A storm environment-oriented demand response type modular bus path optimization method

Abstract

The present application relates to the technical field of urban public transport operation scheduling and path planning, and discloses a demand response type modular bus path optimization method for storm environment. The method collects passenger demand, meteorological data, road network topology and water accumulation data, calculates the structural resilience and functional resilience of the road section, and obtains the comprehensive resilience through the entropy weight method; a nonlinear integer programming model is constructed with the minimum of operation cost, passenger waiting cost, penalty cost and power consumption cost as the target, demand response, dynamic grouping, environment adaptive space-time and energy endurance safety constraints are established; the optimal driving path, carriage configuration and coupling and decoupling nodes are obtained by solving the model, and the central control system is issued to realize dynamic scheduling. The present application quantifies the influence of severe weather on road network traffic capacity, realizes the accurate matching of modular bus transport capacity and dynamic passenger flow, effectively reduces the operation cost and passenger travel delay, and significantly improves the operation resilience and service reliability of the public transport system in the storm environment.

Description

Technical Field

[0001] This invention relates to the field of urban public transportation operation scheduling and route planning technology, specifically a demand-responsive modular public transportation route optimization method for rainstorm environments. Background Technology

[0002] Public transportation systems are a crucial component of urban infrastructure, playing a key role in optimizing travel patterns, alleviating traffic congestion, and promoting sustainable transportation development. With accelerating urbanization, residents' travel demands exhibit significant spatial and temporal imbalances and personalized characteristics. Traditional public transportation often employs a rigid operating model with fixed routes, vehicle types, and timetables, which is insufficiently adaptable to dynamic demand. This can easily lead to overcrowding and passenger congestion during peak hours, while causing idle capacity and increased costs during off-peak hours.

[0003] Modular buses achieve flexible adjustment of transport capacity through the dynamic assembly and decoupling of carriage units: large-capacity assemblies are formed in densely populated areas, while independent units are converted into more efficient connections in sparsely populated areas. This is an effective means to enhance the flexibility of the public transport system and solve the "last mile" problem. However, existing modular bus route planning methods are mainly geared towards normal road networks and still have significant limitations under extreme weather conditions such as heavy rain: First, they lack road network resilience assessment and do not consider the risk of blockages caused by water accumulation and reduced traffic capacity; second, they do not consider energy consumption fluctuations and assembly stability constraints under severe weather conditions, leading to deviations in energy consumption prediction and imbalances in transport capacity matching.

[0004] Therefore, there is an urgent need to develop a modular bus route optimization method that takes into account road network resilience, operating costs, and operational safety, in order to solve problems such as unreasonable route planning, high safety hazards, energy consumption prediction errors, and capacity mismatch in the current technology under heavy rain conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a demand-responsive modular public transport route optimization method for rainstorm environments, which can solve the above-mentioned problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention proposes a demand-responsive modular public transport route optimization method for rainstorm environments, comprising the following steps:

[0008] S1. Collect passenger demand data, meteorological data, road network topology of the target area, road section water accumulation information, and vehicle speeds before and after rainstorms.

[0009] The passenger demand data includes: the passenger's origin and destination, the number of passengers, and the estimated time window for passengers to arrive at the origin.

[0010] The meteorological data includes meteorological forecast data and real-time meteorological data; the meteorological forecast data includes: the time window of impending heavy rain, the area of ​​impending heavy rain, the duration of heavy rain, the expected rainfall, and the predicted evolution of water depth; the real-time meteorological data includes: rainfall per unit time and the real-time water depth of each road section;

[0011] The road network topology data includes the physical length of each road segment, node data in the road network, and road segment connectivity.

[0012] S2. Based on the real-time meteorological data, road section water accumulation information, and vehicle speeds before and after the rainstorm, calculate the structural resilience and functional resilience of each road section. Structural resilience is calculated based on road network topology data, assessing the importance of each road section in the network by calculating its degree centrality, evaluating changes in network connectivity under road section failure conditions by calculating local efficiency, and assessing path redundancy by calculating clustering coefficients. Functional resilience is assessed based on vehicle speed, road section water accumulation information, and changes in traffic capacity. The entropy weighting method is used to obtain the comprehensive resilience of each road section. Based on the real-time meteorological data, road section water depth, and vehicle operating conditions, construct an energy consumption correction model for vehicles under rainstorm conditions, and calculate the corresponding rainstorm energy consumption correction coefficient for each road section.

