain columns with a test number less than 0, and adds these columns as new variables to the restricted main problem, and iterates continuously until the labeling algorithm cannot find a column with a test number less than 0, and finally obtains the solution to the restricted relaxed main problem. If it is not an integer solution, the branching strategy is enabled to branch the restricted main problem to obtain the optimal integer solution.

[0091] S31, solution coding and evaluation;

[0092] In the present invention, the solution to the location path optimization problem consists of the driving paths of all vehicles. The present invention uses natural number coding to represent the solution to the problem. Assuming that there are 6 customers who need delivery services, there are 2 candidate battery swap stations, and the distribution center has 3 vehicles, the solution to the problem in this case can be expressed as follows: Figure 2 The sequence shown is represented by the following. The value 0 represents the distribution center, 1-6 is the customer number served by the vehicle, and 7-8 is the candidate battery swap station number. The sequence between two values ​​0 represents the distribution path of a vehicle, and the distribution path of three vehicles constitutes a complete solution to the problem. Therefore, vehicle 1 takes the path 0-1-3-7-0, vehicle 2 takes the path 0-2-4-8-0, and vehicle 3 takes the path 0-5-7-6-0. According to the encoding rules, the dimension Dim of each solution is N+K+1, where N represents the number of customers and K represents the number of vehicles.

[0093] S32, initialization phase design;

[0094] The generation of the initial solution is divided into two stages. In the first stage, the distance greedy heuristic is used to determine the vehicle path. This method is very fast and easy to implement. First, a vehicle is enabled. The vehicle starts from the distribution center and inserts the unserved customer points closest to the current vehicle in sequence without considering the electric vehicle mileage limit and the battery swap cabinet selection strategy. When the load constraint is not met, the vehicle returns to the distribution center. Then another vehicle is enabled to repeat the above operations until all customer points are inserted into the vehicle path. In the second stage, based on the path generated in the first stage and the electric vehicle mileage constraint, the greedy heuristic battery swap cabinet selection method is used to locate and allocate battery swap cabinets. The method is to insert battery swap station nodes into the solution so that all sub-paths meet the battery power constraint and obtain a complete battery swap station selection and allocation decision. Define the set of sub-paths in the solution as R = {r 1 ,r 2 ,r 3 ,…,r |K|}, the subpath is represented by r k ={o,v 1 ,…,v n ,o′}. For each non-empty subpath r k , each node in the path must determine whether the vehicle violates the battery power constraint when visiting it. Create a list This list is used to store the nodes that currently have the potential to affect the swap station insertion decision. If a node v that violates the constraint is encountered * , v * Previously, nodes at the battery swap station or distribution center were added in sequence. Then, from Starting from the first node in , generate a feasible battery swap station set F v , that is, the battery power constraint is satisfied when the vehicle arrives at any battery swap station in the set. If the feasible battery swap station set is empty, calculate the next node until the feasible battery swap station set of a node is not empty. Define F v The insertion cost of the swap station i after being inserted into the node v is: ΔC iv =β 1 (d v,i +d v+1,i -d v,v+1 )+β 2 d v+1,i +β 3 ρλ f . Among them, β 1 , β 2 and β 3 is a weight coefficient between 0 and 1, β 1 +β2 +β 3 =1. v+1 is the node after node v in the solution. ρ is a binary variable, which takes the value of 1 when the battery swap station i is in the selected state in the solution, and 0 otherwise. Consider d in the insertion cost of the battery swap station. v+1,i The purpose is to avoid the vehicle going to the built battery swap station far away from node v+1 as much as possible, so that the vehicle has a higher remaining power when it arrives at node v+1, which improves the utilization efficiency of the battery and may reduce the subsequent battery swap demand. v Select the battery swap station with the lowest insertion cost i * Insert into the solution node v, then clear Then, starting from the inserted battery swap station node, continue to determine whether the subsequent nodes violate the battery power constraint. Repeat the above operation until all nodes in the sub-path meet the battery power constraint.

