A bi-level programming method for logistics distribution route considering road congestion and carbon tax mechanism

Abstract

The present application relates to a kind of logistics distribution path bi-level programming method considering road network congestion and carbon tax mechanism, belong to logistics and traffic optimization technical field.The method solves the problem that road network congestion and carbon cost cannot be dynamically considered simultaneously in existing low-carbon path planning, leading to poor practical feasibility of scheme.The technical scheme is to construct a bi-level programming model: the upper layer minimizes the total distribution cost including carbon tax to decide vehicle path as target;The lower layer is based on user equilibrium traffic assignment model, and according to the actual congestion distribution time of path scheme feedback.Both are solved by introducing improved genetic algorithm of chaos mapping and Frank-Wolfe algorithm iteration.The present application ensures that path decision and dynamic traffic state are consistent, realizes the collaborative optimization of congestion avoidance and carbon emission reduction, and improves the reliability of distribution scheme and total cost optimization ability.

Description

Technical Field

[0001] This invention belongs to the field of logistics and transportation optimization technology, and relates to a two-level planning method for logistics distribution routes that considers road network congestion and carbon tax mechanisms. Background Technology

[0002] In recent years, driven by e-commerce and on-demand delivery services, urban logistics and distribution demand has shown a continuous growth trend. At the same time, frequent urban road network congestion has led to increased volatility in vehicle travel time. This not only reduces the reliability of delivery timeliness but also significantly increases fuel consumption and carbon emissions due to frequent acceleration, deceleration, and low-speed driving under congested conditions. Against the backdrop of global efforts to address climate change, carbon pricing mechanisms are expanding, making the economic costs of carbon emissions increasingly apparent. Therefore, the uncertainty of delivery time caused by road network congestion, and the carbon emission costs under carbon tax mechanisms, together constitute two key challenges facing the optimization of modern urban logistics and distribution routes.

[0003] Current research on the Low-carbon Vehicle Routing Problem (LC-VRP) has incorporated carbon emissions into its optimization objectives or constraints. However, existing methods typically fail to simultaneously and dynamically consider the interaction between road network congestion and carbon emission costs. Specifically, most studies assume that road network travel time is static or fixed when planning routes, neglecting the impact of delivery vehicles' own route choices on traffic flow distribution and the time feedback caused by congestion. This results in planned routes that may not be optimal or even feasible in actual congested road networks, failing to achieve true cost and carbon emission optimization while ensuring delivery timeliness. Therefore, there is an urgent need for a logistics delivery route planning method that can comprehensively consider the dynamics of road network congestion and carbon tax mechanisms. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a two-layer planning method for logistics distribution routes that takes into account road network congestion and carbon tax mechanisms.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms, the method comprising the following steps: Step 1, input a set of nodes N and road segment collection A The transportation network formed The basic data, the node set N includes distribution center node 0 and n Customer Nodes i The distribution center node 0 has m Delivery vehicles; Step 2: Construct the upper-level model. The upper-level model aims to minimize the total delivery cost, which includes vehicle fixed costs, fuel consumption costs, carbon emission costs, and time window penalty costs. Decision variables include vehicle activation plans and vehicle travel route plans. The calculation of fuel consumption costs and carbon emission costs depends on the actual delivery time of the road segment. ; Step 3: Construct the lower-level model. This lower-level model is based on the User Equilibrium (UE) traffic allocation principle. Its objective is to minimize the total delivery time for all travelers in the road network. It allocates the traffic flow induced by delivery route schemes and existing social traffic flow to the road network, and uses an impedance function to calculate the actual delivery time for each road segment. ; Step 4: Solve the two-level programming model, and iteratively calculate the actual delivery time of the road segment output by the lower-level model. Feedback is sent to the upper-level model to update cost calculations, and the delivery route plan generated by the upper-level model is input into the lower-level model to update traffic allocation, until an optimized delivery route plan consistent with the road network congestion status is obtained.

[0006] Furthermore, in step 2, the objective function of the upper-level model is: ,in, C 1 represents the vehicle's fixed cost. C 2 represents fuel consumption cost. C 3 represents the cost of carbon emissions. C 4 represents the time window penalty cost.

