A Method for Optimizing Charging and Allocating Costs in Multi-Carrier Electric Heavy Truck Plots
By constructing a mixed-integer linear programming model and an approximate core cost allocation model, the charging scheduling and platooning coordination problem in the scenario of multi-carrier electric heavy-duty trucks was solved. The optimization of vehicle-level operation schemes and cost allocation were realized, ensuring the feasibility and stability of the scheme and improving the scalability of the solution.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2026-04-14
- Publication Date
- 2026-06-02
AI Technical Summary
Existing technologies struggle to achieve joint optimization of charging scheduling and fleet coordination in multi-carrier electric heavy-duty truck scenarios, and lack a stable cost allocation mechanism. This results in the generated operating schemes being infeasible or having costs deviating from the optimal level under energy or time window constraints. Furthermore, the solutions lack scalability and are difficult to promote in large-scale scenarios.
A mixed-integer linear programming model is constructed to jointly optimize vehicle departure time, charging amount, and platoon leader role. An approximate core cost allocation model is constructed in the allocation phase, and stability relaxation and subsidy variables are introduced. The sub-alliance that violates the constraints the most is identified through row generation strategy iteration, and the carrier payment vector that satisfies the stability constraints is output.
The system generates vehicle-level operation schemes that meet the requirements of energy feasibility and collaborative synchronization, provides self-executable settlement basis, ensures the feasibility and long-term sustainability of multi-carrier collaborative operation, reduces computational burden, and improves the scalability of the solution.
Smart Images
Figure CN122133878A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent transportation technology, and more specifically to a method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning. Background Technology
[0002] Long-distance trunk road freight is characterized by long transport distances, high vehicle loads, and high energy consumption. With the advancement of zero-emission transportation policies and electrification technologies, the application of electric heavy-duty trucks in trunk logistics is gradually increasing. Their operation is affected by factors such as driving range, battery state of charge, charging time, charging power limitations, and spatial and temporal differences in electricity prices, resulting in a strong coupling between departure time, charging decisions, and arrival feasibility, significantly increasing the planning difficulty. At the same time, platooning can reduce driving energy consumption by reducing air resistance. In the actual trunk transportation market, vehicles often belong to multiple independent carriers, exhibiting heterogeneity in release time, deadlines, battery capacity, and initial battery state of charge, making cross-carrier collaboration face complex decision-making and coordination problems.
[0003] In existing research, charging scheduling and platooning coordination are often treated separately, or assumed to be negligible when replenishing energy under the assumption of diesel vehicles. This makes it difficult to characterize the inverse impact of charging and waiting on synchronization opportunities and feasibility in the electric heavy-duty truck scenario. On the one hand, charging decisions determine the dwell time and available energy of vehicles at stations, directly affecting whether subsequent road segments can depart synchronously with other vehicles to form a platoon. On the other hand, platooning synchronization requires multiple vehicles to depart at the same time, which may force some vehicles to extend their waiting time, thereby changing their charging window and energy status. Existing technologies have failed to make joint decisions on charging amount, departure time, and navigator role under the same optimization framework, resulting in the generated operation plan being infeasible under energy constraints or time window constraints, or significantly deviating from the optimal cost.
[0004] At the same time, there is a general lack of stable cost allocation mechanisms in multi-carrier collaborative scenarios. Many methods default to a single operating entity or centralized scheduling. Even when multiple carriers are involved, the simple settlement rule that each carrier only pays its own charging fee is often adopted. There is no constraint or quantification on whether each sub-alliance can obtain lower costs after deviating from the main alliance. This allocation method does not consider the redistribution of collaborative benefits among carriers caused by the asymmetry of energy consumption between lead and follower and the spatial and temporal differences in electricity prices. This makes it possible for collaborative solutions obtained through joint optimization at the operational level to be unenforceable. Some carriers may obtain lower costs if they operate independently outside the main alliance, making it difficult to promote collaborative alliances in a long-term and stable manner.