[0095] S33, branch and bound stage design;

[0096] The common branching strategy based on path variables is not applicable to the problem of the present invention. It will cause the branch and bound tree to be extremely unbalanced, and many explorations will be invalid and inefficient. Because only one path is prohibited in the left child node, but there are many feasible paths, the operation of the left child node has almost no effect on the efficiency of solving the sub-problem. The operation of the right child node is equivalent to determining a path, and the scale of the problem is greatly reduced. Therefore, this paper adopts the arc-based branching strategy proposed by Ryan and Foster. Based on arc variables The branching is simple and easy to implement, and has good robustness. This branching strategy is currently the most popular strategy.

[0097] Since the arc variable x ij is a 0-1 variable, select the arc closest to 0.5 in the floating point solution and create two child nodes for its branch. ij = 0, by removing all path variables passing through arc (i, j) in the current RMP This ensures that all columns of the current RMP are feasible. When solving the pricing subproblem, the arc (i, j) is deleted from the graph G without changing the pricing subproblem structure. ij = 1, by removing all path variables in the current RMP that do not pass through arc (i, j) but pass through vertex i or j This ensures that the columns of the current RMP are feasible, that is, add a constraint so that all path variables is 0. When solving the pricing subproblem, we need to find a path that must pass through arc (i, j). We need to delete all arcs of the form (i, k), k ≠ j and (k, j), k ≠ i from graph G to ensure that vertex j is always visited after vertex i in any path. (i, j) has three cases: (1) When i is the starting point, remove all path variables in the current RMP that do not pass through arc (i, j) but pass through vertex j. (k,j), k≠i. (2) When j is the end point, remove all path variables in the current RMP that do not pass through the arc (i,j) but pass through vertex i. (i, k), k ≠ j. (3) If vertex i or j is an intermediate node, then the above is true.

[0098] The specific process of solving integer solutions by combining the branch and bound algorithm with the column generation algorithm is as follows:

[0099] Step 1: Initialize the valid feasible path set, generate the initial restricted relaxed master problem, and record it in the root node.

[0100] Step 2: Initialize the search tree and add the root node.

[0101] Step 3: Use the depth-first search strategy to select node N from the search tree, and use the information of node N to generate the restricted relaxed master problem.

[0102] Step 4: Use the column generation algorithm to solve the restricted relaxed master problem and obtain the solution X.

[0103] Step 5: If the solution X is an integer solution, go to Step 6. Otherwise, go to Step 7.

[0104] Step 6: Compare the objective function value of solution X with the current upper bound. If it is less than the upper bound, update the upper bound value. Otherwise, perform pruning and go to Step 8.

[0105] Step 7: If the objective function value of the floating point solution X is less than the current upper bound, select an arc for branching according to the arc branching strategy, generate two left and right child nodes to add to the search tree, and delete the current node. Otherwise, perform pruning.

[0106] Step8: If the search tree is not empty, go to Step3. Otherwise, go to Step9.

[0107] Step9: The current upper bound is the optimal integer solution.

[0108] S34, column generation method stage design;

[0109] The number of valid feasible paths that the labeling algorithm can find is very large. In order to further improve the efficiency of the branch pricing algorithm, the present invention sets a threshold value, and stops searching when the labeling algorithm searches for a certain number of valid feasible paths. Then, the set of valid feasible paths obtained by solving the pricing subproblem with the labeling algorithm is added as a new column to the constrained relaxation main problem. The constrained relaxation main problem is then solved by the commercial solver Gurobi, and the subproblems are repriced after obtaining the optimal dual variables π and σ, and the search for a set of valid feasible paths continues. This iteration is repeated until no valid feasible path can be found. This threshold is set to four times the number of client nodes, and the labeling algorithm used in each iteration is determined by an adaptive selection mechanism. The specific process of the column generation method is as follows:

[0110] Step 1: Initialize the restricted relaxed master problem.

[0111] Step 2: Use Gurobi to solve the restricted relaxed master problem, obtain the optimal dual value, and repricing the subproblems.