[0013] S3. Construct a nonlinear integer programming model with the objective of minimizing the sum of vehicle operating costs, passenger waiting time costs, system penalty costs, and electricity consumption costs;

[0014] S4. Construct a constraint system, including passenger demand response constraints, modular bus dynamic formation consistency constraints, environmental adaptive spatiotemporal constraints, and energy endurance safety constraints, to ensure the feasibility of the scheduling scheme in the spatiotemporal, capacity, and energy dimensions.

[0015] S5. Solve the nonlinear integer programming model to obtain the optimal vehicle driving path, modular carriage quantity configuration and coupling and decoupling nodes, and send the solution to the modular bus central control system to realize dynamic scheduling and coupling control of modular vehicles.

[0016] Preferably, in step S4, the constraint system includes:

[0017] Demand response and service priority constraints include: a road segment skipping rule based on real-time passenger flow to determine whether to stop on a road segment; a low-resilience road segment priority service principle based on the comprehensive resilience weight of road segments; and a timeout demand quantification rule based on the maximum allowable waiting time.

[0018] Modular physical grouping logical constraints include: uniqueness constraints on the coupling / decoupling states of carriages in the same time and space, spatiotemporal uniqueness and state continuity constraints on the ownership relationship of a single carriage, and upper limit constraints on the maximum number of carriages allowed in the operation of modular vehicles;

[0019] Dynamic operating parameters and arrival / departure order constraints include: actual travel time calculation rules based on road segment resilience mapping, maximum allowable number of departures within the entire scheduling cycle, safe time interval constraints between adjacent vehicles leaving the starting node, order constraints that the arrival time window of the next vehicle at any node is no earlier than that of the previous vehicle, and road segment maximum and minimum safe speed control rules determined based on statistical quantiles.

[0020] Dynamic capacity matching and energy safety constraints include capacity matching rules to ensure that the actual passenger capacity of a single vehicle does not exceed the rated capacity of the train, rules for the transition of remaining power state as the mileage and passenger load evolve, minimum safe power red line constraints throughout the operation process, and minimum power reserve limits to meet the requirements for returning to the depot after completing the last task.

[0021] Preferably, step S2 is as follows:

[0022] S21. Calculate the structural resilience of each road segment, that is, based on the road network topology data, calculate the degree centrality of each road segment in the road network to evaluate its core position in the topology, calculate the local to evaluate the road network fault tolerance after the road segment failure, and calculate the clustering coefficient to evaluate the path redundancy of the area where the road segment is located.

[0023] S22. Calculate the functional resilience of each road segment, that is, based on real-time rainstorm data, monitor the evolution of the traffic performance of the road segment under the impact of rainstorm, construct a resilience triangle model, and quantitatively evaluate the real-time service efficiency loss of the road segment in the waterlogged environment by calculating the area of ​​the triangle formed by the performance drop degree and recovery time.

[0024] S23. Calculate the comprehensive resilience based on structural resilience and functional resilience, that is, use the degree centrality, local efficiency, clustering coefficient and resilience triangle area as evaluation indicators, objectively determine the weight of each indicator through entropy weight method, and weighted aggregate to obtain the comprehensive resilience index of each road section under the current rainstorm environment.

[0025] Preferably, the nonlinear integer programming model constructed in step S3 is as follows:

[0026] ,

[0027] For the specific meaning of each variable in the formulas described in this section, please refer to the detailed implementation section of the instruction manual.

[0028] Preferably, step S4 specifically includes:

[0029] S41. Construct passenger demand response constraints; the passenger demand response constraints include demand coverage and service matching constraints, vehicle passenger capacity constraints, capacity demand matching constraints, passenger number conservation constraints, maximum passenger waiting time constraints, and overdue passenger quantification constraints.

[0030] S42. Construct a modular bus dynamic formation consistency constraint; the modular bus dynamic formation consistency constraint includes the upper limit constraint on the number of coupled carriages, the number of coupling and decoupling times and prerequisite constraints, the single coupling constraint of a single carriage, and the carriage state continuity constraint.

[0031] S43. Construct environmental adaptive spatiotemporal constraints; the environmental adaptive spatiotemporal constraints include travel time constraints based on road segment resilience, maximum number of departures within the scheduling cycle constraints, safe interval constraints between departures of adjacent vehicles, arrival sequence constraints of vehicle nodes, and upper and lower bound constraints of safe speed for road segments.

[0032] S44. Construct energy range safety constraints; the energy range safety constraints include vehicle remaining power state transition constraints, minimum safe power constraints throughout operation, range constraints for a single charging cycle, and power reserve constraints for returning to base after the mission; the vehicle remaining power state transition constraints introduce a rainstorm energy consumption correction coefficient; the rainstorm energy consumption correction coefficient is obtained by linear regression fitting based on road resilience and historical energy consumption data.