[0007] Furthermore, the fixed cost of the vehicle ,in For vehicles Fixed costs, To indicate whether the vehicle is in use 0-1 decision variables; fuel consumption cost ,in For fuel unit price, Fuel consumption per unit time For road section The actual delivery time To indicate vehicles Does it pass through this section of road? 0-1 decision variables; The carbon emission cost ,in For carbon tax prices, Carbon emissions per liter of fuel consumed; The time window penalty cost ,in The penalty coefficient for vehicles arriving early. The penalty coefficient for vehicle delay arrival. For customers i The service start time, For customers i Service end time For vehicles k Arrival at the customer i The arrival time.

[0008] Furthermore, in step 3, the objective function of the lower-level model is: ,in R It is the set of feasible paths in the road network. Indicates traffic flow Road sections under conditions Delivery time.

[0009] Furthermore, in step 3, the impedance function is expressed as the BPR function, which is: ,in For free-flow delivery time on the route, and For the parameters of the BPR function, For road section Traffic flow of social vehicles on the road For road section Traffic flow of logistics and delivery vehicles on the road For road section Traffic capacity.

[0010] Furthermore, in step 4, the upper-level model is solved using the genetic algorithm (GA), and the lower-level model is solved using the Frank-Wolfe algorithm.

[0011] Furthermore, the genetic algorithm uses the Tent chaotic mapping for population initialization.

[0012] Furthermore, in the genetic algorithm, an adaptive crossover probability is employed. Perform crossover operation, the adaptive crossover probability Based on the current iteration number Total number of iterations D The relationship needs to be adjusted.

[0013] Furthermore, in the genetic algorithm, an adaptive mutation probability is employed. Perform mutation operation, the adaptive mutation probability ,in d This represents the current iteration number. D This represents the total number of iterations.

[0014] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned two-tiered logistics distribution route planning method that considers road network congestion and carbon tax mechanisms.

[0015] The beneficial effects of this invention are as follows: (1) By introducing a carbon tax mechanism through the upper-level model, carbon emissions are directly converted into economic costs and incorporated into the objective function. At the same time, the lower-level user equilibrium traffic allocation model is used to provide real-time feedback on the changes in travel time caused by congestion. This allows the final planned route to not only avoid congestion and ensure timeliness, but also to actively choose a low-carbon emission driving strategy, thereby coordinating efficiency, cost and environmental protection goals at the source.

[0016] (2) Traditional static route planning is prone to failure in dynamic traffic flow, while the two-layer iterative mechanism of this invention ensures that the route plan is consistent with the real-time road network status, reducing delays or waiting caused by inaccurate time estimation and enhancing the reliability of the delivery plan. At the same time, the model comprehensively considers all core cost items such as vehicle fixed costs, fuel consumption, carbon tax and time window penalties, which can guide a globally better vehicle activation and route scheduling scheme to minimize the total operating cost.

[0017] (3) In view of the nondeterministic polynomial difficulty NP-hard characteristics of the bi-level programming model, the proposed hybrid solution strategy combining the improved genetic algorithm with tent chaotic mapping and the Frank-Wolf algorithm enhances the global search capability and avoids premature convergence, thereby obtaining high-quality and executable optimization solutions within an acceptable time, making the method have the potential to solve large-scale practical problems.

[0018] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart of the method of the present invention; Figure 2 Flowchart for improving the genetic algorithm solution; Figure 3 Road network map of Sioux Falls; Figure 4 This is the path diagram for scenario 1; Figure 5This is the path diagram for scenario 2; Figure 6 This is the path diagram for scenario 3; Figure 7 This is a graph showing the difference between total cost and carbon emission cost. Detailed Implementation

[0020] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0021] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0022] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0023] The implementation flowchart of a two-level logistics distribution route planning method considering road network congestion and carbon tax mechanisms provided in this embodiment of the invention is as follows: Figure 1 As shown, the processing steps include the following: Step 1, Select and input road network topology data: This invention uses transportation networks Based on, among which N For a set of nodes, A A set of road segments. A set of nodes. N Including distribution center node 0 and the remaining customer nodes Distribution center node 0 has m Delivery vehicles, need to ben Each customer node provides delivery services.

[0024] Step 2, propose reasonable assumptions based on the problem: Assumption 1: There is one and only one distribution center that provides delivery services to multiple demand points, and all delivery vehicles depart from this distribution center and return to the distribution center after completing the delivery task; Assumption 2: All delivery vehicles are of the same model and have the same carrying capacity; Assumption 3: The existing cargo capacity of the distribution center can meet the total demand, while the maximum cargo capacity of the delivery vehicles is greater than the delivery demand of each demand point; Assumption 4: Demand is known and remains constant throughout the delivery process; Assumption 5: Each demand point has only one delivery vehicle responsible for delivering goods, and each delivery vehicle can be responsible for multiple demand points on a route; Assumption 6: The delivery vehicle maintains a constant speed throughout the delivery process.

