Demand response type bus and conventional bus hybrid scheduling optimization method

Abstract

The invention discloses a demand response type bus and conventional bus hybrid scheduling optimization method. The method comprises the following steps: S1, obtaining ground bus system operation parameters and passenger travel demand data of a to-be-optimized commuting OD area; s2, constructing a collaborative optimization model based on the ground public transportation system operation parameters and the passenger travel demand data; s3, solving the collaborative optimization model to obtain an optimal vehicle configuration scheme and a passenger flow distribution prediction result corresponding to the optimal vehicle configuration scheme; the solving process realizes interaction and collaborative optimization of a vehicle configuration decision and a passenger flow distribution result through an iteration mode; and S4, according to the optimal vehicle configuration scheme, outputting a scheduling scheme for guiding mixed operation of conventional buses and demand response type buses in the commuting OD area. According to the method, the vehicle resources of the two bus modes can be cooperatively configured under a unified optimization framework, and passenger travel selection behaviors are coupled, so that comprehensive optimization of the overall efficiency and the operation economy of the system is realized.

Description

Technical Field

[0001] This invention relates to the field of urban public transportation and intelligent scheduling optimization technology, specifically to a method for optimizing the hybrid scheduling of demand-responsive public transport and conventional public transport. Background Technology

[0002] With the continued growth in urban commuting demand and the advancement of public transport priority strategies, surface public transport systems are facing increasingly severe challenges. The single conventional bus (CB) operation mode often suffers from problems such as low travel efficiency, high passenger congestion, and long route detours during peak hours, making it difficult to achieve an effective balance between service level and operational economy.

[0003] To improve commuter service quality in specific areas and time periods, demand-response transit (DRT) has been introduced as a flexible operating model. Through reservation mechanisms and dynamic route organization, DRT can provide passengers with high-quality services characterized by fewer stops, direct routes, and zero transfers, significantly improving travel efficiency and passenger comfort. However, DRT typically comes with higher fares and unit operating costs.

[0004] When both conventional buses and DRT operate simultaneously within the same origin-destination (OD) area, system complexity increases significantly, generating a series of new technical challenges: On the one hand, newly introduced DRT lines divert passenger flow from existing conventional buses, necessitating a reallocation of vehicle resources between the two modes given the limited total vehicle resources; on the other hand, passengers gain new travel options, and their decision-making behavior among different modes of transportation and routes dynamically impacts passenger flow distribution and vehicle utilization efficiency on each line, thereby affecting the overall revenue and service capacity of the operating company. Against this backdrop, existing technical solutions mainly face the following three specific problems: (1) The problem of vehicle resource reallocation and route service capacity matching: Under the constraint of a limited total number of vehicles, how to reasonably allocate vehicles between multiple regular bus routes and one commuter DRT route so that each route can meet the travel needs of commuters and non-commuters while keeping the load factor within a reasonable range, thus avoiding both waste of transport capacity and overcrowding, is the primary problem that needs to be solved.

[0005] (2) Modeling the multi-modal route selection behavior of passengers: Commuters can freely choose between DRT and regular buses, and their decisions are influenced by multiple factors such as fare, waiting time, walking time, time on the bus, and perception of congestion; Non-commuter passengers only choose regular buses, and their travel characteristics are relatively dispersed. How to construct a route selection model that can accurately reflect the differentiated behavior of the two types of passengers and transform it into a mathematical expression that can be used for flow allocation calculation is the key to achieving collaborative optimization.

[0006] (3) Modeling and solving the bi-level optimization problem of hybrid travel networks: Vehicle configuration decisions and passenger flow allocation results are interdependent. Upper-level vehicle configuration affects lower-level path costs and passenger flow distribution, while lower-level passenger flow distribution affects upper-level operating costs and service levels. Therefore, it is necessary to construct a bi-level programming model that can describe this interaction mechanism and design a solution algorithm that can converge stably under complex constraints, so as to ultimately achieve the synergistic optimization of vehicle configuration schemes and passenger flow allocation results.

[0007] Currently, optimization research for this mixed operation scenario is insufficient. Existing work often takes a single perspective: some studies focus solely on the route design or vehicle scheduling of the DRT itself, failing to coordinate its optimization with the resource allocation of existing conventional public transport systems; others primarily focus on the departure frequency or vehicle allocation schemes of conventional buses, typically treating passenger travel behavior as a fixed exogenous parameter, lacking a deep characterization of the closed-loop coupling relationship of "vehicle configuration—passenger choice—passenger flow distribution." Therefore, for the mixed operation scenario of DRT and conventional public transport within the commuter origin-destination area, there is still a lack of an optimization method that can systematically solve the above problems, taking into account the generalized travel costs of passengers, the cost constraints of operating companies, and the constraints of route occupancy rates. Furthermore, there is a lack of reliable algorithms that can efficiently solve the problem on a real-scale network.

[0008] In summary, it is necessary to propose a collaborative scheduling optimization method that can fully consider the heterogeneous travel needs and multi-modal route selection behaviors of passengers. The aim is to optimize the vehicle configuration of DRT and conventional buses in an integrated manner under the constraint of a given total number of vehicle resources, so as to achieve a synergistic improvement in the operating company's revenue and the passenger's travel efficiency. Summary of the Invention

[0009] To overcome the shortcomings of existing technologies, the present invention aims to provide a method for optimizing the scheduling of demand-responsive public transport and conventional public transport, which can coordinate the allocation of vehicle resources for both modes of public transport under a unified optimization framework and couple passenger travel choices, thereby achieving comprehensive optimization of the overall system efficiency and operational economy.