[0005] Furthermore, the inadequate characterization of key electrification constraints and poor scalability of solutions further restrict the implementation of the technology. Some models fail to simultaneously consider key factors such as the heterogeneity of station electricity prices and charging power, the dynamic evolution of battery state of charge, the asymmetry of energy consumption between piloting and following, the minimum battery state of charge safety margin, and the hard cutoff period at the end point, resulting in insufficient adaptability to the real corridor operation environment. At the solution level, the superposition of mixed integer programming in the operation phase and exponential stability constraints in the allocation phase makes it too computationally burdensome to directly enumerate all sub-alliances. The lack of a scalable solution framework for the scale of real carriers and a reusable alliance cost calculation mechanism makes it difficult to extend the method from proof of concept to practical application.
[0006] Therefore, how to design a charging optimization and cost allocation method for multi-carrier electric heavy-duty truck fleets, realize the integrated joint optimization of charging scheduling, departure synchronization and the lead role, and build a cost allocation mechanism that meets the stability constraints of each sub-alliance to ensure the scalability of the solution process in large-scale scenarios is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0007] In view of this, the present invention provides a method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platoons. It aims to overcome the problems of disconnect between charging scheduling and platoon collaboration, lack of stable settlement mechanism for multi-carrier collaboration, and insufficient scalability for solving large-scale scenarios in the prior art. It can simultaneously complete charging, synchronous departure, and joint optimization of the lead role in long-distance trunk corridor scenarios, and output a carrier cost allocation scheme that meets the stability constraints of the sub-alliance, thereby ensuring the feasibility and long-term sustainability of the cross-carrier collaborative operation scheme.
[0008] To achieve the above objectives, the present invention adopts the following technical solution:
[0009] A method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning includes the following steps: S1. Construct a long-distance corridor network consisting of a set of stations and a set of road segments, and establish a set of candidate departure times based on discrete time index; S2. During the operation phase, for a given fleet of vehicles belonging to a carrier alliance, perform the following steps: S21. Establish a mixed integer linear programming model. The model uses the departure time of each vehicle on each road segment, the charging amount at each station, and the navigation signage on each road segment as decision variables, the minimum total electricity purchase cost of the alliance as the objective function, and includes multiple preset constraints. S22. Solve the mixed-integer linear programming model to obtain the optimal objective function value and the optimal solution; S23. The optimal objective function value is used as the alliance feature cost, and a vehicle-level cooperative operation scheme is generated based on the values of each decision variable in the optimal solution. S3. In the allocation phase, the alliance characteristic cost is used as the characteristic function value of the cooperative game to construct an approximate core cost allocation model and solve for the carrier payment vector that satisfies the stability constraint and the corresponding stability relaxation or external subsidy demand. S4. Output the vehicle-level collaborative operation scheme and the carrier payment vector.
[0010] Preferably, in S1, the long-distance corridor network consists of an ordered set of stations and a set of road segments formed by adjacent stations; wherein each road segment connects two adjacent stations, and the set of stations includes a subset of charging stations, where vehicles are allowed to recharge at charging stations, but not at destination stations.
[0011] Preferably, in step S1, establishing the candidate departure time set based on the discrete-time index includes: Discretize the continuous time into a set of discrete time points with a step size Δ, and discretely select the departure time of the vehicle on each road segment, satisfying:
[0012] in, The variable is a binary variable, representing the vehicle. Is it on the road section? Index at discrete time Departure; For vehicles and road sections The set of feasible departure indexes.
[0013] Preferably, in step S21, the preset constraints include navigation consistency constraints:
[0014] in, Let be a binary variable, representing vehicle i departing from index n on road segment a and acting as the navigator; The variable for departure is a binary variable.
[0015] Preferably, in step S21, the preset constraints include a maximum formation size constraint:
[0016] in, For vehicles within Alliance C, For the maximum formation size, and These are binary variables: navigation and departure. The maximum formation size constraint is used to ensure that vehicle groups that depart from the same road segment at the same time can be divided into one or more formations under the maximum formation size limit, and each formation contains at least one lead vehicle.
[0017] Preferably, in step S21, the preset constraints include constraints on battery energy dynamics and the asymmetric energy consumption during navigation:
[0018] in, and Vehicle i leaves the road Battery level at the starting station and upon arrival at the next station. To lead energy consumption, To match vehicle energy consumption, To guide the binary variables, For vehicles and road sections The set of feasible departure indexes.
[0019] Preferably, in step S21, the preset constraints include charging feasibility constraints: Charging is not permitted at non-charging stations or destination stations: =0; The charging capacity is limited by the station's effective charging power and the dwell time.
[0020] in, The amount of charge vehicle i receives at station s. For the effective charging power of the station, For charging efficiency, This refers to the time a vehicle spends at the station.
[0021] Preferably, in S23, the alliance feature cost The objective function value for minimizing the total electricity purchase cost during cooperative vehicle operation within Alliance C is expressed as:
[0022] in, The electricity price for charging station s, The amount of charge vehicle i receives at station s. A collection of charging stations, This is a collection of vehicles within Alliance C.
[0023] Preferably, in step S3, the solution of the approximate core cost allocation model satisfies Cost allocation for approximate core constraints:
[0024]
[0025] in, Payment for carrier K, For stability slack variables, For external subsidies or budget gap variables, The feature cost of sub-consortium C, Let L be the characteristic cost of all carriers, and C be any non-empty sub-alliance; Solving the approximate core cost allocation model includes: given Minimize under conditions The first allocation model; or given Minimize under conditions The second allocation model is used to obtain a trade-off between stability and subsidies.
[0026] Preferably, in step S3, a row generation strategy is used to solve the approximate core cost allocation model: Starting from the set of working alliances containing all single carrier alliances, iteratively solve the restricted principal problem to obtain candidate allocation solutions. Identify the sub-alliance that most violates the stability constraint by separating the problem. If the degree of violation is less than the termination threshold, add the sub-alliance to the set of working alliances and continue iterating until there are no sub-alliances that violate the stability constraint, and then output the allocation solution.
[0027] As can be seen from the above technical solution, compared with the prior art, the technical solution of the present invention has the following beneficial effects: 1. This method constructs a mixed-integer linear programming model during the operation phase, using the vehicle's departure time on each road segment, the charging amount at each charging station, and the platooning leadership role on each road segment as decision variables for joint optimization. It also characterizes key constraints such as battery energy dynamics, energy asymmetry between leadership and following, charging power limitations, maximum platoon size, and time windows. Compared to existing technologies that handle charging planning and platooning synchronization separately, this method can generate vehicle-level operation schemes that simultaneously meet energy feasibility and collaborative synchronization requirements from a system-wide perspective, avoiding the problems of infeasibility or cost deviation caused by decision separation.
[0028] 2. In the allocation phase, the characteristic cost of the alliance is used as the characteristic function value of the cooperative game. An approximate core cost allocation model is constructed by introducing stability slack variables and subsidy variables. The carrier payment vector is solved by budget balance equation and stability constraints on all non-empty true sub-alliances. This mechanism can effectively quantify the deviation incentives of each sub-alliance. When the core of the cooperative game exists, it outputs a strictly stable allocation scheme. When the core is empty, it outputs the slack level or subsidy requirement that satisfies approximate stability. It provides a self-executable settlement basis for multi-carrier collaborative operation and overcomes the technical defect that the naive allocation rule is difficult to stabilize in the long term.
[0029] 3. When solving the approximate core cost allocation model, a row generation strategy is adopted. Starting from the working set containing all single-carrier alliances, the sub-alliance that most violates the stability constraint is identified iteratively and dynamically added to the constrained master problem, avoiding the computational burden caused by directly enumerating all exponential sub-alliance constraints. At the same time, the method combines a caching and reuse mechanism for alliance feature costs, so that a stable allocation solution can still be obtained within a controllable time when the number of carriers and the fleet size increase. This provides a scalable solution framework for the engineering deployment of the method in real trunk transportation scenarios. Attached Figure Description
[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0031] Figure 1 A flowchart illustrating a method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the long-distance trunk corridor station-segment structure and charging station distribution provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of cross-carrier electric heavy-duty truck platooning collaborative operation provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the spatiotemporal operation provided in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the trade-off front between stability relaxation ε and supplementary γ, provided in an embodiment of the present invention. Detailed Implementation
[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0033] like Figure 1 As shown, this embodiment provides a method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platoons, including the following steps: S1. Construct a long-distance corridor network consisting of a set of stations and a set of road segments, and establish a set of candidate departure times based on discrete time index; S2. During the operation phase, for a given fleet of vehicles belonging to a carrier alliance, perform the following steps: S21. Establish a mixed integer linear programming model. The model uses the departure time of each vehicle on each road segment, the charging amount at each station, and the navigation signage on each road segment as decision variables, the minimum total electricity purchase cost of the alliance as the objective function, and includes multiple preset constraints. S22. Solve the mixed-integer linear programming model to obtain the optimal objective function value and the optimal solution; S23. The optimal objective function value is used as the alliance feature cost, and a vehicle-level cooperative operation scheme is generated based on the values of each decision variable in the optimal solution. S3. In the allocation phase, the alliance characteristic cost is used as the characteristic function value of the cooperative game to construct an approximate core cost allocation model and solve for the carrier payment vector that satisfies the stability constraint and the corresponding stability relaxation or external subsidy demand. S4. Output the vehicle-level collaborative operation scheme and the carrier payment vector.