[0025] Step 3, consider the carbon tax mechanism to build the upper-level model: For urban delivery scenarios where the distribution center and customer node network are known, customer demand and service time windows are known, and transportation activities must be factored into carbon tax costs, a higher-level model is constructed, comprehensively considering cost components such as vehicle fixed costs, fuel consumption costs, carbon emission costs, and time window penalties. This model is used to decide on vehicle deployment and route options, minimizing the total delivery cost while meeting customer demand and time window constraints. The actual delivery time for each road segment is a key input, calculated by the lower-level congestion feedback model described in step 4 and fed back into the upper-level model's cost calculation and objective function. The parameters, symbols, and their meanings used in the upper-level model are shown below: parameter: m Number of available delivery vehicles (unit: vehicles); n Number of customer nodes (unit: nodes); :vehicle Fixed costs (unit: yuan / vehicle); Fuel price per liter (unit: yuan / liter); Fuel consumption per unit time (unit: liters / hour); Carbon tax price (unit: yuan / kg); Carbon emissions per liter of fuel consumed (unit: kg / L). Penalty coefficient for vehicles arriving early (unit: yuan / minute); Vehicle delay penalty coefficient (unit: yuan / minute); :client Service start time (unit: hour); :client Service end time (unit: hours); :client Demand (unit: tons); : Node subset (used for eliminating constraints in sub-loops); :gather The number of elements (unit: elements); N : A set of nodes, including distribution center node 0 and customer nodes; variable: : Should the vehicle be activated? (0-1 decision variables); :vehicle Does it pass through this section of road? (0-1 decision variables); :vehicle Do you serve customers? (0-1 decision variables); Considering traffic congestion on certain road sections Actual travel time (unit: hours); :vehicle Arrival at the customer Arrival time (unit: hour); In the process of providing delivery services, logistics companies incur significant costs. These costs must be considered not only in terms of fixed vehicle costs and transportation costs, but also in terms of carbon emission costs under low-carbon principles, in order to achieve optimal results. The following will provide a detailed analysis of the various cost factors involved in delivery route optimization: (1) Fixed costs: Each delivery mission incurs a fixed cost, determined by the number of deliveries performed. If the distribution center has... m If there are 100 vehicles, the total fixed cost of logistics and distribution vehicles can be expressed as Equation (1).

[0026] (1) Among them, when the vehicle When enabled Then it is included in the corresponding fixed cost. When not enabled Not included.

[0027] (2) Fuel consumption cost: Delivery vehicles continuously consume fuel during operation, so the fuel consumption cost of logistics delivery vehicles can be represented by equation (2).

[0028] (2) in, Indicates that the vehicle is on the road section The fuel cost corresponding to the above driving, and only if the vehicle Passing through this section of road ( This expense is only accumulated when ( ).

[0029] (3) Carbon emission costs: As carbon tax levels continue to rise, logistics companies face higher delivery costs and need to reduce emission costs through low-carbon transportation route optimization. The carbon emission costs of delivery vehicles during transportation are shown in equation (3).

[0030] (3) This cost varies with the carbon tax price. Changes, and vehicle travel time And decision variables for whether or not to pass through a road segment This linkage allows low-carbon constraints to be incorporated into path optimization.

[0031] (4) Time window penalty cost: During delivery, vehicles may arrive early or late due to various factors, resulting in penalty costs. This invention uses a hybrid time window constraint to characterize this cost, with the main scenarios including: ① if the delivery vehicle arrives before time, an early arrival penalty is incurred; ② if the arrival time is between time and time, no penalty is incurred; ③ if the arrival time is later than time, a late arrival penalty is incurred. Furthermore, different customers have different tolerances for early and late arrivals. Therefore, this invention introduces and as positive penalty coefficients to adjust the penalties for early and late arrivals, respectively. The relevant mathematical relationship is shown in equation (4).

[0032] (4) in, Penalties are only incurred for early or late arrivals, and are calculated separately by [the relevant authority / organization]. , Adjust the severity of penalties for early and late arrivals.