[0112] Step 3: Use an adaptive mechanism to select a labeling algorithm to solve the pricing subproblem and obtain the effective feasible path set P.

[0113] Step 4: If Then add the columns corresponding to all paths in P to the restricted relaxed main problem and go to Step 2. Otherwise, go to Step 5.

[0114] Step 5: Adjust the weights according to the adaptive mechanism and go to Step 2 or Step 6.

[0115] Step 6: Record the optimal solution of the final restricted relaxation master problem.

[0116] In the column generation method, the optimal dual solution of the constrained relaxed main problem is used to price the subproblems. Then, a labeling algorithm is selected to solve the pricing subproblem and obtain a valid feasible path set, and the derived column is added to the constrained relaxed main problem. In the previous article, we proposed four heuristic labeling algorithms for fast and efficient search of valid feasible path sets. Therefore, evaluating and selecting a suitable heuristic labeling algorithm to obtain the negative test sequence is a key issue in the column generation method. Let represents the weight of algorithm a at the Nth iteration, Represents the number of times operator a is used in the N iterations. When the column generation method is initialized, the initial weights of all heuristic labeling algorithms Initial score and initial usage After adaptive scoring, the algorithm will adaptively adjust the weights of the operators used. The adaptive weight adjustment formula is:

[0117]

[0118] Among them, θ∈[0,1] is the reaction factor of adaptive weight adjustment, which is used to control the reaction speed of the algorithm effectiveness change to its own adaptive weight. In the operation process of the column generation method, the heuristic labeling algorithm used If a valid feasible path set is found, otherwise In each iteration, the algorithm independently selects the heuristic labeling algorithm based on the adaptive weights through a roulette wheel mechanism. represents the probability of selecting algorithm a in the Nth iteration, The calculation formula is as follows:

[0119]

[0120] If all heuristic labeling algorithms cannot find a valid feasible path, the exact labeling algorithm is used to search, and the iteration continues until no valid feasible path can be found, and the column generation method is terminated.

[0121] S35, labeling algorithm stage design;

[0122] In this paper, we use the exact labeling algorithm and the heuristic labeling algorithm to solve the pricing subproblem. The label is defined as represents any partial path from vertex 0 to vertex i, where:

[0123] o(L): the distribution center where this part of the route starts

[0124] v(L) = i: the last vertex visited by this part of the path

[0125] S(L): The set of customers served

[0126] q(L): the total amount of customer demand on this part of the path

[0127] Q(L): The remaining power of the vehicle on this part of the path when it leaves vertex i

[0128] t(L): The earliest service start time of the vehicle at vertex i on this part of the path

[0129] The number of tests corresponding to this partial path

[0130] The label is initialized to Then L is extended along the arc (i, j) according to the access record S(L), and the new path label i(L ′ )=o(L), v(L′)=j, S(L′)=S(L)∪{j}, q(L′)=q(L)+qj , t(L′)=max{t(L)+s i +t ij ,e j},

[0131] Let U represent the set of labels that need to be expanded backward, p represent the set of feasible paths that meet resource constraints, and the dynamic array L stores all traversed labels. The specific label algorithm process is as follows:

[0132] Step 1: Initialize the label U={l 0}.

[0133] Step 2: If Then select a label l from U to expand, otherwise go to Step 7.

[0134] Step 3: Label l represents node i. Use the dominance rule to judge label l and all labels in L that represent node i and have the same o(l).

[0135] Step 4: If label l is dominated, go to Step 6.

[0136] Step 5: If the current label l represents node i as the end point and the objective function value is less than 0, add the corresponding path to p. Otherwise, start from node i to expand the labels to all unvisited nodes, and add the labels that meet the resource constraints to U and L.

[0137] Step6: Delete the current label l from U and go to Step2.

[0138] Step7: Select the path with the smallest objective function value based on the set p.

[0139] In the precise rule, only when the remaining capacity of the extended label meets the vehicle load limit, the remaining power of the vehicle meets the power limit, and the access time meets the time window limit, the label is feasible and continues to expand to other nodes, otherwise it is discarded. The precise domination rule is to eliminate some labels that cannot generate the optimal path, thereby reducing the search space. Let L 1 and L 2 For two labels, L 2 is a new label, where o(L 1 )=o(L 2 ),v(L 1 )=v(L 2 ),if: q(L 1 )≤q(L 2 ), t(L 1 )≤t(L2 ), Q(L 1 )≥Q(L 2 ), The label L 1 Dominate L 2 , label L 1 Can be extended to be better than label L 2 The solution that can be expanded, so the label L 2 Can be discarded.

[0140] The exact labeling algorithm explores all possible nodes, which generates a large number of labels and consumes a lot of computing resources. Despite the strict dominance rules, some labels that cannot generate the optimal path are deleted during the label expansion process, but the branch and price algorithm is still too slow to solve. Therefore, we designed four labeling algorithms that incorporate heuristic rules to obtain feasible paths that can improve the objective function of the main problem in a shorter time, so as to improve the overall solving efficiency of the branch and price algorithm.

[0141] (1) Heuristic Rule 1

[0142] In this rule, some feasible labels will be deleted during label expansion. When a label is expanded to a node, if the check count of the new label does not decrease and is greater than 0, the new label will be deleted. For example, v(L) = i, label L is expanded to obtain 4 new labels, where Delete label L after comparison 3 ,because The remaining new tags are then determined by precise dominance rules, and only new tags that are not dominated can be added to the unexpanded tag list.

[0143] (2) Heuristic Rule 2

[0144] This rule is similar to heuristic rule 1, except that it relaxes the constraint on the vehicle's remaining charge in the exact governing rule. q(L 1 )≤q(L 2 ), t(L 1 )≤t(L 2 ), When the label L 1 Dominate L 2 , label L 2 Abandoned.

[0145] (3) Heuristic Rule 3

[0146] This rule is similar to heuristic rule 1, except that it relaxes the constraint on the remaining vehicle load in the exact rule. Q(L 1 )≥Q(L 2 ), t(L 1 )≤t(L 2 ), When the label L 1 Dominate L 2 , label L 2 Abandoned.

[0147] (4) Heuristic Rule 4

[0148] This rule is similar to heuristic rule 1, except that it relaxes the constraint on the remaining vehicle load in the exact rule. Q(L 1 )≥Q(L 2 ), q(L 1 )≤q(L 2 ), When the label L 1 Dominate L 2 , label L 2 Abandoned.

[0149] Experimental results and analysis

[0150] The content of this experiment is mainly divided into two parts: performance verification of the improved branch-based pricing algorithm and comparison of solution speed with the standard branch-based pricing algorithm. These two parts correspond to the following embodiment 1 and embodiment 2 respectively.

[0151] Embodiment 1;

[0152] In Example 1, we tested a small-scale instance to verify the correctness of the model and algorithm, and to evaluate the effectiveness of the proposed IBP-HL algorithm compared with the commercial solver Gurobi9.1.2. The table gives a detailed description of the tested small-scale instance, which contains 10 instances composed of different data. The "Description" part describes the number of each type of node in the instance, and the "|V c |"The column represents the number of customers,"|V F |" column represents the number of candidate battery swap cabinet deployment locations,"|V s The "|" column represents the number of distribution centers. In addition, the "Num" column represents the number of instances in each group. We set each group to have 3 randomly selected instances.

[0153] The “Performance” section of the table provides a summary of the comparison results between Gurobi and the proposed IBP-HL algorithm on small-scale instances. In this section, the “Optimal (Num)” column reports the number of instances that were solved to the optimal solution, the “Feasible (Num)” column reports the number of instances that obtained at least one feasible solution, the “Avg Gap (%)” column reports the average optimality gap obtained within the algorithm termination or solution time limit, and the “Avg Time (s)” column reports the average running time for solving the example. In the computational experiments, we set the upper limit of the running time of the algorithm and Gurobi to solve an instance to 1800 CPU seconds. The optimality gap of the IBP-HL algorithm is calculated as (UB-LB) / UB*100, where UB and LB represent the best upper bound and best lower bound obtained, respectively.

[0154] From the results in Table 1, we can see that the proposed IBP-HL algorithm performs better than Gurobi on average in all small-scale instance groups. For instance groups with 12 or fewer customers, both the IBP-HL algorithm and Gurobi can obtain the optimal solution for all instances, but the IBP-HL algorithm leads slightly in average solution time. However, as the instance scale increases further, the solution performance gap between the IBP-HL algorithm and Gurobi gradually widens. For two instance groups with 15 customers, the IBP-HL algorithm can find the optimal solution for all instances in an average of 74.35s and 78.18s, respectively, while Gurobi can only find the optimal solution for one instance within the running time limit of 1800s, with an average optimality gap of 12.33% and 15.32%, respectively.

[0155] Table 1

[0156]

[0157]

[0158] Embodiment 2

[0159] In Example 2, we will conduct computational experiments on medium and large-scale instances. Because Gurobi takes a very long time to solve medium and large-scale instances, and the IBP-HL algorithm has better solving performance than Gurobi on small-scale instances, the solving performance of the IBP-HL algorithm on medium and large-scale instances is tested separately, and the improvement effect of the algorithm's acceleration technology is emphasized. The medium-scale instances are divided into three groups of instance groups composed of different data, with 20-30 customers. Each group extracts 8 instances according to the customer distribution type, and a total of 24 instances are used for computational experiments. Large-scale instances have more instance groups composed of different data, and the number of customers is greater than 40. The running time limit we set for solving medium-scale instances is 7200 CPU seconds, and for larger-scale instances is set to 18000 CPU seconds.

[0160] We show the performance of the proposed IBP-HL algorithm in solving medium-sized instances in Table 2. The content of the “Description” section is the same as that in Table 1, and the “Instance” column indicates the instance number. The “lb” and “ub” columns report the lower bound and the best upper bound obtained at the root node, i.e., the objective function values ​​of the linear optimal solution and the integer optimal solution of the current restricted relaxed master problem, respectively. root The "(s)" column reports the running time of obtaining the optimal solution of the root node, the "node" column indicates the number of nodes in the branch and bound tree, the "best obj" column reports the integer optimal solution of the final restricted relaxed master problem, the "t(s)" column reports the overall running time of the IBP-HL algorithm, the "col" column reports the number of columns of the final restricted relaxed master problem that obtains the integer optimal solution, and the "t BP The “(s)” column reports the overall running time of the branch-and-price algorithm without applying the heuristic labeling algorithm and the adaptive selection strategy, where “*” represents that the algorithm reached the time limit during the solution process.

[0161] The content reported in Table 2 shows that within the running time limit, for the instance with 20 customers, the IBP-HL algorithm can solve all and obtain the optimal value, with an average operation time of 1062.73s; for the instance with 25 customers, the IBP-HL algorithm can solve 6 out of 8 instances and obtain the optimal value, with an average operation time of 2413.16s; for the instance with 30 customers, the IBP-HL algorithm can solve 5 out of 8 instances and obtain the optimal value, with an average operation time of 3600.41s. After summarizing and analyzing the results, we found that the IBP-HL algorithm has a certain improvement in solving performance compared with the branch-and-price algorithm without applying the heuristic labeling algorithm and adaptive selection strategy. For the three groups of instances with different data scales, the average operation time of the IBP-HL algorithm is lower than that of the basic branch-and-price algorithm. In addition, the performance of the IBP-HL algorithm is inconsistent when solving instances with the same data scale, and the solution time difference between different instances is large. We believe that this is related to factors such as the distribution of customers in the instance, customer time windows, and the location of candidate battery swap cabinet deployment nodes.

[0162] Table 2

[0163]

[0164]

[0165] Finally, we introduce the performance of the IBP-HL algorithm when solving larger-scale instances in Table 3. The explanations of the data in each column of the table are as shown above. The results in Table 3 show that within the running time limit, for the instance with 40 customers, the IBP-HL algorithm can solve all of them and obtain the optimal value, with an average operation time of 3385.82s; for the instance with 50 customers, the IBP-HL algorithm can only solve 1 out of 5 instances and obtain the optimal value, with an average operation time of 14905.91s. It can be seen that when the instance scale increases to a certain extent, the solution of the IBP-HL algorithm becomes very difficult, but the IBP-HL algorithm still has the ability to solve a small part of the larger-scale instances quickly. In addition, the increase in the number of parking lots will expand the magnitude of feasible labels and increase the solution time of the IBP-HL algorithm. In summary, the proposed IBP-HL algorithm performs well in both small-scale and medium-scale instances, and the proposed acceleration strategy has a good computational gain.

[0166] Table 3

[0167]

[0168]

[0169] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for optimizing the location path of a battery swap cabinet for electric bicycles in a takeaway delivery scenario, characterized in that: The following steps are involved: S10, establishing a battery swap cabinet location path optimization model; S20, establishing a set partitioning model; S30, solution algorithm for the design model; Wherein, S10 specifically includes the following steps: S11, determine the problem objectives and constraints; S12, determine the symbolic representation of parameters and variables; S13, establishing a mathematical model; S20 specifically includes the following steps: S21, determine the main problem; S22, determine the pricing sub-problem; S30 specifically includes the following steps: S31, solution coding and evaluation; S32, initialization phase design; S33, branch and bound stage design; S34, column generation method stage design; S35, labeling algorithm stage design; The S11, determines the problem objectives and constraints, where the objective is to minimize the total cost. The specific problem description is as follows: a multi-distribution center and directed network G = (V, A), V represents the set of logistics nodes in the network, including multiple distribution centers, a group of customer nodes and a group of candidate battery swap cabinet nodes, A represents the arc set of the distribution network; the customer's demand, location, and the location of the candidate battery swap cabinet are all known, and each distribution center has an equal-sized takeaway delivery fleet equipped with the same model of electric mopeds; based on the actual situation, it is assumed that the distribution center is equipped with a battery swap cabinet and has a sufficient number of batteries in stock. The driver starts from the distribution center with a full charge and returns to the distribution center at the time of departure after serving a group of customers; each electric vehicle has a maximum loading capacity, so the total demand for a vehicle to serve customers must not exceed its maximum loading capacity; during the delivery process, each electric vehicle balances the electricity In order to use the amount of electricity and keep the remaining power level within the preset range, electric vehicles need to go to the battery swap cabinet to swap batteries; the setting of the battery swap cabinet involves two operational issues, namely the location in the candidate node selection and the design capacity in the available battery swap; the integration of delivery route arrangement, the location of the battery swap station and the battery allocation between multiple sites ensures the operational performance of the delivery system; assuming that the replaced battery cannot be used on the same day after being charged in the battery swap cabinet, in order to meet the battery swap needs of all food delivery drivers within a day, the scale of the battery swap station, that is, the number of batteries configured for the battery swap cabinet, should be greater than the number of battery swaps of electric vehicles in the battery swap cabinet; the total cost consists of two parts, the cost of deploying the battery swap cabinet at the candidate battery swap cabinet node, and the transportation cost incurred by all electric vehicles; the problem aims to make decisions on vehicle routes, the location of the battery swap cabinet and the number of battery storage at the same time to minimize the total cost; The step S12, determining the symbolic representation of parameters and variables, comprises: Decision variables: Auxiliary variables: parameter: The S13 is to establish a mathematical model; specifically, to establish a mathematical model for vehicle path optimization: Objective function (1) aims to calculate the total cost, with the goal of minimizing the sum of the cost of building a battery swap station and the transportation cost of the electric vehicle fleet, and finding the lowest-cost path, battery swap station location and capacity allocation; constraint (2) ensures that each customer node that needs to be served during each delivery process has a vehicle visiting it and that the vehicle leaves after the service is completed; constraint (3) ensures that electric vehicles only replace batteries at locations where battery swap stations have been built; constraint (4) ensures that the flow of each vehicle at all nodes is balanced, that is, a vehicle must leave after visiting a node; constraint (5) indicates that vehicles departing from a distribution center must return to that distribution center and cannot go to other distribution centers; constraint (6) indicates that electric vehicles leaving the distribution center can be assigned to a route at most once to serve the corresponding customers; constraint (7) indicates a vehicle quantity limit, which means that the number of vehicles participating in the delivery of each distribution center should be less than the predetermined fleet size; constraint (8) sets the number of batteries that should be configured in the battery swap station. Constraints, it needs to meet the battery replacement needs of all electric vehicles visiting the battery replacement station, constraint (8) tracks the remaining load of the electric vehicle at each node based on the driving path sequence of the electric vehicle; constraint (9) limits the range of the remaining load of the electric vehicle at each node; constraint (10) tracks the time when the electric vehicle arrives at each node based on the driving path sequence of the electric vehicle; constraint (11) ensures that the time when the delivery person starts to serve the customer meets the customer's time window; constraint (12) tracks the remaining power of the electric vehicle at each node based on the driving path sequence of the electric vehicle; constraint (13) indicates that the electric vehicles all start from the distribution center in a fully charged state; constraint (14) indicates that the battery power level of the electric vehicle is reset to Q after visiting the battery replacement station; constraint (15) ensures that the electric vehicle does not consume battery power when serving the customer point; constraint (16) ensures that the battery power of the electric vehicle remains above the safety line during delivery; constraint (17) represents the binary nature of the decision variable.