[0033] Preferably, in step S41, the construction of passenger demand response constraints involves the following steps:

[0034] S411. Construct demand coverage and service matching constraints to ensure that road segments with passenger demand are covered by at least one modular vehicle. Specific constraints are as follows:

[0035] Constraint 1 ;

[0036] S412, Constructing Modular Vehicles in Arbitrary Spacetime The number of passengers must not exceed the actual total passenger capacity of the modular vehicle, as constrained as follows:

[0037] Constraint 2 ;

[0038] S413, Modular Vehicle Construction The carrying capacity should meet the actual needs of passengers, subject to the following constraints:

[0039] Constraint 3 ;

[0040] S414. Construct the passenger quantity conservation constraint as follows:

[0041] Constraint 4 ,

[0042] Constraint 5 ;

[0043] S415. The constraint that passenger waiting time shall not exceed the maximum allowable waiting time is as follows:

[0044] Constraint 6 ;

[0045] S416. Based on sliding time window logic, dynamically identify and quantify the number of passengers whose waiting time exceeds the maximum allowed waiting time, as detailed below:

[0046] Constraint 7 ,

[0047] Preferably, in step S42, the construction of the consistency constraints for the dynamic formation of modular buses involves the following steps:

[0048] S421, Modular Vehicle Construction The coupling length is not subject to the constraint that the maximum number of carriages shall not exceed the following:

[0049] Constraint 8 ,

[0050] S422. The total number of coupling and decoupling operations for the modular vehicle and the preconditions and constraints are as follows:

[0051] Constraint 9 ,

[0052] Constraint 10 ,

[0053] Constraint 11 ,

[0054] S423. The following constraints prohibit multiple couplings within the same time window for a single carriage:

[0055] Constraint 12 ,

[0056] Constraint 13 ;

[0057] S424, Construction of the Carriage The state continuity constraints are as follows:

[0058] Constraint 14 .

[0059] Preferably, in step S43, the construction of the environment-adaptive spatiotemporal operational constraints involves the following specific steps:

[0060] S431. The adaptive travel time mapping constraints for the construction environment are as follows:

[0061] Constraint 15 ,

[0062] Constraint 16 ,

[0063] Constraint 17 ,

[0064] Constraint 18 ;

[0065] S432, the priority service constraints for constructing low-strength road sections are as follows:

[0066] Constraint 19 ;

[0067] S433. The constraint that the number of times all modular vehicles added to the road network within any time window does not exceed the maximum allowed number of departures is as follows:

[0068] Constraint 20 ;

[0069] S434, Construction of Vehicles Reaching the node and leaving the node The timing and departure interval specifications are constrained as follows:

[0070] Constraint 21 ,

[0071] Constraint 22 ,

[0072] Constraint 23 ,

[0073] Constraint 24 ,

[0074] Constraint 25 ;

[0075] S435. Construct a safe speed range constraint for vehicles based on statistical quantiles to limit the speed boundary of modular vehicles in heavy rain conditions, as follows:

[0076] Constraint 26 ,

[0077] Constraint 27 ,

[0078] Constraint 28 ,

[0079] Constraint 29 .

[0080] Preferably, in step S44, the construction of the energy range safety constraint involves the following specific steps:

[0081] S441. The state transition constraints for the remaining battery power of a modular vehicle, considering the rainstorm energy consumption correction coefficient, are as follows:

[0082] Constraint 30 ,

[0083] Constraint 31 ,

[0084] Constraint 32 ;

[0085] S442. The minimum safe power supply constraints for the entire operation of modular vehicles are as follows:

[0086] Constraint 33 ,

[0087] Constraint 34 ;

[0088] S443. The feasibility constraints for constructing the vehicle's full-range driving capability based on a single charging cycle are as follows:

[0089] Constraint 35 ;

[0090] S444. The return-to-base power reserve constraint after the completion of the modular vehicle construction mission is as follows:

[0091] Constraint 36 ,

[0092] Constraint 37 .

[0093] The beneficial effects of this invention are as follows:

[0094] (1) The present invention provides a demand-responsive modular bus route optimization method for rainstorm environments. It introduces a road network resilience assessment mechanism based on the entropy weight method, comprehensively calculates the structural resilience and functional resilience of road sections, quantifies the impact of rainstorm water accumulation on road traffic capacity and safety, and can intelligently identify and avoid low-lying high-risk road sections, reduce the risk of bus vehicles breaking down in water, and ensure the continuity and reliability of bus services in rainstorm environments.