[0010] To achieve the objectives of this invention, the following solution is adopted: A method for optimizing the scheduling of demand-responsive public transport and regular public transport includes the following steps: S1. Obtain the operating parameters of the ground public transport system and passenger travel demand data for the commuter OD area to be optimized; S2. Based on the operating parameters of the ground public transport system and passenger travel demand data, a collaborative optimization model is constructed. The collaborative optimization model is used to jointly optimize the vehicle configuration scheme of conventional buses and demand-responsive buses under the total resource constraints of the ground public transport system, and to simulate the travel choices and passenger flow distribution of passengers under this vehicle configuration scheme. The optimization objective of the vehicle configuration scheme integrates passenger travel efficiency and operator operating costs, and the passenger travel choice behavior is described based on generalized travel costs. S3. Solve the collaborative optimization model to obtain an optimal vehicle configuration scheme and its corresponding passenger flow distribution prediction result; the solution process realizes the interaction and collaborative optimization of vehicle configuration decision and passenger flow allocation result through an iterative method; S4. Based on the optimal vehicle configuration scheme, output a scheduling scheme to guide the mixed operation of regular buses and demand-response buses within the commuter OD area.

[0011] Furthermore, in step S1, the operating parameters of the ground public transport system include vehicle fixed costs, variable costs, maximum capacity of a single vehicle, upper limit of the total number of vehicles available in the system, reasonable range of departure frequency for each route, and reasonable range of full load rate; the passenger travel demand data includes commuting demand from each demand point to the destination, as well as non-commuting demand related to commuting demand.

[0012] Furthermore, in step S2, the collaborative optimization model is a two-level programming model, including: an upper-level vehicle configuration optimization model, used to decide the number of vehicles to be configured with the goal of minimizing the overall cost; and a lower-level passenger flow distribution equilibrium model, used to simulate the passenger route selection and passenger flow distribution results given the number of vehicles.

[0013] Furthermore, the comprehensive cost is the weighted sum of the total travel time cost for commuting passengers and the total operating cost of the public transport company; the total operating cost of the public transport company is the difference between vehicle operating costs and total fare revenue.

[0014] Furthermore, in the lower-level passenger flow distribution equilibrium model, the route selection of commuter passengers follows the stochastic user equilibrium principle based on generalized travel costs, and the selection probability is calculated using a multinomial Logit model; the passenger flow of non-commuter passengers is evenly distributed among various regular bus routes.

[0015] Furthermore, the generalized travel cost, for regular public transport routes, integrates fare, waiting time cost, on-vehicle time cost, and perceived congestion cost; for demand-responsive public transport routes, it integrates fare, time cost of walking to the carpooling station, and on-vehicle time cost.

[0016] Furthermore, the constraints imposed by the upper-level vehicle configuration optimization model include: the sum of the number of vehicle configurations does not exceed the upper limit of the total number of available vehicles in the system; the departure frequency corresponding to the number of vehicle configurations for each regular bus route is within a preset range; and the full load rate of each route is between the preset minimum and maximum full load rates.

[0017] Furthermore, in step S3, the solution process of the iterative method is specifically as follows: a genetic algorithm framework is used to generate and iteratively update the vehicle configuration scheme population. For each scheme in the population, the passenger flow allocation algorithm is called to simulate its passenger flow distribution, and the fitness of the scheme is evaluated based on the comprehensive cost, so as to achieve collaborative optimization of vehicle configuration and passenger flow allocation.

[0018] Furthermore, in the passenger flow allocation algorithm, the continuous averaging method is used to solve the random user equilibrium allocation problem for commuter passengers; and the average allocation strategy is used for non-commuter passengers.

[0019] Furthermore, the specific solution process for step S3 includes: S31. Initialize the initial population for generating vehicle configuration schemes; S32. For each vehicle configuration scheme in the population, calculate the corresponding commuter and non-commuter passenger flow distribution using a passenger flow allocation algorithm; S33. Based on the passenger flow distribution, calculate the comprehensive cost corresponding to the vehicle configuration scheme as the fitness value; S34. Determine whether the algorithm termination condition is met; if it is met, output the current optimal vehicle configuration scheme and passenger flow distribution; if it is not met, perform genetic operations on the current population to generate a new generation population, and return to step S32.

[0020] The present invention provides a method for optimizing the scheduling of demand-responsive public transport and conventional public transport, comprising the following: 1. System Scenario and Basic Assumptions: Within a commuter origin-destination (OD) area, the starting area contains multiple demand points, while the destination is unique. Several regular bus routes serve different demand points within the area, and a new commuter DRT line directly connects the demand points and the destination. Each demand point experiences both commuter and non-commuter demand. Commuter demand is a fixed given value, while non-commuter demand is correlated with commuter demand at a fixed ratio. Commuter passengers can choose between regular buses and the DRT, while non-commuter passengers can only choose regular buses. Regular buses depart at equal intervals, all routes use the same vehicle type, and the total number of regular buses and DRT vehicles does not exceed the system's maximum vehicle capacity.

[0021] 2. Construction of the upper-level vehicle configuration optimization model: Given a passenger flow distribution, the model aims to determine the number of vehicles needed for each regular bus route and DRT line, with the goal of minimizing the weighted sum of "total commuter travel time cost" and "total operating cost for the operating company." Commuter travel time cost consists of walking time, waiting time, and travel time; operating cost consists of fixed vehicle costs and variable costs related to mileage. The model imposes the following constraints: (1) Total vehicle limit, ensuring that the sum of the number of vehicles on each line does not exceed the upper limit of available vehicles in the system; (2) Constraints on the frequency of departures of regular bus routes, corresponding the number of vehicles to the reasonable frequency range of departures during peak periods; (3) Line service capacity constraints: the line load factor is expressed as the ratio of total passenger flow to total transport capacity, so that it is between the preset minimum and maximum load factor, which correspond to the service quality and economic requirements respectively.

[0022] 3. Construction of the lower-level passenger flow distribution equilibrium model: Given the number of vehicles on each route, a passenger flow allocation model is established. Commuter passengers follow the stochastic user equilibrium principle based on generalized travel costs, and a multinomial Logit model is used to describe the probability of route selection. Generalized travel costs integrate ticket price, time value, and congestion level. For regular buses, waiting time and perceived congestion are considered, while for DRT (Dedicated Transportation Rail) buses, walking time and on-board time under the condition of one seat per passenger are considered. Non-commuter passengers are allocated among the regular bus routes according to an average allocation strategy, satisfying the constraints of demand conservation and the commuter-non-commuter demand ratio, thus obtaining the commuter and non-commuter passenger flow on each route.

[0023] 4. Design of a bi-level programming solution algorithm: For the aforementioned two-level programming model, this invention employs a solution framework combining an improved genetic algorithm and a continuous averaging method. The upper level uses a genetic algorithm to encode the vehicle configuration vector in binary form, with each gene segment representing the number of vehicles on a route. Candidate solutions are generated iteratively through selection, crossover, and mutation operations, using a weighted comprehensive cost as the fitness function. Individuals that violate constraints on total vehicle quantity, frequency, and load factor are penalized. The lower level uses a continuous averaging method to solve the stochastic user equilibrium allocation problem, iteratively updating the flow of each path and verifying the difference in selection probabilities as a convergence condition. The passenger flow distribution results obtained from the lower level are fed back into the upper-level model to update the fitness value, forming an iterative loop of "vehicle configuration—passenger flow allocation" until a preset termination criterion is met, outputting the optimal collaborative scheduling scheme for the system.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention achieves coordinated resource optimization for two public transport modes. By simultaneously addressing vehicle allocation issues for both conventional public transport and demand-response public transport (DRT) within a unified optimization framework, this invention can scientifically coordinate resource allocation between the two service modes under the hard constraint of a given total vehicle volume. This allows DRT, which provides efficient direct services, and conventional public transport, with its extensive coverage, to complement each other's strengths, thereby improving the overall capacity utilization efficiency and service level of ground public transport at the system level.

[0025] 2. This invention accurately depicts passenger choice behavior in multimodal travel networks. Innovatively, it introduces the concept of generalized travel costs into the modeling process and, combined with stochastic user equilibrium theory, quantifies various factors such as walking time, waiting time, time on the vehicle, ticket price, and perceived crowding into the passenger's perceived cost. Simultaneously, the model distinguishes between the different decision-making logics of commuters and non-commuters, making the simulated passenger flow distribution more closely resemble real-world travel patterns. This provides a reliable and accurate demand input basis for upstream vehicle resource optimization.

[0026] 3. This invention comprehensively balances the revenue of operating companies with passenger travel efficiency. By constructing an optimization model with the weighted sum of the total commuter travel time cost and the company's total operating cost as the objective function, this invention enables the final scheduling scheme to find the optimal balance between minimizing passenger travel time and controlling operator costs. This method can provide operating companies with decision support adapted to different management preferences, helping to effectively manage operational economic risks while ensuring basic service quality.

[0027] 4. This invention provides an efficient solution strategy suitable for large-scale real-world networks. For the established complex bi-level programming model, this invention designs a solution framework that integrates an improved genetic algorithm and the continuous average method (MSA). This framework decomposes the original problem into two interactive iterative sub-processes: "vehicle configuration optimization" and "passenger flow balancing." Chromosome encoding, fitness evaluation, and convergence criteria ensure the stable operation of the algorithm. This method is characterized by its clear principle, ease of implementation, and strong scalability, making it applicable to the scale and complexity of real-world urban public transport networks and possessing promising engineering application prospects. Attached Figure Description

[0028] Figure 1 This is a flowchart of the demand-responsive bus and conventional bus hybrid scheduling optimization method in an embodiment of the present invention; Figure 2 This is a schematic diagram of a mixed public transport operation scenario in the commuter origin-destination (OD) area studied in this embodiment of the invention; Figure 3 This is a schematic diagram of the framework of the two-layer collaborative optimization model proposed in this embodiment of the invention; Figure 4 This is a flowchart of the solution algorithm provided in the embodiments of the present invention. Detailed Implementation

[0029] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0030] like Figure 1-4 As shown, this embodiment of the invention provides a method for optimizing the hybrid scheduling of demand-responsive public transport and regular public transport. The following description uses a typical commuter origin-destination (OD) area as an example: 1. Commuting scenarios and route settings: Between a pair of commuter origin-destination (OD) zones in a city, there are multiple residential or employment clusters within the starting area, with the destination being a major employment center. The existing system has several regular bus routes with fixed routes and equal-interval timetables to cover different demand points, but it suffers from problems such as long detours, extended on-board times, and long waiting times. To improve commuting efficiency during peak hours, a demand-response commuter bus (DRT) line is proposed to be added within this OD zone. Passengers will make reservations and gather at designated boarding points, with vehicles operating on a one-passenger-one-seat basis, transporting passengers to the destination along a relatively direct route.

[0031] 2. Travel demand and passenger modeling: Based on historical passenger flow data and survey results, the commuter demand from each demand point to the destination is determined, and the corresponding non-commuter demand is estimated using empirical coefficients. Commuter and non-commuter passengers are modeled separately: commuter passengers can choose between regular buses and DRT (Dedicated Rapid Transit) modes of transportation, while non-commuter passengers only use regular buses. Based on the characteristics of the study area and actual operation, parameters such as fare levels for regular buses and DRT, vehicle operating speed, average passenger walking speed, waiting time estimation methods, and maximum vehicle passenger capacity are set to provide basic data for subsequent optimization and simulation calculations.

[0032] 3. Vehicle configuration initialization and passenger flow allocation: During implementation, the upper limit of the total number of available vehicles in the system is determined based on the existing vehicle fleet. Within this range, a set of feasible vehicle configuration schemes is provided for each regular bus route and DRT route, and these schemes are encoded into the initial population of the genetic algorithm. Each individual in the population is decoded to obtain the number of vehicles corresponding to each route, and then calculations are performed according to the lower-level passenger flow allocation model. For commuter passengers, based on the current vehicle configuration, the walking time, waiting time, on-vehicle time, and congestion level on each feasible path are calculated to obtain the generalized travel cost and path selection probability for each path. The continuous averaging method is used to iteratively update the path passenger flow until the path flow converges. For non-commuter passengers, the non-commuter demand of each OD pair is allocated to all regular bus routes according to the average allocation principle to obtain the distribution of non-commuter passenger flow on regular bus routes.

[0033] 4. Fitness assessment and constraint handling: After obtaining a stable passenger flow distribution, the total travel time of commuters, the company's ticket revenue, and vehicle operating costs under the current vehicle configuration plan are calculated. A weighted total cost is then constructed based on this cost and used as the fitness value for the genetic algorithm. For solutions that do not meet the constraints of total vehicle quantity, reasonable departure frequency range, or upper and lower limits of route occupancy, a penalty term is added to the fitness function. This causes such solutions to be gradually eliminated during the evolution process, ensuring that the retained solutions have both good cost performance and meet operational and service requirements.

[0034] 5. Genetic Iteration and Optimal Solution Output: After completing the fitness assessment, selection, crossover, and mutation operations are performed on the current population to generate a new generation of vehicle configuration schemes. The calculation process of "passenger flow allocation—cost calculation—fitness assessment" is repeated for the new population. As the number of generations increases, the weighted total cost of individuals in the population gradually decreases, and the vehicle configuration vector and corresponding passenger flow distribution gradually stabilize. When the improvement in fitness is less than a preset threshold, or when the preset maximum number of iterations is reached, the algorithm terminates, and the optimal or near-optimal vehicle configuration vector and corresponding passenger flow distribution results are output. This result provides the number of vehicles that should be configured for each regular bus route and DRT route during peak hours, which can directly provide a basis for operating companies to formulate vehicle allocation schemes and departure plans.

[0035] This invention provides a method for optimizing the scheduling of demand-responsive public transport and conventional public transport, comprising the following steps: S1. Obtain the operating parameters of the ground public transport system and passenger travel demand data for the commuter OD area to be optimized.

[0036] S2. Based on the operating parameters of the ground public transport system and passenger travel demand data, a collaborative optimization model is constructed. The collaborative optimization model is used to jointly optimize the vehicle configuration scheme of conventional buses and demand-responsive buses under the total resource constraints of the ground public transport system, and to simulate the travel choices and passenger flow distribution of passengers under this vehicle configuration scheme. The optimization objective of the vehicle configuration scheme integrates passenger travel efficiency and operator operating costs, and the passenger travel choice behavior is described based on the generalized travel cost.

[0037] The present invention aims to study how to optimize the vehicle resource allocation between conventional bus (CB) and DRT lines in a commuter origin-destination (OD) area after the opening of a commuter demand-responsive bus (DRT) line.

[0038] It is understandable that the introduction of DRT lines will have two mutually reinforcing effects: First, the new lines will share the passenger flow of the original regular buses, and under the condition of limited vehicle resources, the vehicle resources of each line must be redistributed; second, passengers will have a new mode of travel, and their travel choices will in turn affect the passenger flow distribution of each line, which in turn will affect the decision-making process of vehicle allocation.

[0039] This invention focuses on a commuter origin-destination (OD) area, consisting of multiple demand points within a starting area and a destination point. Before the DRT line was established, several regular bus routes already served different demand points. After the DRT was established, vehicle resources throughout the commuter area needed to be reallocated. Simultaneously, commuters at the demand points could choose to take the DRT directly to their destination. The research problem of this invention can be described as: rationally allocating vehicle resources while meeting passenger travel needs and ensuring appropriate route occupancy rates to achieve a balance between the interests of operators and passengers. Considering the symmetrical characteristics of commuter traffic during morning and evening peak hours, this model focuses on analyzing a single flow direction during the morning peak. Therefore, this invention constructs a two-layer programming model to simultaneously consider the impact of both vehicle resource reallocation and passenger travel choices.

[0040] In this embodiment, the collaborative optimization model is a two-level programming model, which is used to simultaneously consider the impact of both vehicle resource reallocation and passenger travel choices.

[0041] Upper-level planning model: This model determines the number of vehicles allocated to each route based on the optimal interests of passengers and the company. This decision is constrained by the total number of vehicles, departure frequency, and route occupancy rate.

[0042] Lower-level planning model: This model determines passenger flow on each route based on passenger travel choices. Different types of passengers have different route selection strategies. For commuter passengers, route selection is considered based on the generalized travel cost of the route; for non-commuter passengers, a passenger flow equalization strategy is adopted, allocating them to the various regular bus routes of the OD pair.

[0043] The upper-level model, assuming that the passenger flow on each route remains constant, executes a vehicle resource reallocation strategy and outputs the number of vehicles allocated to each route; the lower-level model, assuming that the number of vehicles allocated to each route remains constant, executes a passenger flow allocation strategy and outputs the passenger flow on each route.

[0044] To construct this model, the following basic assumptions are proposed: 1. Passengers at each demand point can choose between DRT and regular public transport.

[0045] 2. Each demand point includes both commuter and non-commuter passengers. Assume the commuting demand from each demand point to the destination is a known, fixed value. rather than commuting needs Commuting needs proportional relationship .

[0046] 3. Commuters can choose any mode of transportation, while non-commuter passengers can only choose regular buses.

[0047] 4. Regular bus routes depart at equal intervals.

[0048] 5. When choosing the DRT service mode, there is no waiting time because this mode allows you to reserve seats and times in advance. When choosing regular buses, there will be a waiting time. .

[0049] 6. All vehicle types are identical. The number of vehicles on regular bus routes and DRT routes is arbitrary, but their total number cannot exceed the maximum number of vehicles in the system.

[0050] 7. This invention is limited to the decision-making of the number of vehicles and does not involve the formulation of timetables or specific driving plans.

[0051] In this embodiment, the upper-level model determines the number of vehicles allocated to each route, mainly including the following: (1) Objective function Public transportation operation involves multiple parties, including bus operators and passengers. When constructing a collaborative optimization model for the ground public transportation system, the needs of both parties must be fully considered. Therefore, the upper-level model is designed as a multi-objective optimization model, aiming to maximize the total operating revenue of the bus operating company while minimizing the total travel time of commuters. The objective function specifically includes: 1) Total travel time cost for commuters The total travel time cost for commuters is the sum of the travel times of commuters at all demand points. At each demand point, commuters can choose either regular public transport or demand-responsive public transport. When choosing regular public transport, the waiting time and boarding time need to be considered. When choosing demand-responsive public transport, the walking time and boarding time to the ride-sharing station need to be considered. For the sake of consistent model representation, we assume that the walking time is zero when choosing regular public transport and the waiting time is zero when choosing demand-responsive public transport.

[0052] In the formula, This represents the set of all boarding stations; This represents the set of all drop-off points; Represents a set of modes of transportation; yes Interval method path Commuter passenger flow; The average walking distance from passengers to the ride-sharing station. Average walking speed; For path The total length is determined by the road segments traversed by the path. length It is accumulated; For transportation The speed of travel; Representing a path A collection of the road sections traversed.

[0053] 2) Total operating costs of public transport companies The total operating cost of a public transport company can be calculated by subtracting the total fare revenue from passengers from the vehicle operating cost, as shown below: in, , These represent the company's total ticket revenue and vehicle operating costs, respectively.

[0054] a) Total ticket revenue Businesses generate total fare revenue by operating different modes of transportation. Specifically, total fare revenue equals the sum of the number of passengers choosing each mode of transportation at each demand point multiplied by the corresponding fare.

[0055] In the formula, yes Interval method path Non-commuter passenger traffic Indicates the mode of transportation The ticket price.

[0056] b) Vehicle operating costs Vehicle operating costs mainly include fixed costs and variable costs Fixed costs mainly consist of the regular maintenance and management expenses of vehicles, reflecting the basic investment required to maintain service operations. Variable costs mainly consist of fuel costs incurred during vehicle operation, which increase as the vehicle's mileage increases. Variable costs are directly related to the scale and scope of service provision.

[0057] In the formula, Indicates the line The number of vehicles, This indicates a collection of regular bus routes. This represents a set of demand-responsive bus routes.

[0058] (2) Constraints 1) Total number of vehicles constraint For operators, the number of vehicles in operation directly affects operating expenses. Too many vehicles will lead to a waste of resources. Therefore, determining the upper limit of the number of vehicles is crucial for achieving cost-effective operation.

[0059] In the formula, This indicates the maximum number of vehicles allowed in the operating area.

[0060] 2) Frequency constraints for regular bus routes Taking the morning rush hour as a cycle, within this cycle, the number of departures of regular buses on each route is equal to the number of regular buses allocated to that route, and it needs to be ensured that this is within a reasonable range.

[0061] In the formula, and These represent the minimum and maximum departure frequencies on regular bus routes, respectively.

[0062] 3) Line service capacity constraints Whether it's regular buses or DRT, the number of vehicles on each line must not only meet the travel needs of the destinations but also be kept within an acceptable range in terms of economy and efficiency. Too many vehicles on each line will lead to resource waste, while too few will fail to meet passenger demand. Therefore, it is necessary to maintain the passenger service capacity of each line within a certain range based on the number of vehicles. The service capacity of a line is constrained by the number of vehicles and the maximum capacity of each vehicle. For regular buses, the maximum capacity of a single vehicle is the number of passengers it can carry. For DRT, since one seat per passenger is implemented, the maximum capacity of a single vehicle is the number of seats in the vehicle.

[0063] In the formula, and They represent the modes of transportation. Minimum and maximum load factors for each line Indicates the line Total commuter passenger flow This indicates the maximum capacity of a single vehicle.

[0064] In this embodiment, the lower-level model is a passenger flow allocation model. Passenger flow on the routes is based on passengers' route selection behavior. Since passengers at each demand point are limited to choosing between regular buses and DRT, their route selection is also limited to the routes offered by these modes. Different route selection strategies are considered for different types of passengers. For commuters within the commuting area, based on Wardrop's first principle (i.e., the user-optimal principle), it is assumed that they will always tend to choose the routes with the lowest generalized travel costs. For non-commuter passengers, considering that they are not constrained by commuting needs, they will not choose DRT commuter routes. This invention assumes that this portion of passenger flow is allocated to different regular routes according to a uniform distribution strategy.

[0065] First, for commuter passengers, this invention employs a stochastic user equilibrium principle for modeling. This principle posits that when travelers choose a path between OD pairs (r,s), they always select the path with the lowest cost based on their perceived generalized travel costs for each path. For all travelers between OD pairs, the path selection probability can be used... To estimate the chosen path Number of people: In the formula, express Commuting demand between them express Non-commuting demand between them.

[0066] Multinomial Logit models are typically used to simulate and estimate passenger route preferences. Selection probability: in It is a natural constant. It's about travelers' routes. The utility function of perceived travel time is given. Therefore, considering a Logit-based stochastic equilibrium model, path flow in the network can be specifically expressed as follows: in, It is the utility cost coefficient. It is a path The generalized travel cost function, for travelers, mainly includes time cost and fare. This invention defines the generalized travel cost function for conventional public transportation and demand-responsive public transportation as follows: (1) General travel costs of choosing regular public transport routes The general cost of commuting by regular public transportation includes the fare and the time cost while on the vehicle, taking into account perceived congestion, and can be expressed as: in, This refers to the general cost of taking regular public transportation. This indicates the fare for a regular bus ride. This indicates the speed of a regular bus. This represents the passenger's perceived time coefficient. Representing a path The congestion coefficient is related to the number of departures on the route and the capacity of each vehicle. Representing a path A collection of the road sections traversed. This can be expressed using a piecewise function as follows: In the formula, , , respectively representing the lines Normal capacity and maximum capacity This indicates the number of seats in a single vehicle. and They represent the lines respectively. Total commuter and non-commuter passenger traffic. and These represent congestion coefficient 1 and congestion coefficient 2, respectively.

[0067] (2) Generalized travel costs of choosing the DRT route The general cost of commuting by demand-responsive public transport includes the fare and the time spent on the bus. Since demand-responsive buses provide seating for each passenger, crowding is not a factor. The total cost of the trip is expressed as follows: in, This represents the general cost of using demand-responsive public transportation. This indicates the fare for demand-responsive public transport. This indicates the travel speed of the demand-responsive bus.

[0068] Then, for non-commuter passengers, due to the strategy of evenly distributing passenger flow, the path flow in the network can be specifically expressed as follows: In the formula, Indicates taking the regular bus number Non-commuter passenger traffic along the route express The number of regular bus routes between them Indicates taking the demand-responsive bus. Non-commuter passenger traffic along the route.

[0069] In this embodiment, the upper-level optimization problem is: The goal of the upper-level planning model is to find an optimal vehicle configuration scheme. To minimize a weighted total cost function consisting of passenger travel time costs and business operating costs. .

[0070] Upper-level decision variables The following constraints must be met during the optimization process: In the formula, C1 represents the total number of vehicles constrained to ensure the number of vehicles deployed on all regular bus routes and demand-responsive bus routes. The sum of these figures cannot exceed the maximum total number of vehicles owned by the operating company. C2 represents the frequency constraint for regular bus routes, which specifies the number of vehicles allocated to each regular bus route. Must be at the set minimum departure frequency and maximum departure frequency Between. C3 is the line service capacity constraint, which controls service quality through the line's load factor. Total passenger flow of the line. With the total capacity of the line The ratio must be within the set minimum load factor. and maximum load factor between.

[0071] In this embodiment, the lower-level optimization problem is: The lower-level model is a passenger flow allocation equilibrium problem. Its goal is to solve for a given upper-level vehicle configuration. Below, commuter passenger flow Non-commuter passenger flow How to distribute them in the road network and achieve a stable equilibrium state.

[0072] The passenger flow variables in the lower equilibrium state must satisfy the following conservation constraints: In the formula, C1 represents the commuting demand satisfaction constraint, which ensures that commuting demand is satisfied across all modes of transportation. and all paths The commuter passenger flow allocated above The sum must equal the total commuting demand. C2 satisfies the constraint for non-commuter demand, which ensures that all regular bus routes meet this constraint. Non-commuter passenger flow allocated The sum must equal the total non-commuting demand. C3 is a passenger flow correlation constraint, which defines the non-commuter demand. and commuting demand The relationship between the two is through a fixed proportional coefficient. Related.

[0073] S3. Solve the collaborative optimization model to obtain an optimal vehicle configuration scheme and its corresponding passenger flow distribution prediction result; the solution process realizes the interaction and collaborative optimization of vehicle configuration decision and passenger flow distribution result through iteration.

[0074] In this embodiment, the present invention establishes a two-level programming model aimed at optimizing the economic benefits of bus companies and the travel efficiency of passengers after the introduction of demand-responsive bus routes. The upper-level model aims to minimize the total travel cost for passengers and the total operating cost for the company, with the decision variable being the number of departures on each route. , In the lower-level model, these parameters will be fixed and known, and then the multimodal traffic network distribution model will be solved. The decision variable in this model is the mode of transportation. Passenger flow on each path , During the iteration process, these parameters will be used as known parameters in the upper-level model, thus allowing for further solution. The process continues until the model meets the predetermined iteration criteria, at which point the optimal solution for the system is obtained.

[0075] In this embodiment, the upper-level model includes two cost-related objective functions. To unify the measurement of these two costs, the objective functions are transformed into a single objective function, using a time value perception coefficient. Converting travel time into equivalent monetary cost, the objective function of the upper-level model can be expressed as: In this embodiment, the lower-level model is a passenger flow allocation model. For non-commuter passengers, an average passenger flow allocation strategy is adopted, directly distributing the non-commuter passenger flow between OD pairs evenly across all regular bus routes. For commuter passengers, a Logit-based stochastic user equilibrium passenger flow allocation strategy is adopted, which is typically solved using the MSA (Method of Successive Averages) algorithm. First, algorithms are designed and solved separately for the upper and lower-level models. Finally, considering the interaction between the upper and lower-level models, an algorithm is designed to embed the solution from the lower-level model into the upper-level model.

[0076] (1) Solution process of the upper-level model The upper-level model is a single-objective optimization model with minimum cost, solved using a genetic algorithm. Its key steps are as follows: 1) Gene encoding The decision variable of the upper-level model is the number of vehicles configured for each route. The gene sequence of the chromosome is encoded in binary, with each five bits representing the number of vehicles configured for a route.

[0077] 2) Determining the fitness function The fitness function is used to quantitatively analyze the performance of each individual. In this model, the fitness function comprehensively considers two key indicators: the total travel time cost for passengers and the total operating cost of the operator. To implement penalty measures for individuals that do not meet the model constraints, such as those exhibiting... Individuals with a fitness value of 0, a total number of vehicles exceeding the maximum limit, or that do not meet the line service capacity constraints will be assigned a maximum fitness value.

[0078] (2) Solution process of the lower-level model For commuter traffic on each path, the continuous averaging method is used to solve the stochastic user equilibrium distribution model. The algorithm steps are as follows: Step 1: Initialize path flow. Set the iteration counter. Set to 1 for each path. Initialize traffic Given the total demand for OD pairs is The initial traffic allocation for each path is ,in This indicates the number of all paths between OD and rs.

[0079] Step 2: Update path cost. Based on the current path traffic. And use equations (11) and (13) from the previous text to calculate the cost of each path. .

[0080] Step 3: Calculate the path selection probability. Calculate the selection probability of each path according to equation (9). .

[0081] Step 4: Calculate auxiliary flow For each path k, calculate the auxiliary flow. .

[0082] Step 5: Update path traffic. Update the traffic of each path using the continuous averaging method, as shown in the following formula.

[0083] Step 6: Check convergence. Calculate the maximum difference in selection probability across all paths. If... If the number of iterations is less than the predetermined threshold or the maximum number of iterations is reached, the model is considered to have converged; otherwise, the iteration counter I is incremented by 1.

[0084] (3) Solution process of bi-level programming model The bi-level programming model established in this section is solved by designing a genetic algorithm that integrates multiple passenger flow allocation algorithms. The steps of the algorithm are as follows: Step 1: Initialize parameters and population Initialize the parameters of the genetic algorithm and generate an initial population, with each individual representing a set of possible vehicle configurations. The solution.

[0085] Step 2: Generate a collaborative optimization scheme Each individual in the genetic algorithm is decoded to determine the number of vehicles on each path. This step generates a collaborative optimization scheme for the bus company's operation, namely, a set X of vehicle configurations including both regular buses and demand-responsive buses.

[0086] Step 3: Calculate flow distribution and fitness The vehicle configuration set X for each of the above routes is applied to the lower-level model, namely the traffic network flow distribution model. The commuter passenger flow set for each route is calculated using a continuous averaging algorithm. Meanwhile, the non-commuter passenger flow of each path is obtained based on the passenger flow average distribution algorithm. Based on the distribution results, the system returns to the upper-level model to calculate the objective function value and fitness value of each individual in order to evaluate the performance of each optimization scheme.

[0087] Step 4: Determine the termination condition Verify whether the algorithm has reached its termination condition, such as whether the number of iterations has reached a predetermined limit. If so, the algorithm stops and obtains the current optimal solution; otherwise, proceed to the next stage.

[0088] Step 5: Perform genetic operations The core operations of the genetic algorithm, including selection, crossover, and mutation, are performed on the population to generate a new generation. Then, we return to Step 2 and continue the iterative process using the updated population.

[0089] S4. Based on the optimal vehicle configuration scheme, output a scheduling scheme to guide the mixed operation of regular buses and demand-response buses within the commuter OD area.

[0090] This invention proposes and constructs a two-layer programming model to achieve coordinated optimization of demand-responsive public transport and conventional public transport vehicle resources in a ground public transport system. The model fully considers the differences between the two service modes and the key factors influencing passenger choices, incorporating them into the modeling process to accurately predict passenger travel behavior and formulate reasonable vehicle allocation strategies accordingly. The upper layer of the model aims to maximize enterprise operating revenue and minimize total passenger travel time; the lower layer uses a logit-based choice probability approach to simulate passenger preferences for different travel modes, with the core assumption that passengers always tend to choose the mode that minimizes their generalized travel costs.

[0091] This invention, for the first time, constructs a two-layer programming model for vehicle allocation in commuter origin-destination (OD) areas under a mixed operation scenario of demand-response public transport and regular public transport. The upper layer optimizes vehicle allocation, while the lower layer characterizes passenger path selection and passenger flow equilibrium distribution within a multi-modal transport network, thereby achieving system-level collaborative scheduling optimization. Specifically, this invention proposes to differentiate between commuter and non-commuter passengers in its modeling: it describes the choice behavior of commuter passengers between DRT and regular public transport based on generalized travel costs and the Logit stochastic user equilibrium principle, while adopting an average allocation strategy for non-commuter passengers. This allows the model to effectively reflect the real impact of different passenger types on the distribution of passenger flow on the route. In the generalized travel cost function, the model comprehensively considers walking time, waiting time, on-vehicle time, fare, and congestion perception described by a piecewise function, cleverly linking the route load factor constraint with the passenger's congestion experience, thus ensuring that vehicle allocation decisions not only meet capacity safety requirements but also take into account passenger comfort. Finally, to effectively solve this complex model, this invention designs a solution framework that combines an improved genetic algorithm with a continuous averaging method. By embedding the lower-level passenger flow allocation results into the optimization loop of the upper-level vehicle configuration, a collaborative optimization algorithm that can run efficiently on a real-scale public transport network is formed, providing a practical and feasible technical approach for vehicle resource allocation in such hybrid public transport systems.