[0034] It solves the problem of infeasibility or cost deviation caused by the disconnect between charging scheduling and platooning coordination in existing technologies by constructing a mixed-integer linear programming model to jointly optimize vehicle departure time, charging amount, and platooning leadership role, and characterizes key constraints such as battery energy dynamics, energy consumption asymmetry, and charging power. On this basis, it constructs a cooperative game based on alliance characteristic costs, introduces an approximate core allocation model with stability relaxation and subsidy variables, and outputs a carrier payment vector that satisfies the stability constraints of any sub-alliance, providing a self-executable settlement mechanism for multi-carrier collaboration. At the same time, it adopts a row generation strategy to iteratively identify the sub-alliance that most violates the constraints and dynamically adds it to the restricted master problem, avoiding the enumeration calculation of exponential constraints and improving the scalability of the solution for large-scale scenarios.
[0035] The following provides further explanation of each step in the above method and its related technical features; In this embodiment, S1, a long-distance corridor network consisting of a set of stations and a set of road segments is constructed, and a set of candidate departure times is established based on a discrete-time index. The long-distance corridor network consists of an ordered set of stations and a set of road segments formed by adjacent stations. Each road segment connects two adjacent stations, and the set of stations includes a subset of charging stations. Vehicles are allowed to recharge at charging stations, but not at the destination station. like Figure 2As shown, the long-distance corridor network consists of an ordered set of stations and a set of road segments formed by adjacent stations. In specific implementation, a single-line corridor with a total length of about 800 kilometers can be selected, consisting of a starting point, an ending point, and multiple intermediate stations along the way. Road segments are formed between adjacent stations. Charging stations are distributed at the starting point and some intermediate stations. Each station is configured with different charging power and time-of-use electricity price. For example, station S00 is configured with a charging power of 350kW and an electricity price of 0.49 yuan / kWh, station S02 is configured with a charging power of 500kW and an electricity price of 0.46 yuan / kWh, and station S06 is configured with a charging power of 750kW and an electricity price of 0.53 yuan / kWh. Charging is not allowed at the destination station. This configuration can truly reflect the heterogeneity of charging resources in terms of space and price, and provide basic network data for subsequent joint optimization of charging and platooning.
[0036] Furthermore, the set of candidate departure times built based on discrete-time indexes in S1 includes: Discretize the continuous time into a set of discrete time points with a step size Δ, and discretely select the departure time of the vehicle on each road segment, satisfying:
[0037] in, The variable is a binary variable, representing the vehicle. Is it on the road section? Index at discrete time Departure; For vehicles and road sections The set of feasible departure indexes; In establishing the discrete-time index, continuous time is discretized with a step size of Δ = 0.25 hours to form a finite set of discrete time points. For each vehicle-segment pair, the feasible departure index set can be filtered based on the earliest release time and the latest arrival deadline of the vehicle, eliminating obviously infeasible departure times. This discretization process transforms the originally complex continuous-time optimization problem into a solvable mixed-integer linear programming form, enabling the coupling relationship between charging decisions, waiting time, and formation synchronization opportunities to be accurately characterized by linear constraints, providing a feasible modeling foundation for integrated joint optimization in the subsequent operation phase.