[0095] (2) The present invention provides a demand-responsive modular bus route optimization method for rainstorm environments. It adopts a modular carriage dynamic grouping and flexible coupling strategy, combines the tidal characteristics of passenger travel in rainy weather and the uneven distribution of time and space, optimizes the number of vehicles in dynamic grouping and coupling nodes, realizes precise deployment of transport capacity, solves the problem of insufficient transport capacity during peak hours and empty waste during off-peak hours, and balances operating costs and passenger service levels.

[0096] (3) The present invention provides a demand-responsive modular bus route optimization method for rainstorm environments. It constructs a nonlinear integer programming model that includes the cost of electricity consumption, introduces an environmental correction coefficient to calculate the additional energy consumption of wet and slippery roads and water wading, and truly reflects the operating characteristics of electric buses in rainstorm environments. It prevents vehicles from breaking down midway due to deviations in electricity prediction and provides a scientific basis for electric bus route decision-making and energy management under complex weather conditions. Attached Figure Description

[0097] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0098] The present invention will be further described below with reference to the embodiments. It should be noted that these are merely examples and descriptions of the inventive concept. Those skilled in the art can make various modifications or additions to the specific embodiments described or use similar methods to replace them, as long as they do not deviate from the inventive concept or exceed the scope defined in the claims, they should all be considered to fall within the protection scope of the present invention.

[0099] Example 1:

[0100] Figure 1 This is a schematic flowchart of the method of the present invention. Figure 1 As shown, the present invention proposes a demand-responsive modular public transport route optimization method for rainstorm environments, comprising the following steps:

[0101] S1. Collect passenger demand data, real-time weather data, road network topology of the target area, road water accumulation information, and vehicle speeds before and after rainstorms.

[0102] The passenger demand data includes: the passenger's origin and destination, the number of passengers, and the estimated time window for passengers to arrive at the origin and destination.

[0103] Meteorological data includes meteorological forecast data and real-time meteorological data; meteorological forecast data includes: the time window when heavy rain is expected, the area where heavy rain is expected, the possible duration of heavy rain, the expected rainfall, and the predicted evolution of water depth; real-time heavy rain data includes: rainfall per unit time and real-time water depth of various road sections.

[0104] Road network topology data includes: the physical length of each road segment, node data in the road network, and road segment connectivity.

[0105] This step aims to build a multi-source data foundation and map real-world physical scenarios into input parameters for mathematical models, specifically including data construction in the following four dimensions:

[0106] S11. Constructing the road network topology and time window model, which is specifically divided into the following steps:

[0107] S111. Abstract the traffic network of the target area into a directed graph. ;

[0108] S112, Define the set of road segment nodes ,in Represents the total number of stations and intersections in the road network. Elements in the set are typically represented by... This indicates a specific node index in the road network;

[0109] S113, Define the set of road segments For any road segment It starts from the starting node. and termination node Composition, representation And satisfy ,definition For road section The physical length of a metric unit: kilometers;

[0110] S114. Introduce the time dimension, dividing the entire day's operating time into a set of discrete time windows. Unit: minutes.

[0111] S12. Based on the characteristics of modular buses, the following sets and physical parameters are defined:

[0112] S121. Define a modular vehicle number set. ,in This represents the total number of vehicles in operation, in units of vehicles.

[0113] S122, Define the modular carriage physical set ,in This represents the total number of available carriage units, in carriages.

[0114] S123, Define the set of carriage formation numbers ,in The maximum number of carriages allowed by technology, in carriages;

[0115] S124. Set the maximum passenger capacity of a single modular carriage as follows: Unit: person / section;

[0116] S125. Define energy consumption-related parameters: basic energy consumption per unit mileage for a single modular car. Units: kilowatt-hours per kilometer; energy consumption per unit passenger load. Unit: kWh / person·km; Minimum safe electrical charge threshold for vehicle operation. Unit: kilowatt-hour; Minimum power reserve required for the vehicle to return to the depot after completing its mission. Unit: kilowatt-hour.

[0117] S13. Collect and quantify passenger travel demand;

[0118] S131. Establish a demand-responsive public transport service platform to receive real-time travel orders through passenger mobile terminal applications;

[0119] S132. The system backend receives travel requests sent by passengers in real time. Each request includes information such as the passenger's departure point, destination, number of passengers, and expected departure time.

[0120] S133. Using a GIS geographic information system, the passenger's departure point and destination are matched to the corresponding road segment nodes in the road network structure at both ends.