[0092] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for optimizing the scheduling of demand-responsive public transport and conventional public transport, characterized in that, Includes the following steps: S1. Obtain the operating parameters of the ground public transport system and passenger travel demand data for the commuter OD area to be optimized; S2. Based on the operating parameters of the ground public transport system and passenger travel demand data, construct a collaborative optimization model; The collaborative optimization model is used to jointly optimize the vehicle configuration scheme of conventional buses and demand-responsive buses under the total resource constraints of the ground public transport system, and to simulate passenger travel choices and passenger flow distribution under this vehicle configuration scheme; wherein, the optimization objective of the vehicle configuration scheme integrates passenger travel efficiency and operator operating costs, and passenger travel choice behavior is described based on generalized travel costs; S3. Solve the collaborative optimization model to obtain an optimal vehicle configuration scheme and its corresponding passenger flow distribution prediction result; the solution process realizes the interaction and collaborative optimization of vehicle configuration decision and passenger flow allocation result through an iterative method; S4. Based on the optimal vehicle configuration scheme, output a scheduling scheme to guide the mixed operation of regular buses and demand-response buses within the commuter OD area.

2. The method for optimizing the mixed scheduling of demand-responsive public transport and conventional public transport according to claim 1, characterized in that, In step S1, the operating parameters of the ground public transport system include vehicle fixed costs, variable costs, maximum capacity of a single vehicle, upper limit of the total number of vehicles available in the system, reasonable range of departure frequency for each route, and reasonable range of full load rate; the passenger travel demand data includes commuting demand from each demand point to the destination, as well as non-commuting demand related to commuting demand.

3. The demand-responsive bus and conventional bus hybrid scheduling optimization method according to claim 2, characterized in that, In step S2, the collaborative optimization model is a two-level programming model, including: an upper-level vehicle configuration optimization model, used to decide the number of vehicles to be configured with the goal of minimizing the overall cost; and a lower-level passenger flow distribution equilibrium model, used to simulate the passenger route selection and passenger flow distribution results given the number of vehicles.

4. The method for optimizing the mixed scheduling of demand-responsive public transport and conventional public transport according to claim 3, characterized in that, The comprehensive cost is the weighted sum of the total travel time cost for commuters and the total operating cost of the public transport company; the total operating cost of the public transport company is the difference between vehicle operating costs and total fare revenue.

5. The method for optimizing the mixed scheduling of demand-responsive public transport and conventional public transport according to claim 3, characterized in that, In the lower-level passenger flow distribution equilibrium model, the route selection of commuter passengers follows the stochastic user equilibrium principle based on generalized travel costs, and the selection probability is calculated using a multinomial Logit model; the passenger flow of non-commuter passengers is evenly distributed among various regular bus routes.

6. The method for optimizing the mixed scheduling of demand-responsive public transport and conventional public transport according to claim 5, characterized in that, The generalized travel cost, for regular public transport routes, includes fare, waiting time cost, on-vehicle time cost, and perceived congestion cost; for demand-responsive public transport routes, it includes fare, time cost of walking to the carpooling station, and on-vehicle time cost.

7. The demand-responsive bus and conventional bus hybrid scheduling optimization method according to claim 3, characterized in that, The constraints imposed by the upper-level vehicle configuration optimization model include: the sum of the number of vehicle configurations does not exceed the upper limit of the total number of available vehicles in the system; the departure frequency corresponding to the number of vehicle configurations for each regular bus route is within a preset range; and the load factor of each route is between the preset minimum and maximum load factors.

8. The method for optimizing the mixed scheduling of demand-responsive public transport and conventional public transport according to claim 1, characterized in that, In step S3, the solution process of the iterative method is as follows: a genetic algorithm framework is used to generate and iteratively update the vehicle configuration scheme population. For each scheme in the population, the passenger flow allocation algorithm is called to simulate its passenger flow distribution, and the fitness of the scheme is evaluated based on the comprehensive cost, so as to achieve collaborative optimization of vehicle configuration and passenger flow allocation.

9. The method for optimizing the mixed scheduling of demand-responsive public transport and conventional public transport according to claim 8, characterized in that, In the passenger flow allocation algorithm, the continuous averaging method is used to solve the random user equilibrium allocation problem for commuter passengers; the average allocation strategy is used for non-commuter passengers.

10. The demand-responsive bus and conventional bus hybrid scheduling optimization method according to claim 8 or 9, characterized in that, The specific solution process for step S3 includes: S31. Initialize the initial population for generating vehicle configuration schemes; S32. For each vehicle configuration scheme in the population, calculate the corresponding commuter and non-commuter passenger flow distribution using a passenger flow allocation algorithm; S33. Based on the passenger flow distribution, calculate the comprehensive cost corresponding to the vehicle configuration scheme as the fitness value; S34. Determine whether the algorithm termination condition is met; if it is met, output the current optimal vehicle configuration scheme and passenger flow distribution; if it is not met, perform genetic operations on the current population to generate a new generation population, and return to step S32.

Images