[0038] In this embodiment S2, during the operation phase, for a given set of vehicles of a carrier alliance, the following steps are performed: S21. Establish a mixed integer linear programming model. The model uses the departure time of each vehicle on each road segment, the charging amount at each station, and the navigation signage on each road segment as decision variables, the minimum total electricity purchase cost of the alliance as the objective function, and includes multiple preset constraints. S22. Solve the mixed-integer linear programming model to obtain the optimal objective function value and the optimal solution; S23. The optimal objective function value is used as the alliance feature cost, and a vehicle-level cooperative operation scheme is generated based on the values of each decision variable in the optimal solution. Among them, the preset constraints include navigation consistency constraints:
[0039] in, Let be a binary variable, representing vehicle i departing from index n on road segment a and acting as the navigator; The variable for departure is a binary variable.
[0040] Furthermore, the preset constraints include a maximum formation size constraint:
[0041] in, For vehicles within Alliance C, For the maximum formation size, and These are binary variables: navigation and departure. The maximum formation size constraint is used to ensure that vehicle groups that depart from the same road segment at the same time can be divided into one or more formations under the maximum formation size limit, and each formation contains at least one lead vehicle.
[0042] Furthermore, the preset constraints include battery energy dynamics and the asymmetric constraint of following energy consumption during navigation:
[0043] in, and Vehicle i leaves the road Battery level at the starting station and upon arrival at the next station. To lead energy consumption, To match vehicle energy consumption, To guide the binary variables, For vehicles and road sections The set of feasible departure indexes.
[0044] Furthermore, the preset constraints include charging feasibility constraints: Charging is not permitted at non-charging stations or destination stations: =0; The charging capacity is limited by the station's effective charging power and the dwell time.
[0045] in, The amount of charge vehicle i receives at station s. For the effective charging power of the station, For charging efficiency, This refers to the time a vehicle spends at the station.
[0046] Furthermore, the cost of alliance features The objective function value for minimizing the total electricity purchase cost during cooperative vehicle operation within Alliance C is expressed as:
[0047] in, The electricity price for charging station s, The amount of charge vehicle i receives at station s. A collection of charging stations, This is a collection of vehicles within Alliance C.
[0048] The following details the specific implementation process of S2 during the operation phase; In practical implementation, firstly, based on the power and electricity price parameters of the long-distance corridor network and each charging station mentioned in the above steps, the basic data of all vehicles in the alliance are input, including the release time, deadline, battery capacity, initial state of charge, and baseline energy consumption rate of each vehicle, as well as parameters such as the electricity price, charging power, and road segment mileage of the corridor network; then, the continuous time is discretized according to a step size Δ=0.25 hours, and a feasible departure index set is screened for each vehicle-road segment: discrete slots earlier than the vehicle release time are directly eliminated; if a discrete slot causes the vehicle to be unable to meet the deadline or minimum state of charge even if it is recharged along the way, that slot is also deleted; Figure 3 As shown, vehicle B1 is released earliest, and its first feasible departure set includes earlier slots; vehicle A1 is released later, and the first slots earlier than its release time are not included in the solution. This screening process ensures that the subsequent model only makes formation and charging decisions within physically feasible discrete moments. Secondly, establish a binary variable based on departure. Leading binary variables Continuous variable of charging quantity Off-site power and the battery level upon arrival The model is a mixed-integer linear programming model with decision variables. The objective function is to minimize the total electricity purchase cost for all vehicles in the alliance across all charging stations. Four key constraints are imposed on the model: a leader consistency constraint, ensuring that only vehicles that actually depart can be designated as leaders; a maximum platoon size constraint, guaranteeing that the platoon size within the same departure slot does not exceed the upper limit; a battery energy dynamics and energy consumption asymmetry constraint, distinguishing between leader and follower energy consumption and recursively calculating the start and end energy consumption for each segment; and a charging feasibility constraint, prohibiting charging at non-charging stations and at the destination, and limiting the charging amount to no more than [a certain value]. ; Then, the above mixed-integer linear programming model is solved. During the solution process, the model automatically synchronizes the departure timing of each vehicle within feasible departure slots, determines which vehicles can depart together on the same road segment at the same discrete time, and decides the lead vehicle in each convoy. Simultaneously, the model optimizes the charging amount at each station based on real-time electricity price differences and power constraints. Figure 3 As shown, the electricity price at the S00 station is relatively high, so only B1, which has the lowest electricity consumption, is charged at 63.09 kWh, and the other vehicles are not charged. The electricity price at the S03 station is relatively low, so A2, B1, B2, and C1 are charged together at 163.75 kWh, and A1 is still not charged. The final total electricity purchase cost is c(L) = 75.64 yuan, which is taken as the characteristic cost of the alliance. Finally, based on the values of the decision variables in the optimal solution, the complete vehicle-level cooperative operation scheme is reconstructed, including the departure time of each vehicle on each road segment, the charging amount and dwell time at each charging station, and the navigation sign on each road segment. Figure 3 The video visually demonstrates the formation and reorganization process of the five vehicles. From the starting point to the first station, A1, B1, and C1 form one team, and A2 and B2 form another team. Only B1 refuels at the first station. The four vehicles refuel at station S03 and then reorganize. At the end, they split into two teams again to reach the destination. Furthermore, for larger-scale scenarios, such as Figure 4 The 40 vehicles and 8 stations shown can be used to generate a spatiotemporal operation diagram after solving the problem. The overlapping broken lines indicate convoy driving, green triangles mark merging convoys, and red inverted triangles mark merging convoys. The relevant output results can be directly used by the scheduling platform to generate departure slot tables, charging reservation tables, and navigator rotation tables, which can be issued and executed without secondary manual interpretation. The above process realizes the complete steps from input data, discretization and filtering, modeling and solving to outputting alliance feature costs and vehicle-level collaborative operation schemes, providing a reliable basis for subsequent cost allocation.
[0049] In this embodiment, S3, during the allocation phase, the alliance characteristic cost is used as the characteristic function value of the cooperative game to construct an approximate core cost allocation model, and the carrier payment vector that satisfies the stability constraint and the corresponding stability relaxation or external subsidy demand is obtained. Among them, the solution of the approximate core cost allocation model satisfies Cost allocation for approximate core constraints:
[0050]
[0051] in, Payment for carrier K, For stability slack variables, For external subsidies or budget gap variables, The feature cost of sub-consortium C, Let L be the characteristic cost of all carriers, and C be any non-empty sub-alliance; Solving the approximate core cost allocation model includes: given Minimize under conditions The first allocation model; or given Minimize under conditions The second allocation model is used to obtain a trade-off between stability and subsidies.
[0052] Furthermore, a row generation strategy is employed to solve the approximate core cost allocation model: Starting from the set of working alliances containing all single carrier alliances, iteratively solve the restricted principal problem to obtain candidate allocation solutions. Identify the sub-alliance that most violates the stability constraint by separating the problem. If the degree of violation is less than the termination threshold, add the sub-alliance to the set of working alliances and continue iterating until there are no sub-alliances that violate the stability constraint, and then output the allocation solution.
[0053] In this step, the construction of the cooperative game depends on the feature costs of all sub-alliances calculated in the S2 stage. Taking 3 carriers as an example, it is necessary to solve the operation optimization models of the all-carrier alliance, the 3 single-carrier alliances and the 3 two-carrier alliances (a total of 7 sub-alliances) to obtain the corresponding feature costs c(L) and c(C). Based on this, stability slack variables are introduced. External subsidy variables , build An approximate core cost allocation model is proposed, which provides two optimization perspectives: the first allocation model minimizes stability relaxation ε given external subsidy γ, and can be used to assess the stability that a coordinated scheme can achieve when policy subsidies are at a certain level; the second allocation model minimizes external subsidy γ given stability relaxation ε, and can be used to calculate the minimum subsidy amount required to achieve the desired level of stability. The combination of the two models can generate, for example... Figure 5 The stability-subsidy trade-off frontier shown is as follows: Figure 5 The horizontal axis represents the external subsidy γ, and the vertical axis represents the stability relaxation ε. Each point on the curve represents a cost allocation scheme. As the subsidy increases, the required stability relaxation gradually decreases until strict stability is achieved. The minimum subsidy required when =0) provides a quantitative basis for platform operators to make decisions: they can choose the corresponding stability level based on their actual subsidy capacity, or determine the required subsidy based on acceptable stability relaxation. In terms of solution strategy, since the number of sub-alliances increases exponentially with the increase in the number of carriers, a row generation strategy is adopted for efficient solution. Specifically, starting from the initial working set Ω containing all single-carrier alliances, the restricted master problem is solved iteratively to obtain candidate allocation solutions; the violation degree of each sub-alliance is calculated by separating the problem. The method identifies the sub-coalition that most violates the stability constraint. If the violation degree is less than the termination threshold (e.g., -0.01), the sub-coalition is added to the working set for further iteration. In test cases with 2 to 4 carriers and a total of 20 to 60 vehicles, the method can obtain feasible solutions. In multiple instances, strict core assignments with ε=0 and γ=0 appear, indicating that the collaboration can be spontaneously stable under the measured scale and heterogeneity. At the same time, by caching the feature cost of the solved sub-coalition, the overhead of repeated computation can be further reduced.
[0054] In this embodiment, S4, the vehicle-level collaborative operation scheme and the carrier payment vector are output.
[0055] The vehicle-level collaborative operation scheme includes: the departure time of each vehicle on each road segment, the charging amount at each station, the dwell time at each station, and the navigation markers on each road segment; the carrier payment vector is used to allocate the total electricity purchase cost among the carriers.
[0056] The vehicle-level collaborative operation plan output in this step can be directly used for actual operation scheduling. Specifically, it specifies the departure time of each vehicle on each road segment. It can be used by the dispatching platform to generate a departure slot table, specifying when each vehicle should depart from each station in the corridor to form a platoon; and the charging capacity at each station. Duration of stay It can be used to generate charging station reservation schedules, guiding vehicles on the duration of their stay at charging stations and their charging plans, thus avoiding conflicts with charging station resources; and to provide navigation signs for various road sections. It can be used to generate a pilot rotation table, clarify the allocation scheme of the pilot vehicle in each segment of the formation, and balance the additional burden caused by the high energy consumption of piloting for each carrier. These output results are presented in the form of specific spatiotemporal instructions, which can be issued to the vehicles of each carrier for execution without the need for secondary human interpretation. The operator can directly verify whether the departure time of each vehicle and the formation structure are consistent with the output scheme. Output carrier payment vector It satisfies the budget balance constraints of the grand alliance and the stability constraints of all non-empty sub-alliances, ensuring that no carrier or carrier combination can obtain lower costs by leaving the grand alliance. When the core exists (i.e., ε=0, γ=0), the output can be directly used as the settlement basis for each carrier. When the core is empty, the output includes both stability relaxation ε and external subsidies γ, forming a stability-subsidy interface. This allows for a quantitative assessment of the level of external support required to maintain collaboration, providing a quantitative basis for platform operators to formulate subsidy policies or incentive measures. In addition, by combining the carbon intensity parameters of the sites, the carbon emissions of the collaboration scheme on the grid side can be calculated, providing data support for the green policy interface, thereby transforming social emission reduction benefits into private incentives to maintain collaborative stability.
[0057] This embodiment constructs a long-distance corridor network and a discrete-time index to jointly optimize departure times, charging volume, and platoon leader roles during the operation phase, minimizing the alliance's total electricity purchase cost and outputting a vehicle-level collaborative operation plan. During the allocation phase, an approximate core cost allocation model is constructed based on cooperative game theory, and a row generation strategy is used to efficiently solve for carrier payment vectors that satisfy stability constraints. This method effectively solves the problem of infeasible solutions or cost deviations from optimality caused by the separation of charging scheduling and platoon collaboration, providing a self-executable collaborative optimization and cost allocation mechanism for multi-carrier electric heavy-duty truck platoon charging. The output operation plan and payment vector can directly support actual operational decisions.
[0058] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.
[0059] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning, characterized in that, Includes the following steps: S1. Construct a long-distance corridor network consisting of a set of stations and a set of road segments, and establish a set of candidate departure times based on discrete time index; S2. During the operation phase, for a given fleet of vehicles belonging to a carrier alliance, perform the following steps: S21. Establish a mixed integer linear programming model. The model uses the departure time of each vehicle on each road segment, the charging amount at each station, and the navigation signage on each road segment as decision variables, the minimum total electricity purchase cost of the alliance as the objective function, and includes multiple preset constraints. S22. Solve the mixed-integer linear programming model to obtain the optimal objective function value and the optimal solution; S23. The optimal objective function value is used as the alliance feature cost, and a vehicle-level cooperative operation scheme is generated based on the values of each decision variable in the optimal solution. S3. In the allocation phase, the alliance characteristic cost is used as the characteristic function value of the cooperative game to construct an approximate core cost allocation model and solve for the carrier payment vector that satisfies the stability constraint and the corresponding stability relaxation or external subsidy demand. S4. Output the vehicle-level collaborative operation scheme and the carrier payment vector.
2. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning according to claim 1, characterized in that, In S1, the long-distance corridor network consists of an ordered set of stations and a set of road segments formed by adjacent stations; each road segment connects two adjacent stations, and the set of stations includes a subset of charging stations, where vehicles are allowed to recharge at charging stations but not at destination stations.
3. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning according to claim 1, characterized in that, In step S1, establishing the candidate departure time set based on the discrete-time index includes: Discretize the continuous time into a set of discrete time points with a step size Δ, and discretely select the departure time of the vehicle on each road segment, satisfying: in, It is a binary variable, representing the vehicle. Is it on the road section? Index at discrete time Departure; For vehicles and road sections The set of feasible departure indexes.
4. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning according to claim 1, characterized in that, In S21, the preset constraints include navigation consistency constraints: in, Let be a binary variable, representing vehicle i departing from index n on road segment a and acting as the navigator; The variable for departure is a binary variable.
5. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platoons according to claim 1, characterized in that, In S21, the preset constraints include a maximum formation size constraint: in, For vehicles within Alliance C, For the maximum formation size, and These are binary variables: navigation and departure. The maximum formation size constraint is used to ensure that vehicle groups that depart from the same road segment at the same time can be divided into one or more formations under the maximum formation size limit, and each formation contains at least one lead vehicle.
6. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning according to claim 1, characterized in that, In S21, the preset constraints include battery energy dynamics and the asymmetric constraints of following energy consumption during navigation: in, and Vehicle i leaves the road Battery level at the starting station and upon arrival at the next station. To lead energy consumption, To match vehicle energy consumption, To guide the binary variables, For vehicles and road sections The set of feasible departure indexes.
7. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning according to claim 1, characterized in that, In step S21, the preset constraints include charging feasibility constraints: Charging is not permitted at non-charging stations or destination stations: =0; The charging capacity is limited by the station's effective charging power and the dwell time. in, The amount of charge vehicle i receives at station s. For the effective charging power of the station, For charging efficiency, This refers to the time a vehicle spends at a station.
8. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning according to claim 1, characterized in that, In S23, the alliance feature cost The objective function value for minimizing the total electricity purchase cost during cooperative vehicle operation within Alliance C is expressed as: in, The electricity price for charging station s, The amount of charge vehicle i receives at station s. A collection of charging stations, This is a collection of vehicles within Alliance C.
9. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platooning according to claim 1, characterized in that, In S3, the solution of the approximate core cost allocation model satisfies Cost allocation for approximate core constraints: in, Payment for carrier K, For stability slack variables, For external subsidies or budget gap variables, The feature cost of sub-consortium C, Let L be the characteristic cost of all carriers, and C be any non-empty sub-alliance; Solving the approximate core cost allocation model includes: given Minimize under conditions The first allocation model; or given Minimize under conditions The second allocation model is used to obtain a trade-off between stability and subsidies.
10. The method for optimizing charging and allocating costs in multi-carrier electric heavy-duty truck platoons according to claim 1, characterized in that, In S3, a row generation strategy is used to solve the approximate core cost allocation model: Starting from the set of working alliances containing all single carrier alliances, iteratively solve the restricted principal problem to obtain candidate allocation solutions. Identify the sub-alliance that most violates the stability constraint by separating the problem. If the degree of violation is less than the termination threshold, add the sub-alliance to the set of working alliances and continue iterating until there are no sub-alliances that violate the stability constraint, and then output the allocation solution.