[0121] S134. Based on the above mapping results, statistics are compiled within the time window. Inner and Road Sections The total number of trips reported online is defined as the number of new passengers. ;

[0122] S135. Considering the psychological impact of heavy rain on passengers, a passenger demand amplification factor under severe weather conditions is introduced. This is used for subsequent calculations of actual transport capacity demand;

[0123] S136. Set cost parameters related to passenger service: cost per unit waiting time for passengers. Unit: Yuan / minute; Maximum allowed waiting time for passengers. Unit: minutes, and overtime penalty cost for passengers waiting longer than the maximum allowed waiting time. .

[0124] S14. Collect the raw meteorological data required for calculation and define the relevant environmental parameter boundaries, which is specifically divided into the following steps:

[0125] S141. Collect real-time meteorological information and historical operational data as input for subsequent resilience assessment and model constraints; connect to the meteorological department's data interface to obtain the distribution of upcoming rainstorm time windows and expected rainfall.

[0126] S142. Obtain information on each road segment in the road network using roadside sensors or urban hydrodynamic models. In various time windows The projected water depth within the area is used as the raw input for calculating functional resilience.

[0127] S15. To constrain vehicle speed during heavy rain in subsequent models, statistical analysis is performed based on historical vehicle operation data during heavy rain:

[0128] S151, Dual-scenario historical speed data acquisition;

[0129] S152. Extract historical vehicle GPS trajectory data from the bus dispatch center database, and combine it with meteorological records to construct two independent road segments. Speed ​​dataset;

[0130] S153. Real-time vehicle operation data is collected during periods of "sunny / rainless" weather to calculate the road segment. Set of average driving speeds under normal weather conditions ;

[0131] S154. Vehicle operation data collected in real time during periods of "heavy rain / extremely heavy rain" weather conditions are used to calculate the road section. Set of average driving speeds during heavy rain ;

[0132] S155. Using the dataset obtained in step

[0051] , calculate the road segments respectively. The velocity constraint boundary parameters are used as input constants for subsequent models:

[0133] S156, Speeding up during heavy rain weather Substitute the values ​​into the quantile function to calculate its 0.90 quantile: This value represents the maximum safe driving speed a vehicle can reach in a flooded environment. During model solving, the planned speed of any vehicle must not exceed this value to ensure safety.

[0134] S157, Take the speed of heavy rain. And calculate its 0.10 quantile: This value represents the minimum effective speed required for a vehicle to maintain normal operation in heavy rain conditions.

[0135] S16. Addressing the physical characteristics of increased driving resistance and energy consumption in electric buses due to flooded roads caused by heavy rain, an energy consumption correction coefficient is constructed using historical battery management system data. The specific process is as follows:

[0136] S161. Initialization of basic energy consumption parameters:

[0137] S162, Define the unit electricity price Unit: Yuan / kWh, used as the economic conversion factor for calculating vehicle energy consumption costs in subsequent models;

[0138] S163, Fitted road section resilience-energy consumption mapping coefficient;

[0139] S164. To accurately calculate the energy consumption growth pattern under waterlogged conditions, a linear regression model was trained on historical data. The specific calculation steps are as follows:

[0140] (1) Data preprocessing and sample construction: Extract several sets of vehicle operation samples during historical rainstorms from the database. Obtain the actual total energy consumption and travel distance of the trip, and calculate the actual energy consumption per unit mileage. Unit: kilowatt-hours per kilometer; Meanwhile, the basic energy consumption per unit journey, defined in scheduling step S125. As a benchmark;

[0141] (2) Constructing the regression equation: With the relative increase in unit energy consumption as the dependent variable and the road section resilience loss as the independent variable, the linear relationship is constructed as follows: ;

[0142] (3) Least squares method: The goal is to minimize the sum of squared errors, i.e., to eliminate... The influence of all sample data is used to calculate the coefficients. The optimal estimate: .

[0143] S2. Based on the real-time meteorological data, road section water accumulation information, and vehicle speeds before and after the rainstorm, calculate the structural resilience and functional resilience of each road section, and use the entropy weight method to obtain the comprehensive resilience of each road section.

[0144] S21. Calculate the structural resilience of each road segment, that is, based on the road network topology data, calculate the degree centrality of each road segment in the road network to assess its core position in the topology, calculate the locality to assess the road network's fault tolerance capability after a road segment failure, and calculate the clustering coefficient to assess the path redundancy of the area where the road segment is located.

[0145] First, the road network topology map constructed in step S111 is... The specific process of converting it into matrix form is as follows:

[0146] S211. