Semi-flexible bus vehicle scheduling optimization method and system based on scene demand fluctuation

Abstract

The application provides a semi-flexible bus scheduling optimization method and system based on scene demand fluctuation, belongs to the technical field of urban bus transportation system operation management, and constructs a pre-booking demand scene set containing multiple discrete passenger flow states and a three-dimensional space-time state network integrating space nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional space-time state network, a tactical and operation joint optimization model with the minimum system expected total cost as the target is established, the joint optimization model is embedded with cross-level route consistency constraints; a decomposition algorithm based on the augmented Lagrange relaxation and the alternating direction multiplier method is used to solve the joint optimization model, and a vehicle fleet main route, a vehicle fleet plan and a sub-route scheduling scheme of each scene operation layer are obtained. The application effectively solves the problems of blind detouring of vehicles and poor service reliability caused by the disconnection between tactics and operation, and endogenizes unpredictable uncertainty fluctuation into multiple determined scene constraints.

Description

Technical Field

[0001] This invention relates to the field of urban public transport system operation and management technology, specifically to a semi-flexible public transport vehicle scheduling optimization method and system based on scenario demand fluctuations. Background Technology

[0002] In urban public transportation systems, semi-flexible bus systems have become an important means of addressing travel needs in low-demand urban areas due to their combination of the reliability of traditional fixed-route buses and the flexibility of on-demand responsive bus services. However, because passenger booking demands are highly random and subject to spatiotemporal uncertainty, the efficient scheduling of semi-flexible buses in complex road networks has become a key focus and challenge for public transportation operation and management.

[0003] In recent years, research on semi-flexible bus scheduling has mainly focused on demand response strategies and real-time route planning. However, most existing scheduling schemes rely on single and static average passenger flow expectations, which are insufficient in characterizing demand fluctuations and easily lead to severe mismatches between capacity and passenger flow in actual operation. Moreover, existing methods often separate tactical-level trunk route planning from micro-level operational scheduling, resulting in a lack of a stable common framework for the system when facing drastic fluctuations in passenger flow, and vehicles are prone to blindly detouring. In addition, existing scheduling models, due to their cross-level decision-making and multi-vehicle state transitions, have strong coupling between variables and are highly dependent on traditional commercial solvers or heuristic algorithms, making them prone to the curse of dimensionality or local optima, and unable to provide rigorous theoretical quality assessment and convergence guarantees for large-scale scheduling schemes. Summary of the Invention

[0004] The purpose of this invention is to provide a semi-flexible bus dispatching optimization method and system based on scenario demand fluctuations, so as to solve at least one of the technical problems existing in the background art.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] In a first aspect, the present invention provides a semi-flexible bus dispatching optimization method based on scenario demand fluctuations, comprising:

[0007] Obtain basic traffic data and booking demand;

[0008] Construct a set of booking demand scenarios that include multiple discrete passenger flow states and a three-dimensional spatiotemporal state network that integrates spatial nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional spatiotemporal state network, establish a joint optimization model of tactics and operations with the goal of minimizing the expected total cost of the system, and the joint optimization model embeds cross-level route consistency constraints.

[0009] The joint optimization model is solved using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method, resulting in the fleet's main route, fleet plan, and sub-route scheduling schemes for each scenario's operational layer.

[0010] As a further limitation of the first aspect of the present invention, the goal of the joint optimization model is to minimize the total expected cost of fleet operation in all scenarios, including the comprehensive driving cost of the spatiotemporal state arc, which covers the time cost of regular operation and the penalty cost of activating additional vehicles; for the main route flow balance constraint, the main route of each vehicle must start from the starting node and reach the destination, and maintain inflow and outflow conservation in all intermediate nodes; for the sub-route flow balance constraint, under any demand scenario, it is stipulated that the main route of each vehicle starts from the starting node and reaches the destination, and maintains inflow and outflow conservation in all intermediate nodes; for the state transition and passenger capacity constraints, in order to accurately characterize the changes in the number of passengers in the vehicle when responding to passenger flow, state transition rules are established; for the consistency constraint between the main route and the sub-route, for any vehicle, under any demand scenario, its generated dynamic yaw sub-route must completely include the pre-defined main route in terms of spatial topology.

[0011] As a further limitation of the first aspect of the present invention, the route consistency constraint is processed by the Lagrange relaxation method. Lagrange multipliers are introduced to relax the route consistency constraint into the objective function. Through this relaxation, the original problem is decomposed into two independent subproblems: the main route planning subproblem and the comprehensive subroute planning subproblem.

[0012] As a further limitation of the first aspect of the present invention, in the comprehensive sub-route planning sub-problem, Lagrange multipliers are introduced, the augmented Lagrange relaxation method is used for processing, and a quadratic penalty parameter is used to penalize the deviation of the state transition constraint to prevent the symmetry problem in multi-vehicle scheduling. The comprehensive sub-route planning sub-problem is further decomposed into two sub-problems: sub-route planning and service allocation.

[0013] As a further limitation of the first aspect of the present invention, the total demand satisfied by all vehicles other than the current vehicle is introduced as an auxiliary variable. The sub-route planning sub-problem is expanded and linearized using the characteristics of binary variables to obtain the expansion objective function for the sub-route planning sub-problem of a single vehicle. This function minimizes the cost of the single vehicle's sub-route while incorporating penalties for violations of state transitions.