[0033] The upper-level model focuses on logistics and distribution scenarios with road congestion and carbon tax mechanisms: goods originate from the distribution center (node ​​0) and are transported using a vehicle pool. For the set of nodes distributed in the road network Each customer node in the process completes delivery services on demand, while meeting customer needs. With service time window Under these circumstances, determine the vehicle deployment plan and travel route plan. Traffic congestion will alter the actual delivery time for certain sections of the road. This affects fuel consumption and carbon emission costs during the delivery process, thus influencing the total delivery cost. To address this, the upper-level model decomposes the total delivery cost into fixed costs, fuel consumption costs, carbon emission costs, and time window penalty costs. Based on this, an upper-level optimization model is constructed with the objective of minimizing the total delivery cost, as follows: (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Equation (5) is the objective function of the upper-level model, aiming to minimize the total cost, including fixed cost (C1), fuel consumption cost (C2), carbon emission cost (C3), and time window penalty cost (C4). C2 and C3 contain the delivery time function for each road segment, which is obtained from the lower-level model. Constraint (6) limits the number of vehicles available for delivery, ensuring that the total number of vehicles assigned to delivery routes does not exceed the total number of vehicles owned by the delivery center. m Constraint (7) ensures that the total amount of goods delivered by all vehicles to each customer equals the customer's demand. Constraint (8) ensures that each customer in the network is served by exactly one vehicle to avoid duplicate services and improve delivery efficiency. Equation (9) ensures that each customer... i At least one vehicle is required for service, Equation (10) states that each vehicle serves at least one customer. Equation (11) ensures that all customers are visited. Constraint (12) is the vehicle flow balance equation for the distribution center, indicating that all vehicles depart from and return from the distribution center after completing their tasks. Equation (13) ensures that the resulting routes are continuous and do not form sub-loops, i.e., each vehicle's route does not have closed-loop sub-loops. Here...S For a set of nodes N proper subsets of The number of nodes in the subset. Indicates inclusion The proper subset of each node can have at most 10^30 nodes. The edges do not form a closed loop. Constraint (14) stipulates that the decision variable takes values ​​in the range of 0-1.

[0034] Step 4: Construct the lower-level model based on user balance: To obtain actual delivery times for road segments that correspond to the road network congestion status and to provide congestion feedback to the upper-level model, a lower-level model is constructed based on User Equilibrium (UE) given fundamental data such as road network topology, free-flow delivery times for road segments, and road segment traffic capacity. The model solves for the equilibrium traffic flow of road segments through traffic assignment and establishes a nonlinear mapping relationship between total traffic flow, capacity, and delivery time using the BPR impedance function. The obtained actual delivery times for road segments are then output as congestion feedback to the upper-level model described in step 3 to support the linked calculation of cost items such as fuel consumption costs, carbon emission costs, and time window penalties. The parameters, symbols, and their meanings used in the lower-level model are shown below: parameter: The set of feasible paths in a road network; : A set of nodes; Total number of vehicles in the road network (unit: vehicles). :path Path traffic / path allocation coefficient; : Path-segment association parameters, representing the path Does it include road sections? ; Free-flow delivery time for road sections (unit: hours); Considering traffic congestion on certain road sections Actual travel time (unit: hours); Road section Traffic capacity (unit: vehicles); BPR impedance function parameters; BPR impedance function parameters; :path Traffic flow (unit: vehicles); Road section Traffic flow of social vehicles on the road (unit: vehicles); Road section Traffic flow of logistics delivery vehicles (unit: vehicles); variable: :vehicle Does it pass through this section of road? (0-1 decision variables); Road section Actual delivery time (unit: hours); The lower-level model is based on a given social vehicle traffic flow. Traffic flow of logistics and delivery vehicles Under these conditions, traffic flow in each road segment is determined through traffic assignment relationships, and the BPR impedance function is used to map the traffic flow of each road segment to the actual delivery time of that segment. From this, we obtain As a congestion feedback input to the upper-level model, it enables the joint solution of traffic assignment and route optimization.

[0035] In response, the underlying model built based on User Equilibrium (UE) is as follows: (15) (16) (17) (18) (19) Equation (15) aims to minimize the total delivery time for all paths, where represents the node under traffic flow conditions. i To the node j Delivery time for each road segment. Equation (16) represents the total traffic constraint, ensuring that the sum of social traffic flow and logistics traffic flow on all road segments equals the total traffic demand. Q Equation (17) is a non-negative flow constraint, ensuring that the traffic flow of each road segment is not negative. Equation (18) is a traffic assignment constraint, indicating that the traffic flow of each road segment is equal to the sum of the flows of all paths containing that road segment. Equation (19) is the BPR impedance function: using the total flow of the road segment... With capacity The ratio is used to calculate the actual delivery time. .when When the road becomes larger (i.e., the road segment becomes more congested), Will , The nonlinear increase under the influence of the system achieves the feedback that "the greater the congestion, the longer the travel time".