2. The method according to claim 1, characterized in that The step S21, determining the main problem, specifically includes: Let R be the set of all feasible paths that satisfy the constraints of the pricing subproblem, c r is the total cost of the path r∈R; let the symbol pair (r,s) be used to represent the correspondence between the route and the distribution center, s represents the distribution center to which the route belongs; let the binary variable The symbol pair (r, s) represents the specific information of the path; if the vehicle goes from node i to node j in path r, then Otherwise, it is 0; if the path represented by (r, s) is adopted in the final solution, the binary decision variable Otherwise it is 0; if path r passes through node i, then the binary variable Otherwise, 0; Therefore, the specific formula of the main problem is as follows: The objective function (20) aims to find a set of feasible paths containing BSS construction planning with the minimum cost as the goal; constraint (21) ensures that each customer is visited once; constraint (22) ensures that the number of vehicles used by each distribution center does not exceed the actual number; constraint (23) defines the binary decision variables; The number of feasible paths contained in R of the master problem is very large. One column represents a feasible path. It is difficult to solve the master problem containing all columns. Therefore, we simplify the master problem into a restricted master problem based on the column generation method. Let Ω represent the set of all feasible paths generated in the current restricted master problem.

3. The method according to claim 2, characterized in that S22, determining the pricing sub-problem, is specifically: The purpose of this pricing subproblem is to find a feasible path with a negative test number attached to the restricted main problem. The pricing subproblem is essentially a shortest path problem with resource constraints. Its objective function is closely related to the dual information of the restricted main problem. The constraint is to ensure that a vehicle completes a delivery task under the premise of satisfying the resource constraints. The specific formula of the pricing subproblem is as follows: Constraints(4)-(6)and(8)-(16) (26) The objective function (25) represents the number of tests of a feasible path, where is the modified cost of arc (i,j), λ b is the fixed unit capacity and operating cost of the battery swap cabinet, π i and σ s They correspond to the dual variables of constraints (21) and (22) of the restricted main problem respectively. Constraint (26) includes the vehicle flow balance constraint in the context of multiple distribution centers, vehicle load constraint, power constraint and time window constraint. Only when the objective function value is less than 0, the new column obtained from the pricing subproblem can be added to the restricted main problem for iteration to make the objective function of the main problem better.