[0014] As a further limitation of the first aspect of the present invention, in the joint optimization model, the... At the end of the iteration, based on the theoretical lower bound and theoretical upper bound, the optimality gap of the current scheme is calculated, reflecting the relative deviation of the current feasible solution from the global theoretical optimal solution; the definition of the... The update step size of each iteration adopts a step size strategy that decreases with the number of iterations to ensure stable convergence of the algorithm in the later stages. In the dynamic update of the multipliers, the first type of multiplier is used to constrain the yaw sub-route when solving the lower bound to cover the main route, and the second type of multiplier is used to constrain the passenger-carrying state transition of the vehicle to match the actual passenger demand.

[0015] Secondly, the present invention provides a semi-flexible bus dispatching optimization system based on scenario demand fluctuations, comprising:

[0016] The acquisition module is used to acquire basic traffic data and booking requests;

[0017] The construction module is used to construct a set of booking demand scenarios containing multiple discrete passenger flow states and a three-dimensional spatiotemporal state network that integrates spatial nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional spatiotemporal state network, a tactical and operational joint optimization model is established with the goal of minimizing the expected total cost of the system, and the joint optimization model embeds cross-level route consistency constraints.

[0018] The solution module is used to solve the joint optimization model using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method, to obtain the main route of the fleet, the fleet plan, and the sub-route scheduling schemes of each scenario operation layer.

[0019] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described in the first aspect.

[0020] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described in the first aspect.

[0021] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described in the first aspect.

[0022] Terminology Explanation: Semi-flexible Bus System: A semi-flexible bus system is a modern public transportation model that combines the advantages of traditional fixed-route buses with on-demand bus services. It primarily operates on pre-set main routes, allowing vehicles to flexibly deviate from the main route to pick up and drop off passengers at optional stops based on advance bookings. Demand Scenario: In bus system operation and management, a demand scenario refers to the task environment formed by organizing and classifying passenger booking demands collected within a specific time period to address changes and uncertainties in passenger travel behavior. Semi-flexible Bus Vehicle Scheduling Optimization: Semi-flexible bus vehicle scheduling optimization refers to a series of key activities and decisions in planning, managing, and coordinating bus operations within a semi-flexible bus system. This mainly includes the rational allocation of fleet size, the design and formulation of basic main routes, the scheduling and operation control of sub-routes to address dynamic passenger demands, and the effective allocation and management of vehicle and other transportation resources.

[0023] The beneficial effects of this invention are as follows: While endowing vehicles with dynamic yaw response capabilities, it ensures the stability of the public transportation infrastructure, effectively solving the problems of blind vehicle detours and poor service reliability caused by the disconnect between tactics and operations in existing technologies. Simultaneously, it endogenizes unpredictable uncertainties into multiple deterministic scenario constraints, achieving precise matching of transport capacity resources in the spatiotemporal dimensions, overcoming the capacity mismatch defects caused by traditional models relying on a single static expectation. Furthermore, the proposed decomposition algorithm, while addressing the curse of dimensionality in commercial solvers, provides a rigorous theoretical convergence gap as a measure of solution quality, ensuring the accuracy and efficiency of solving large-scale scheduling schemes.

[0024] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the technical solution of the semi-flexible bus dispatching optimization method based on scenario demand fluctuations as described in an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram of the network vehicle route optimization results according to an embodiment of the present invention. Detailed Implementation

[0028] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0029] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0030] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0031] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0032] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0033] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0034] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0035] This invention provides a semi-flexible bus scheduling optimization method based on scenario-driven demand fluctuations. Specifically, it involves a semi-flexible tactical and operational joint scheduling method for buses based on spatiotemporal state networks and dynamic demand, and a decoupled solution method based on Augmented Lagrange Relaxation and Alternating Direction Multiplier Method (ALR-ADMM). This solves the technical problems of existing scheduling schemes, such as the separation of tactics and operations, difficulty in coping with spatiotemporal fluctuations in passenger flow, and the difficulty in solving large-scale road networks. By acquiring basic traffic data and booking demand, a set of booking demand scenarios is constructed to characterize the spatiotemporal random fluctuations of passenger flow. A three-dimensional spatiotemporal state network integrating spatial topology, discrete time steps, and continuous vehicle passenger-carrying status is constructed. In this network, a joint tactical and operational optimization model is established with the goal of minimizing the expected total cost of the system. This model is the first to incorporate cross-level route consistency constraints, which force that the dynamic yaw sub-routes in each scenario must completely cover the preset trunk route in physical space. Finally, the model is efficiently solved using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multipliers (ALR-ADMM). The original global high-dimensional optimization problem is precisely decoupled into three parallel sub-problems: trunk route planning, scenario sub-route planning, and service allocation, which are then solved iteratively. This effectively breaks through the computational bottleneck of large-scale road networks and provides a rigorous theoretical lower bound guarantee for convergence, thereby outputting the final scheduling optimization result. This invention achieves a deep synergy between tactical framework stability and micro-operational flexibility, overcomes the dimensionality curse of solving large-scale complex road networks, and significantly improves the robustness of public transportation systems in dealing with unknown passenger flow fluctuations and the accuracy of spatiotemporal capacity allocation.

[0036] Example 1

[0037] In this embodiment 1, a semi-flexible bus dispatch optimization system based on scenario demand fluctuations is first provided, including: an acquisition module for acquiring basic traffic data and booking demand; a construction module for constructing a set of booking demand scenarios containing multiple discrete passenger flow states and a three-dimensional spatiotemporal state network integrating spatial nodes, discrete time steps, and continuous passenger-carrying states of vehicles; in the three-dimensional spatiotemporal state network, a tactical and operational joint optimization model is established with the goal of minimizing the expected total cost of the system, the joint optimization model embedding cross-level route consistency constraints; and a solution module for solving the joint optimization model using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method to obtain the main routes of the fleet, the fleet plan, and the dispatch schemes of sub-routes at the operational level of each scenario.

[0038] In this embodiment, based on the aforementioned system, a semi-flexible bus dispatch optimization method based on scenario-driven demand fluctuations is implemented. This includes: First, acquiring the basic road network topology, vehicle operating parameters, and passenger booking demands to construct a set of demand scenarios containing multiple discrete passenger flow distribution states, thus characterizing the random fluctuations of passenger flow in the spatiotemporal dimension. Then, constructing a three-dimensional spatiotemporal state network integrating geospatial nodes, discrete time steps, and continuous vehicle passenger-carrying states to track the physical trajectory, time window constraints, and passenger volume transfer process of vehicles under each demand scenario. Within the three-dimensional spatiotemporal state network, a joint tactical and operational optimization model is established with the goal of minimizing the system's expected total cost. This model introduces cross-level route consistency constraints, mandating that dynamically eccentric sub-routes generated under any specific demand scenario must completely cover the fixed trunk route arcs planned at the tactical level in terms of physical spatial topology.

[0039] This embodiment also proposes a decomposition solution algorithm based on Augmented Lagrange Relaxation and Alternating Direction Multiplier Method (ALR-ADMM) to solve the model. This algorithm relaxes the route consistency constraint by introducing Lagrange multipliers and a quadratic penalty term. It then uses the ADMM framework to decouple the original global optimization problem into three parallel subproblems: trunk route planning, scenario sub-route planning, and service allocation, iterating them alternately to obtain the theoretical lower bound of the system. Given the trunk route skeleton obtained by solving for the fixed lower bound, feasible solutions for each scenario are constructed to obtain the theoretical upper bound. The optimality gap between the theoretical lower and lower bounds is calculated in the current iteration cycle, and the Lagrange multipliers are dynamically updated if the convergence condition is not met. The decomposition solution steps are then returned until the optimal tactical-level fleet configuration, trunk route scheme, and operational-level scheduling scheme for each scenario are output.

[0040] like Figure 1 As shown, the semi-flexible bus dispatching optimization method based on scenario demand fluctuations described in this embodiment specifically includes the following steps:

[0041] Step 1: Obtain road network topology, vehicle parameters, and booking demand data, and introduce a set of demand scenarios to characterize the random fluctuations of passenger flow in the spatiotemporal dimension; at the same time, construct a three-dimensional spatiotemporal state network that integrates geospatial, discrete time, and vehicle passenger status, establish a tactical-operation joint optimization mathematical model with the goal of minimizing the total system cost, and complete the initialization settings of the algorithm's initial multiplier, penalty parameters, and iteration counter.

[0042] Step 2: Utilize Augmented Lagrange Relaxation (ALR) techniques to decouple strongly coupled constraints such as route consistency, breaking down the complex global optimization problem into multiple sub-problems that can be solved in parallel, such as trunk route planning, scenario sub-route planning, and service allocation; iteratively solve each sub-problem using the Alternating Direction Multiplier Method (ADMM) framework to obtain the lower bound of the global theory of the system under the current iteration cycle, providing a mathematical benchmark for evaluating the optimality of the solution.

[0043] Step 3: Based on the backbone route obtained from the lower bound solution, fix it as a hard constraint. For each specific passenger flow fluctuation scenario, use the optimization framework again to finely adjust the single vehicle deviation sub-route and service allocation. By introducing a quadratic penalty term to correct the variable deviation, we can construct the current optimal feasible solution that strictly satisfies all physical and logical constraints and obtain the theoretical upper bound of the system.

[0044] Step 4: Based on the theoretical upper bound and theoretical lower bound generated in real time during the current iteration cycle, calculate the optimality gap between the two to quantitatively evaluate the relative deviation of the current feasible scheduling scheme from the theoretical global optimal scheme; then, based on the preset accuracy threshold or the maximum number of iterations, determine whether the system has reached the expected convergence state.

[0045] Step 5: If the gap is less than the preset accuracy threshold, the system is considered converged. If the optimality gap does not meet the convergence condition, the subgradient method is used to dynamically adjust the Lagrange multipliers at each level based on the actual degree of violation of the relaxation constraints by the current solution, and the penalty parameters and iteration counters are updated simultaneously. Then, the updated parameters are returned to Step 2 to restart the lower bound solution loop. This closed-loop feedback mechanism drives the upper and lower bounds to continuously approach each other until the termination condition is met and the final scheduling scheme is output.

[0046] The objective function of the joint optimization model in step 1 is to minimize the total expected cost of fleet operation under all scenarios, as shown in equation (1):

[0047] ; (1)

[0048] in, Indicate the demand scenario, Let V represent a vehicle, i and j represent nodes in the road network, t and t' represent discretized time intervals, and w and w' represent the vehicle's passenger-carrying state. (i,j,t,t',w,w') represents the spatiotemporal state arc traversed by vehicle v, meaning the vehicle departs from node i in state w at time t and arrives at node j in state w' at time t'. S represents the set of demand scenarios, and V represents the initial planned fleet vehicle set. * A represents the assembly of vehicles in the additional convoy. v This represents the set of spatiotemporal state arcs traversed by vehicle v in the road network. Let represent the overall driving cost of the spatiotemporal state arc (i,j,t,t',w,w'). The variable represents the sub-route selection decision variable. If, under the demand scenario s, the sub-route of vehicle v passes through physical segment (i,j) within the time window (t,t') and the passenger status changes from w to w' during the time window, then the value is 1; otherwise, the value is 0.

[0049] Comprehensive driving cost of spatiotemporal state arc It covers the time cost of regular operations as well as the penalty cost of activating additional vehicles. Its specific piecewise function definition is as follows:

[0050] ; (2)

[0051] in, This represents the travel time for road segment (i,j). This indicates the starting node of vehicle v. This represents the penalty cost incurred by deploying additional vehicles; if no additional vehicles are deployed, this value is 0.

[0052] Step 1 involves constructing the main route flow balance constraints. This specifies the constraints for each vehicle. The main route must start from the starting node Departure, arrival at the destination And maintain the conservation of inflow and outflow at all intermediate nodes. This constraint can be expressed as equations (3) to (5).

[0053] (3)

[0054] (4)

[0055] (5)

[0056] in, This represents the decision variable for choosing the main route; if the vehicle... The fixed trunk route passes through physical road sections If the value is 1, then the value is 1; otherwise, the value is 0. Similarly. Indicates vehicle End point.

[0057] The sub-route flow balancing constraint construction in step 1. Applicable to any requirement scenario. Below, it is stipulated that each vehicle The main route must start from the starting node Departure, arrival at the destination And maintain the conservation of inflow and outflow at all intermediate nodes. This constraint can be expressed as equations (6) to (8).

[0058] (6)

[0059] (7)

[0060] (8)

[0061] in, Indicates that the vehicle starts from the starting node. Departure time Indicates the vehicle starts from the starting node. Initial passenger capacity at departure; This indicates that the vehicle has reached the destination node. Arrival time This indicates that the vehicle has reached the destination node. The final passenger capacity at that time.

[0062] State transition and passenger capacity constraint in step 1. In order to accurately characterize the change in the number of people in the vehicle when responding to passenger flow, a state transition rule is established. The constraint can be expressed as Equation (9) to Equation (10).

[0063] (9)

[0064] (10)

[0065] in, This represents the set of spatiotemporal state arcs in the road network that are actually served by vehicles and include on-demand stopping stations. This represents the set of road segments in the road network that include on-demand stopping points. This represents the set of road segments in the road network that do not include on-demand stops. Representing a scene Lower section The number of passengers who submitted ride requests. This represents a service allocation variable, which is relevant to the specific requirements of the application scenario. The system then determines it as a physical road segment. If the on-demand stop provides pick-up and drop-off services, the value is 1; otherwise, the value is 0.

[0066] The consistency constraint between the main route and sub-routes in step 1. For any vehicle In any demand scenario The generated dynamic yaw sub-routes must completely encompass the tactical layer's pre-defined trunk routes in terms of spatial topology, as given by formula (11):

[0067] (11)

[0068] in, Indicates vehicles in the road network A collection of physical road segments traversed.

[0069] The binary decision variables in step 1 are defined by formulas (12)-(14).

[0070] (12)

[0071] (13)

[0072] (14)

[0073] The ALR-based model in step 2 is decoupled for the first time. To simplify the model representation, the state arcs are represented in the following model solution process. Simplified to First, the route consistency constraint (11) is processed using the Lagrange relaxation method, and Lagrange multipliers are introduced. By relaxing the route consistency constraint into the objective function, we obtain formula (15). This objective function consists of two parts. The first part represents the total driving cost generated by the vehicle actually executing the yaw sub-route under various demand scenarios; the second part is a penalty term, used to quantify the spatial difference between the tactical layer main route decision and the operational layer sub-route decision, and to apply corresponding Lagrange multipliers as penalty weights. Through this relaxation, the original complex problem is decomposed into two independently solvable low-dimensional sub-problems.

[0074] (15)

[0075] in, Represents the simplified state arc The cost of driving This represents the simplified sub-route selection decision variables. It represents the Lagrange multiplier.

[0076] The main route planning subproblem Py in step 2. The objective function is formula (16), and the constraints are formulas (3) to (5). For formula (16), since the sub-route selection decision variables are mathematically decoupled from the main route selection decision variables, the global optimization objective of this subproblem is transformed into minimizing the total cost directly related to the main route decision variables. The algorithm model will comprehensively consider the accumulated Lagrange multiplier weights of each physical segment under all random passenger flow scenarios, and through continuous iterative optimization, select and construct an optimal robust trunk route skeleton that can minimize the expected penalty cost of the system.

[0077] (16)

[0078] The comprehensive sub-route planning sub-problem Pxz in step 2. The objective function is formula (17), and the constraints are formulas (6) to (8), (9) and (10). For formula (17), the optimization objective of this sub-problem is to find an economic equilibrium point, that is, the system should minimize the physical cost of the actual driving of vehicles in the spatiotemporal state network, and guide the vehicles to follow the expected main route as much as possible.

[0079] (17)

[0080] The ALR-based model in step 2 is decoupled again. In the subproblem Pxz, the variables... and They are still coupled through state transition constraints (9). Therefore, this embodiment introduces Lagrange multipliers. The augmented Lagrange relaxation method was used for processing, and a quadratic penalty parameter was employed. To prevent symmetry problems in multi-bus scheduling, a penalty is imposed on deviations from state transition constraints, resulting in formula (18). For formula (18), the objective function consists of three parts. The first part is the basic operational physical cost inherited from the previous decoupling operation; the second part is a linear penalty term, using Lagrange multipliers to apply basic economic deductions to any deviations from the established state transition rules; the third part is a quadratic penalty term, imposing a quadratic cost penalty on behaviors that violate state transition equilibrium. This effectively breaks the path selection symmetry trap caused by multiple homogeneous buses facing the same high-revenue passenger demand, forcing the optimization algorithm to quickly converge to a uniquely determined physically feasible solution. Through this relaxation, Pxz is further decomposed into two independent sub-problems: sub-route planning Px and service allocation Pz.

[0081] (18)

[0082] in, Represents the Lagrange multipliers. This represents the simplified change in passenger capacity:

[0083] .

[0084] The service allocation subproblem Pz in step 2 has the objective function as formula (19) and the constraints as formula (14).

[0085] (19)

[0086] The sub-route planning sub-problem Px in step 2. The objective function is Equation (20), and the constraints are Equations (6) to (8) and Equation (10). For Equation (20), the objective function consists of three parts. The first part is the basic physical cost of the vehicle executing the yaw sub-route in the spatiotemporal network, minus the reward for maintaining consistency between the main and secondary routes; the second part is a linear penalty term, used to quantify the basic linear relationship between the passenger state change caused by the vehicle's current route and the Lagrange multiplier; the third part is a quadratic penalty term, used to calculate the squared error between the total actual service demand of all vehicles and the total demand allocated by the system. By minimizing this comprehensive cost including the quadratic penalty, the algorithm guides the vehicles to find the optimal physical path while using the nonlinear penalty gradient to force the overall service volume of the fleet to approach the target demand, thereby effectively preventing the symmetry of path selection when multiple vehicles face the same high-yield node.

[0087] (20)

[0088] Linearization in step 2. To handle variable coupling caused by quadratic terms, auxiliary variables are introduced. Indicates excluding the current vehicle The total demand satisfied by all vehicles other than the vehicle itself is given by formula (21). The logical principle behind formula (21) is that the quadratic penalty term inevitably generates cross terms when expanding the decision variables of different vehicles, making it impossible to plan the path of a single vehicle independently and in parallel. In order to overcome this computational bottleneck, the core idea of ​​alternating optimization is adopted. By treating the decision results of other vehicles in the previous iteration as known constants and aggregating them in a unified manner, the originally intertwined state transition constraints of multiple vehicles are decoupled, laying a solid mathematical foundation for the subsequent independent parallel solution of a single vehicle.

[0089] (twenty one)

[0090] Subsequently, the properties of binary variables were utilized. The subproblem Px is expanded and linearized. Further decomposition yields a solution for a single vehicle. The objective function of the sub-route planning subproblem SPx is expanded. This function minimizes the cost of a single vehicle's sub-route while incorporating penalties for state transition violations, and is given by formula (22). The objective function is formula (22), and the constraints are formulas (6) to (8) and formula (10). For formula (22), the objective function minimizes the various physical travel costs of a single vehicle in the spatiotemporal network while merging all the originally complex nonlinear state transition penalty terms, converting them into fixed additional costs on the road network arcs. This transformation reduces the complex joint planning problem for the entire fleet to a standard single-vehicle shortest path problem with resource constraints, improving the timeliness of the system solution.

[0091] (twenty two)

[0092] in, Indicates excluding the current vehicle The total demand met by all vehicles other than those mentioned above.

[0093] Step 2 involves solving the ADMM-based model. For the multiple sub-problems derived from the decomposition, the ADMM algorithm employs a block coordinate descent strategy for alternating iterative computation. In the specific solution steps, the algorithm solves each low-dimensional sub-problem one by one through dynamic programming by fixing the states of other vehicles as constants and independently optimizing only the target decision variable in the current sub-problem through alternating updates while maintaining the state of other vehicles as constants.

[0094] Step 2 involves solving for the theoretical lower bound. Since the main routes have been forcibly covered, the scheduling scheme obtained at this point strictly satisfies all route consistency and physical logic constraints, making it a directly implementable solution. Summarizing its costs yields the theoretical upper bound of the system.

[0095] Consistency restoration in step 3. During the upper bound calculation, the main route decision variables... Instead of being used as a variable to be optimized, the main path topology scheme obtained by solving the subproblem Py in the theoretical lower bound calculation stage of the current iteration cycle is directly adopted as input and set as a fixed constant. The objective function of the subproblem Pxz is given by formula (23). For formula (23), the objective function consists of three parts. The first term is the basic physical driving cost of the vehicle executing a specific route in the spatiotemporal network, and the latter two terms are the linear penalty and quadratic penalty imposed on the passenger-carrying state transition constraint by using the augmented Lagrange mechanism, respectively.

[0096] (twenty three)

[0097] in This represents the quadratic penalty parameter used in the upper bound calculation, which penalizes deviations from state transition constraints to prevent symmetry issues in multi-vehicle scheduling.

[0098] The service allocation subproblem P'z in step 3 has the objective function as formula (24) and the constraints as formula (14).

[0099] (twenty four)

[0100] The sub-route planning sub-problem P'x in step 3. The objective function is formula (25), and the constraints are formulas (6) to (8), (10), and (11). For formula (25), the objective function aims to find the driving trajectory with the lowest physical cost within a given fixed constraint framework, which is composed of three parts of cost superposition. The first part represents the basic physical driving cost of the vehicle performing a specific yaw action in the three-dimensional spatiotemporal network, the second part is the basic linear penalty imposed on the behavior that deviates from the passenger-carrying state transition rule using Lagrange multipliers, and the third part is the cost of parameters. This is a secondary penalty term for the weights. By minimizing this comprehensive objective function that includes the secondary penalty, the algorithm can eliminate any infeasible paths that do not meet the supply-demand balance, thus successfully searching for a globally feasible scheduling scheme that perfectly fits the actual physical operation logic in a complex road network, providing a realistic and rigorous cost ceiling for the entire joint scheduling model.

[0101] (25)

[0102] Step 4 involves the calculation of the optimal gap. At the end of the iteration, the system is based on the theoretical lower bound that has been obtained. With theoretical upper limit Calculate the optimality gap of the current scheme. This gap reflects the relative deviation of the current feasible solution from the global theoretical optimal solution, and the calculation method is given by formula (26):

[0103] (26)

[0104] The update step size iteration in step 4. Define the first... Update step size of the next iteration A step size strategy that decreases with the number of iterations is adopted to ensure stable convergence in the later stages of the algorithm, as given by formula (27):

[0105] (27)

[0106] Step 5: Dynamic update of multipliers. Multipliers of the first kind. The yaw sub-path used for constraining the lower bound must cover the main path, as given by formula (28). Second type multiplier The passenger-carrying state transitions used to constrain vehicles must match the actual passenger demand, as given by formulas (29) and (30). Specifically, the new multiplier value generated in the current iteration is equal to the multiplier value in the previous iteration, plus the product of the update step size and the constraint violation. For the first type of multiplier... The algorithm quantifies the degree of route disconnect by calculating the difference between the tactical main route decision and the actual yaw sub-route decision. When a vehicle is planned to take a main route on a certain road segment, but its actual yaw sub-route fails to cover that segment, the constraint violation is positive, and the value of the first type of multiplier will increase accordingly, thus imposing a more severe penalty on this deviating behavior in the next iteration. For the second type of multiplier... The algorithm quantifies constraint violations by calculating the algebraic difference between the actual change in vehicle passenger load and the system's allocated passenger flow demand. When the actual change is greater than the allocated demand, the violation is positive, and the multiplier value increases accordingly; when the actual change is less than the allocated demand, the violation is negative, and the multiplier value decreases accordingly.

[0107] (28)

[0108] (29)

[0109] (30)

[0110] in, Indicates the first During each algorithm iteration, the system uses a dynamic step size parameter to control the multiplier update magnitude. Indicates the first In the theoretical lower bound calculation phase of the next iteration, specific requirements are considered. Get off the vehicle Sections of road passed through , used as the first type of Lagrange multiplier for relaxing path consistency constraints; Indicates the first In the theoretical lower bound calculation phase of the next iteration, specific requirements are considered. The following section of road On-demand docking stations are used for the second type of Lagrange multipliers to relax state transition constraints; Indicates the first In the theoretical bound calculation phase of the next iteration, for specific demand scenarios... The following section of road On-demand docking stations are used for the second type of Lagrange multipliers to relax state transition constraints. Indicates the first The vehicle obtained in the next iteration Regarding the road section The decision results of the main route; Indicates the first In the theoretical lower bound calculation phase of the next iteration, the vehicle In specific passenger flow scenarios The actual path through a specific spatiotemporal state arc The yaw sub-path decision results; Indicates the first In the theoretical bound calculation stage of the next iteration, the vehicle In specific passenger flow scenarios The actual path through a specific spatiotemporal state arc The yaw sub-path decision results. Indicates that the representative is in the In the theoretical lower bound calculation stage of the next iteration, located in the road segment On-demand sites in scenarios The total passenger flow demand actually met by the system; Indicates that the representative is in the In the theoretical bound calculation stage of the next iteration, located in the road segment On-demand sites in scenarios The total passenger flow demand that is actually met by the system.