[0036] Step 5, Solve the bi-level programming model: The bi-level programming model (including an upper-level model and a lower-level model) constructed in this invention belongs to a typical NP-hard problem. For large-scale instances, exact solvers such as CPLEX or GAMS often struggle to obtain the optimal solution within an acceptable timeframe, thus heuristic and metaheuristic algorithms are preferred. Genetic algorithms (GA) have been proven to have several advantages: Advantage 1: Strong global exploration capability, which can alleviate premature convergence; low dependence on initial solution; Advantage 2: Natural parallelism, which can accelerate the simultaneous evaluation of multiple individuals; Advantage 3: It has a high adaptability to complex non-convex problems.

[0037] Based on these advantages, this invention proposes a genetic algorithm (GA-Tent & Frank-Wolfe hybrid algorithm) that incorporates the Tent chaotic map and combines it with the Frank-Wolfe algorithm to efficiently solve this bi-level programming model. The specific algorithm flow is as follows: (1) Upper-level model solution algorithm: Improved genetic algorithm; Genetic algorithms possess strong global exploration capabilities, low dependence on initial solutions, the ability to evaluate multiple individuals in parallel, and adaptability to complex non-convex problems. They can be used to solve higher-level models to obtain better candidate delivery solutions. Specific calculation steps (see...) Figure 2 )as follows: ① Chaotic Initialization To overcome the problems of premature convergence and getting trapped in local optima in genetic algorithms, chaotic variables are combined with genetic algorithms to improve the solution quality of vehicle path models. Among various chaotic sequences, the Tent mapping is chosen due to its good uniformity and search efficiency. This invention uses the Tent mapping to generate chaotic sequences with an initial population size of 100, and its expression is shown in equation (20): (20) in, Indicates the first Chaotic variables generated in the next iteration. For the reason The next item obtained after the update, and By iterating over equation (20), a set of equations with relatively uniform distribution and strong ergodicity can be generated. A sequence is used to replace ordinary random numbers to improve initialization coverage. In implementation, chaotic sequences can be mapped to chromosome construction parameters: the access sequence can be obtained by assigning "chaotic key values" to client nodes and sorting them by key values; or chaotic values ​​can be mapped to discrete choices (such as vehicle split points / candidate path indices, etc.) to generate diverse initial individuals.

[0038] ② Fitness function To evaluate the fitness of gene chromosomes in the genetic algorithm, this invention designs a fitness function that is inversely proportional to the total delivery cost, so that the path with lower cost has higher fitness, and its expression is shown in equation (21): (twenty one) in, fit ( i () represents the fitness function value of the corresponding chromosome i in the genetic algorithm. C ( i The expression denoted by represents the objective function value of the logistics distribution route optimization problem from a low-carbon perspective studied in this invention. A monotonic relationship of "lower cost, higher fitness" is adopted to ensure that genetic operations tend to retain lower-cost solutions.

[0039] ③ Probability of choice Solutions with higher fitness values ​​have a greater probability of being included in the next generation, and their selection probability is calculated according to equation (22): (twenty two) Equation (22) normalizes the fitness of each individual into a probability, which serves as the basis for roulette wheel selection or equivalent selection strategies, thereby achieving survival of the fittest.

[0040] ④ Crossover operator and adaptive crossover probability Crossover is used to combine superior gene fragments from different parents to generate new individuals. To avoid excessive crossover utilization that destroys excellent structures or insufficient exploration due to excessively low crossover utilization, this invention employs an adaptive crossover probability. Its expression is shown in equation (23): (twenty three) in, , ; This represents the current iteration number in the genetic operation. This represents the total number of iterations in the genetic operation. A cyclic crossover method is used to perform the crossover operation, identifying cyclic mappings formed at several positions on the two parent chromosomes (i.e., starting from a gene value at a certain position in parent 1, finding the same gene value in parent 2, then returning to parent 1 to continue tracing until returning to the starting point). The set of these cyclically corresponding positions is recorded as a cyclic node. The specific steps are as follows: 1. Select two chromosomes from the parent generation for crossover; 2. Based on adaptive crossover probability Identify the paternal chromosomes involved in the crossing over; 3. Based on the cycle nodes obtained in step 2, select the corresponding parent gene and copy it to the corresponding position in the offspring; 4. Based on the cycle node of the other parent chromosome, copy the remaining nodes to the empty slots in the offspring; 5. Repeat the above method for the remaining offspring.