4. The method according to claim 3, characterized in that The S31, encoding and evaluation of the solution; specifically: the solution to the location path optimization problem is composed of the driving paths of all vehicles, and the solution to the problem is represented by natural number encoding.

5. The method according to claim 4, characterized in that S32, initialization phase design; Specifically, the generation of the initial solution is divided into two stages. In the first stage, the distance greedy heuristic is used to determine the vehicle path. First, a vehicle is enabled. The vehicle starts from the distribution center and inserts the unserved customer points closest to the current vehicle in sequence without considering the electric vehicle mileage limit and the battery swap cabinet selection strategy. When the load constraint is not met, the vehicle returns to the distribution center. Then another vehicle is enabled to repeat the above operations until all customer points are inserted into the vehicle path. In the second stage, based on the path generated in the first stage and the electric vehicle mileage constraint, the greedy heuristic battery swap cabinet selection method is used to locate and allocate the battery swap cabinet. This method is to insert the battery swap station node into the solution so that all sub-paths meet the battery power constraint and obtain a complete battery swap station selection and allocation decision. The set of sub-paths in the solution is defined as R = {r1, r2, r3, …, r |K| }, the subpath is represented by r k ={o,v1,…,v n ,o′}, for each non-empty subpath r k , each node in the path must determine in turn whether the vehicle violates the battery power constraint when visiting; create a list This list is used to store the nodes that currently have the potential to affect the insertion decision of the swap station. If a node v that violates the constraint is encountered * , v * Previously, nodes at the battery swap station or distribution center were added in sequence. Then, from Starting from the first node in , generate a feasible battery swap station set F v , that is, the vehicle satisfies the battery power constraint when arriving at any battery swap station in the set. If the feasible battery swap station set is empty, the next node is calculated until the feasible battery swap station set of a node is not empty. Define F v The insertion cost of the swap station i after being inserted into the node v is: ΔC iv =β1(d v,i +d v+1,i -d v,v+1 )+β2d v+1,i +β3ρλ f , where β1, β2 and β3 are weight coefficients between 0 and 1, β1+β2+β3=1; v+1 is the node after node v in the solution, ρ is a binary variable, which takes the value of 1 when the battery swap station i is in the selected state in the solution, otherwise it takes the value of 0. The insertion cost of the battery swap station is considered to be d v+1,i The purpose is to avoid the vehicle from going to the built battery swap station far away from node v+1 as much as possible, so that the vehicle has a higher remaining power when it arrives at node v+1, which improves the utilization efficiency of the battery and may reduce the subsequent demand for battery swapping. v Select the battery swap station with the lowest insertion cost i * Insert into the solution node v, then clear Then, starting from the inserted battery swap station node, continue to determine whether the subsequent nodes violate the battery power constraint; repeat the above operation until the nodes of all sub-paths meet the battery power constraint.

6. The method according to claim 5, characterized in that In the design of the branch and bound method stage S33, an arc-based branching strategy is adopted.

7. The method according to claim 6, characterized in that The method for solving integer solutions by combining the branching strategy with the column generation algorithm comprises the following steps: Step 1: Initialize the valid feasible path set, generate the initial restricted relaxed master problem, and record it in the root node; Step 2: Initialize the search tree and add the root node; Step 3: Use the depth-first search strategy to select node N from the search tree, and use the information of node N to generate the restricted relaxed master problem; Step 4: Use the column generation algorithm to solve the restricted relaxed master problem and obtain the solution X; Step 5: If the solution X is an integer solution, go to Step 6; otherwise, go to Step 7; Step 6: Compare the objective function value of solution X with the current upper bound. If it is less than the upper bound, update the upper bound value. Otherwise, perform pruning and go to Step 8. Step 7: If the objective function value of the floating point solution X is less than the current upper bound, select an arc for branching according to the arc branching strategy, generate two left and right child nodes to add to the search tree, and delete the current node; otherwise, perform pruning; Step8: If the search tree is not empty, go to Step3; otherwise, go to Step9; Step9: The current upper bound is the optimal integer solution.

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