[0111] In this embodiment, a network containing 24 physical nodes is selected as the test environment. All vehicles are set to depart from the same common starting point, perform a shuttle task, and then proceed to a common destination. Eight candidate passenger demand stations are distributed throughout the network. The basic operating fleet size is set at 4 vehicles, with a fixed maximum passenger capacity of 6 people per vehicle, and a maximum service duration of 30 time units for a single task. If the basic capacity cannot meet fluctuating demand, the system can call upon additional vehicles, with a penalty cost of 10 per call.

[0112] Analysis of the path planning performance of the joint scheduling model. Figure 2 The visualization results of the above-mentioned calculation examples are presented. The results show that the joint optimization model proposed in this embodiment successfully generates stable tactical-level trunk routes for all operating vehicles and derives flexible operational-level yaw sub-routes under different passenger flow fluctuation scenarios. In multi-scenario tests, the model successfully and effectively allocated all passenger booking requests within their corresponding time windows, ensuring full service coverage for all demand stations. From the perspective of specific vehicle operating trajectories, when facing demand fluctuations in different scenarios, the system can adaptively decide whether vehicles should strictly follow the trunk routes and achieve full load, or dynamically yaw at specific nodes to connect with demand on surrounding sub-routes. It is particularly noteworthy that regardless of how the operational sub-routes of vehicles in various scenarios spatially detour due to dynamic demand, the sub-routes always completely contain the pre-planned tactical trunk routes of the corresponding vehicles in terms of physical topology.

[0113] Table 1 shows the computational accuracy and efficiency of the ALR-ADMM algorithm compared to the commercial solver Gurobi 12.0.0. In the basic multi-scenario example, the algorithm of this invention converged on the 5th iteration, taking only 12.54 seconds, with the optimality gap converging to 1.18%. In contrast, Gurobi took 307.76 seconds to solve the global model, meaning this method achieved a 95.93% reduction in computation time. Furthermore, in 13 sets of complex instance tests involving different combinations of the number of scenarios and vehicle scales, the average computation time of this algorithm was significantly reduced by 94.93% compared to Gurobi, with the average objective cost function value differing by only 0.57%. The experimental results fully demonstrate that the algorithm proposed in this embodiment overcomes the curse of dimensionality, exhibits excellent computational scalability, and highly guarantees the accuracy of the global optimal solution.

[0114] Table 1 Comparison of computational efficiency between the ALR-ADMM-based solving algorithm and the Gurobi solver.

[0115]

[0116] The semi-flexible bus vehicle scheduling optimization method based on scenario demand fluctuations provided in this embodiment has high reliability. It considers the impact of multi-dimensional factors such as the spatiotemporal fluctuations of passenger flow in multiple scenarios and the coordinated linkage between the tactical backbone and micro-sub-routes on the in-transit resource allocation of the semi-flexible bus system. It has higher computational efficiency and solution accuracy, and opens up a decision-making closed loop between macro-operational stability and micro-response flexibility. It provides strong technical support for improving the robustness and service consistency of public transportation systems in response to unknown passenger flow fluctuations, and provides a solid theoretical foundation for building a modern, highly reliable on-demand response public transportation network.

[0117] Example 2

[0118] This embodiment 2 provides a non-transitory computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, they implement the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described above. The method includes:

[0119] Obtain basic traffic data and booking demand;

[0120] Construct a set of booking demand scenarios that include multiple discrete passenger flow states and a three-dimensional spatiotemporal state network that integrates spatial nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional spatiotemporal state network, establish a joint optimization model of tactics and operations with the goal of minimizing the expected total cost of the system, and the joint optimization model embeds cross-level route consistency constraints.

[0121] The joint optimization model is solved using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method, resulting in the fleet's main route, fleet plan, and sub-route scheduling schemes for each scenario's operational layer.

[0122] Example 3

[0123] This embodiment 3 provides a computer device, including a memory and a processor, wherein the processor and the memory communicate with each other, and the memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described above, the method including:

[0124] Obtain basic traffic data and booking demand;

[0125] Construct a set of booking demand scenarios that include multiple discrete passenger flow states and a three-dimensional spatiotemporal state network that integrates spatial nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional spatiotemporal state network, establish a joint optimization model of tactics and operations with the goal of minimizing the expected total cost of the system, and the joint optimization model embeds cross-level route consistency constraints.

[0126] The joint optimization model is solved using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method, resulting in the fleet's main route, fleet plan, and sub-route scheduling schemes for each scenario's operational layer.

[0127] Example 4

[0128] This embodiment 4 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes instructions to implement the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described above. The method includes:

[0129] Obtain basic traffic data and booking demand;

[0130] Construct a set of booking demand scenarios that include multiple discrete passenger flow states and a three-dimensional spatiotemporal state network that integrates spatial nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional spatiotemporal state network, establish a joint optimization model of tactics and operations with the goal of minimizing the expected total cost of the system, and the joint optimization model embeds cross-level route consistency constraints.

[0131] The joint optimization model is solved using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method, resulting in the fleet's main route, fleet plan, and sub-route scheduling schemes for each scenario's operational layer.

[0132] In summary, this invention, while endowing vehicles with dynamic yaw response capabilities, ensures the stability of the public transportation infrastructure, effectively solving the problems of blind vehicle detours and poor service reliability caused by the disconnect between tactics and operations in existing technologies. Simultaneously, it endogenizes unpredictable uncertainties into multiple deterministic scenario constraints, achieving precise matching of transport capacity resources in the spatiotemporal dimensions, overcoming the capacity mismatch defects caused by traditional models relying on a single static expectation. Furthermore, the decomposition algorithm proposed in this invention, while addressing the curse of dimensionality in commercial solvers, provides a rigorous theoretical convergence gap as a measure of solution quality, ensuring the accuracy and efficiency of solving large-scale scheduling schemes.

[0133] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0134] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0135] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0136] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0137] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A semi-flexible bus dispatching optimization method based on scenario demand fluctuations, characterized in that, include: Obtain basic traffic data and booking demand; Construct a set of booking demand scenarios that include multiple discrete passenger flow states and a three-dimensional spatiotemporal state network that integrates spatial nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional spatiotemporal state network, establish a joint optimization model of tactics and operations with the goal of minimizing the expected total cost of the system, and the joint optimization model embeds cross-level route consistency constraints. The joint optimization model is solved using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method, resulting in the fleet's main route, fleet plan, and sub-route scheduling schemes for each scenario's operational layer.

2. The semi-flexible bus dispatching optimization method based on scenario demand fluctuations according to claim 1, characterized in that, The goal of the joint optimization model is to minimize the total expected cost of fleet operation across all scenarios, including the comprehensive driving cost of the spatiotemporal state arc, which covers the time cost of regular operation and the penalty cost of activating additional vehicles. For the main route flow balance constraint, each vehicle's main route must start from the starting node and reach the destination, maintaining inflow and outflow conservation at all intermediate nodes. For the sub-route flow balance constraint, under any demand scenario, each vehicle's main route is specified to start from the starting node and reach the destination, maintaining inflow and outflow conservation at all intermediate nodes. For the state transition and passenger capacity constraints, state transition rules are established to accurately characterize the changes in the number of passengers in the vehicle when responding to passenger flow. For the consistency constraint between the main route and sub-route, for any vehicle, under any demand scenario, its generated dynamic yaw sub-route must completely contain the pre-defined main route in terms of spatial topology.

3. The semi-flexible bus dispatching optimization method based on scenario demand fluctuations according to claim 2, characterized in that, The route consistency constraint is handled using the Lagrange relaxation method. By introducing Lagrange multipliers, the route consistency constraint is relaxed into the objective function. Through this relaxation, the original problem is decomposed into two independent subproblems: the main route planning subproblem and the comprehensive route planning subproblem.

4. The semi-flexible bus dispatching optimization method based on scenario demand fluctuations according to claim 3, characterized in that, In the comprehensive sub-route planning subproblem, Lagrange multipliers are introduced, and the augmented Lagrange relaxation method is used for processing. A quadratic penalty parameter is used to penalize deviations from the state transition constraints to prevent symmetry problems in multi-vehicle scheduling. The comprehensive sub-route planning subproblem is further decomposed into two sub-routes: sub-route planning and service allocation.

5. The semi-flexible bus dispatching optimization method based on scenario demand fluctuations according to claim 4, characterized in that, By introducing the total demand satisfied by all vehicles other than the current vehicle as an auxiliary variable, and using the properties of binary variables to expand and linearize the sub-route planning subproblem, we obtain the expansion objective function for the sub-route planning subproblem of a single vehicle. This function minimizes the cost of the single vehicle's sub-route while incorporating penalties for state transition violations.

6. The semi-flexible bus dispatching optimization method based on scenario demand fluctuations according to claim 5, characterized in that, In the joint optimization model, the first At the end of the iteration, based on the theoretical lower bound and theoretical upper bound, the optimality gap of the current scheme is calculated, reflecting the relative deviation of the current feasible solution from the global theoretical optimal solution; the definition of the... The update step size of each iteration adopts a step size strategy that decreases with the number of iterations to ensure stable convergence of the algorithm in the later stages. In the dynamic update of the multipliers, the first type of multiplier is used to constrain the yaw sub-route when solving the lower bound to cover the main route, and the second type of multiplier is used to constrain the passenger-carrying state transition of the vehicle to match the actual passenger demand.

7. A semi-flexible bus dispatching optimization system based on scenario demand fluctuations, characterized in that, include: The acquisition module is used to acquire basic traffic data and booking requests; The construction module is used to construct a set of booking demand scenarios containing multiple discrete passenger flow states and a three-dimensional spatiotemporal state network that integrates spatial nodes, discrete time steps and vehicle continuous passenger carrying states; in the three-dimensional spatiotemporal state network, a tactical and operational joint optimization model is established with the goal of minimizing the expected total cost of the system, and the joint optimization model embeds cross-level route consistency constraints. The solution module is used to solve the joint optimization model using a decomposition algorithm based on augmented Lagrange relaxation and alternating direction multiplier method, to obtain the main route of the fleet, the fleet plan, and the sub-route scheduling schemes of each scenario operation layer.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described in any one of claims 1-6.

9. A computer device, characterized in that, The device includes a memory and a processor, which communicate with each other. The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described in any one of claims 1-6.

10. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions that implement the semi-flexible bus dispatch optimization method based on scenario demand fluctuations as described in any one of claims 1-6.

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