[0041] ⑤ Mutation Operator and Adaptive Mutation Probability Based on the crossover operation, this invention also uses adaptive probability to calculate the mutation probability, as shown in equation (24), where d Let the current iteration algebra be... D This represents the total number of iterations, typically ranging from [0.001, 0.01].

[0042] (twenty four) The reverse flip mutation is used as the mutation control operation. Two nodes at random locations on the chromosome are selected, and the gene segment between the two nodes is completely flipped to generate a new access sequence. This mutation method effectively perturbs individuals while maintaining solution feasibility, thereby improving their ability to escape local optima. The specific steps are as follows: 1. Using the mutation probability formula, determine the parent individuals that need to be mutated; 2. Randomly select two nodes at different positions on the parent chromosome determined in step 1, and perform the corresponding flipping operation; 3. Obtain offspring individuals through the flipping mutation in step 2, thus completing the mutation operation; Among them, the number of genetic iterations reaches the preset maximum number of iterations. D Stop when the optimal fitness improvement is less than a threshold for several consecutive generations; in an alternative implementation, a stopping condition can also be added to reduce unnecessary calculations.

[0043] (2) Lower-level model solution algorithm: Frank-Wolfe algorithm For the lower-level model, the Frank-Wolfe algorithm is used to solve for the road traffic flow and actual delivery time of road segments under equilibrium conditions. The core idea of ​​the Frank-Wolfe algorithm is to first find an all-or-nothing auxiliary flow as the descent direction under the current road segment impedance (delivery time), and then determine the step size and update the flow through line search until convergence.

[0044] The specific solution process is as follows: ① Initialization: Let the segment time be... Traffic flow is allocated to each road segment using an all-in, all-out allocation method, resulting in a set of road segment flow rates. The number of iterations is denoted as n =1; ② Update the impedance of each segment (road section): ; ③ Determine the direction of the next iteration. Based on the updated impedance of each road segment. Find the shortest path between road segments, and then use the all-or-nothing assignment method to distribute traffic flow again to obtain the additional flow. ; ④ Determine the optimal iteration step size That is, to find the expression (25) value: (25) ⑤ Update the traffic flow of the road segment and determine the new iteration starting point: ; ⑥ Convergence test. If it exists, , If it is a preset precision parameter, then If the desired equilibrium solution is found, stop the algorithm; otherwise, let... Then proceed to step ②. The BPR function is selected as the time impedance function for the road segment.

[0045] (3) Description of the two-level planning In each generation of the genetic algorithm, when evaluating the fitness of individuals, the delivery plan obtained from decoding the individual is used to deduce the delivery vehicle plan and input into the lower-level model; the lower-level model solves and outputs the equilibrium segment delivery time. Feedback is fed back to the upper-level model to calculate fuel consumption costs, carbon emission costs, and time window penalties, thereby driving the genetic algorithm to update and achieve two-layer closed-loop collaborative optimization.

[0046] The present invention will now be described in detail with reference to the accompanying drawings and embodiments: This invention selects a representative Sioux Falls transportation network (see...) Figure 3 Numerical analysis was performed.

[0047] According to the method steps of this invention, the solution process is as follows: Step 1: Select and input the road network topology and basic logistics task data: Taking the Sioux Falls transportation network as an example, this network consists of 24 nodes, 76 links, and 576 OD pairs. The vehicle demand for each OD pair on different road segments is detailed in Appendix Table 1. In this transportation system, node 10 is a freight distribution center, with 10 demand nodes (nodes 1, 5, 7, 11, 13, 14, 18, 19, 20, and 22) requiring service. Table 1 summarizes the demand, service duration, and service time window for these demand nodes. The distribution center dispatches transport vehicles with a carrying capacity of 10 tons to provide services to these demand nodes. Key network characteristics include road segment distance, actual road segment capacity (…). The zero-flow (free-flow) travel time for each road segment is shown in Table 2.

[0048] Table 1 Transportation Task Information Table

[0049] Table 2 Road Section Parameters

[0050] Step 2, propose reasonable assumptions based on the problem: Assumption 1: There is one and only one distribution center that provides delivery services to multiple demand points, and all delivery vehicles depart from this distribution center and return to the distribution center after completing the delivery task; Assumption 2: All delivery vehicles are of the same model and have the same carrying capacity.

[0051] Assumption 3: The existing cargo capacity of the distribution center can meet the total demand of customers, and the maximum cargo capacity of the delivery vehicles is greater than the cargo demand of each customer.

[0052] Assumption 4: Each customer’s needs are known and remain constant throughout the delivery process.

[0053] Assumption 5: Each demand point has only one delivery vehicle responsible for delivering goods, and each delivery vehicle can be responsible for multiple demand points on a route.

[0054] Assumption 6: The distribution vehicle maintains a constant speed throughout the distribution process.

[0055] Step 3, consider the carbon tax mechanism to construct the upper-level model: The parameters used in the optimization model constructed above include: fixed operating costs of delivery vehicles. The cost is 400 yuan per vehicle; fuel consumption per unit time. Take 120L / hour; carbon emissions per liter of fuel consumed Take 2.63 kg CO2 / L; carbon tax price Take 0.5 yuan / kg CO2. Penalty coefficient for vehicles arriving early. The penalty for delayed vehicle arrival is calculated at 0.2 yuan per minute. A cost of 1 yuan per minute was used. To compare the impact of road congestion and carbon emission costs on delivery results, three comparative scenarios were set up based on the SiouxFalls traffic network, and solutions were obtained for each scenario using the same data. Specifically: Scenario 1: Ignoring traffic congestion, used as a baseline; Scenario 2: Based on Scenario 1, consider traffic congestion but do not consider carbon emission costs; Scenario 3: The constructed two-level planning model simultaneously incorporates carbon emission costs and traffic congestion dynamics.

[0056] For the scenarios mentioned above, comparative experiments were conducted with total delivery cost as the optimization objective.

[0057] Step 4: Constructing the lower-level model based on user equilibrium: In this embodiment, the lower-level model calculates congestion feedback using the Sioux Falls road network as the object. Segment delivery time is calculated using the BPR impedance function, with parameters... It is 0.15. The value is 4, used to reflect the congestion effect of increased delivery time when road segment traffic volume increases. For a candidate delivery route given in step 3, the delivery traffic induced by this route and the existing social traffic OD demand of the road network are input into the lower-level model for allocation to obtain the total traffic volume of each road segment, and the delivery time of each road segment is calculated accordingly. The road segment delivery time output by the lower-level model is returned to step 3 for cost accounting of the upper-level model. On the one hand, it is used to estimate the arrival time of vehicles to each customer and calculate the time window penalty cost; on the other hand, it is used to calculate the fuel consumption and carbon emission costs related to travel time, and further calculate the carbon emission cost. In this way, each candidate route in the upper-level model corresponds to a set of delivery time data obtained from congestion feedback, so that the route optimization results obtained by the upper-level model are consistent with the traffic conditions of the lower-level model.

[0058] Step 5, Solving the bi-level programming model: Obtain the optimal path schemes for scenarios 1, 2, and 3 through an improved genetic algorithm (e.g., Figure 4-6 The detailed routes are given in Table 3, and the corresponding total cost, fuel consumption cost, and carbon emission cost are shown in Table 4. Scenario 3's route plan demonstrates the avoidance of congested road sections and the priority use of alternative routes: such as... Figure 6 In the corresponding route selection, for the trip from node 10 to customer point 20, although route 29-49-53-59 (24km) is shorter, the actual delivery time is longer and the congestion cost is higher. In the end, the more traffic-efficient route 29-50-56 (27km) is adopted, thereby reducing fuel and carbon emission costs and reducing time window penalties.

[0059] Based on scenario 3, the impact of different congestion levels on delivery costs was further examined by setting the travel demand multiple as a baseline value of 1.1, 1.3, and 1.5. This was to test the adaptability of the present invention under different congestion intensities. The corresponding results are shown in Table 5: When the travel demand multiple increases from 1.1 to 1.5, the total cost increases from RMB 2007.76 to RMB 2377.85, the fuel consumption cost increases from RMB 220.67 to RMB 545.60, and the carbon emission cost increases from RMB 16.57 to RMB 47.24. This indicates that increased congestion will be transmitted to the cost accounting stage through delivery time feedback, causing the total cost and carbon emissions to change synchronously with the degree of congestion, thereby ensuring that the route evaluation is consistent with the traffic conditions.

[0060] To determine the optimal range for carbon tax price parameters, a sensitivity test was conducted on the parameters based on Scenario 3: the carbon price was gradually increased from 0.05 yuan / kg to higher levels, and the trends in total cost and carbon emissions were compared. The relevant comparison results can be found in [reference needed]. Figure 7 The results of the examples show that when the carbon tax is increased from 0.05 yuan / kg to 6 yuan / kg, carbon emissions can be reduced by 30.53%; when the carbon tax is further increased to 16 yuan / kg, the additional emission reduction is only 13.09%, and the total cost and carbon emission cost increase even faster. Therefore, it is preferable to control the carbon tax price parameter within a range not exceeding 6 yuan / kg to achieve a better balance between emission reduction effect and cost affordability.

[0061] Table 3 Vehicle Routes

[0062] Table 4 Total Cost Composition

[0063] Table 5. Delivery Costs under Different Traffic Conditions

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A two-level planning method for logistics distribution routes considering road network congestion and carbon tax mechanisms, characterized in that: The method includes the following steps: Step 1, input a set of nodes N and road segment collection A The transportation network formed The basic data, the node set N includes distribution center node 0 and n There are customer nodes i, and the distribution center node 0 has... m Delivery vehicles; Step 2: Construct the upper-level model. The upper-level model aims to minimize the total delivery cost, which includes vehicle fixed costs, fuel consumption costs, carbon emission costs, and time window penalty costs. Decision variables include vehicle activation plans and vehicle travel route plans. The calculation of fuel consumption costs and carbon emission costs depends on the actual delivery time of the road segment. ; Step 3: Construct the lower-level model. This lower-level model is based on the User Equilibrium (UE) traffic allocation principle. Its objective is to minimize the total delivery time for all travelers in the road network. It allocates the traffic flow induced by delivery route schemes and existing social traffic flow to the road network, and uses an impedance function to calculate the actual delivery time for each road segment. ; Step 4: Solve the two-level programming model, and iteratively calculate the actual delivery time of the road segment output by the lower-level model. Feedback is sent to the upper-level model to update cost calculations, and the delivery route plan generated by the upper-level model is input into the lower-level model to update traffic allocation, until an optimized delivery route plan consistent with the road network congestion status is obtained.

2. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 1, characterized in that: In step 2, the objective function of the upper-level model is ,in, C 1 represents the fixed cost of the vehicle. C 2 represents fuel consumption cost. C 3 represents the cost of carbon emissions. C 4 represents the time window penalty cost.

3. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 2, characterized in that: The vehicle fixed cost ,in For vehicles Fixed costs, To indicate whether the vehicle is in use 0-1 decision variables; fuel consumption cost ,in For fuel unit price, Fuel consumption per unit time For road section The actual delivery time To indicate vehicles Does it pass through this section of road? 0-1 decision variables; The carbon emission cost ,in For carbon tax prices, Carbon emissions per liter of fuel consumed; The time window penalty cost ,in The penalty coefficient for vehicles arriving early. The penalty coefficient for vehicle delay arrival. For customers i The service start time, For customers i Service end time For vehicles k Arrival at the customer i The arrival time.

4. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 1, characterized in that: In step 3, the objective function of the lower-level model is ,in R It is the set of feasible paths in the road network. Indicates traffic flow Road sections under conditions Delivery time.

5. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 4, characterized in that: In step 3, the impedance function is expressed as the BPR function, which is: ,in For free-flow delivery time on the route, and For the parameters of the BPR function, For road section Traffic flow of social vehicles on the road For road section Traffic flow of logistics and delivery vehicles on the road For road section Traffic capacity.

6. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 1, characterized in that: In step 4, the upper-level model is solved using the genetic algorithm (GA), and the lower-level model is solved using the Frank-Wolfe algorithm.

7. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 6, characterized in that: The genetic algorithm uses the Tent chaotic mapping for population initialization.

8. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 7, characterized in that: In the genetic algorithm, an adaptive crossover probability is used. Perform crossover operation, the adaptive crossover probability Based on the current iteration number Total number of iterations D The relationship needs to be adjusted.

9. The two-tiered logistics distribution route planning method considering road network congestion and carbon tax mechanisms according to claim 8, characterized in that: In the genetic algorithm, an adaptive mutation probability is used. Perform mutation operation, the adaptive mutation probability ,in d This represents the current iteration number. D This represents the total number of iterations.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the two-level planning method for logistics distribution routes that considers road network congestion and carbon tax mechanisms as described in any one of claims 1 to 9.

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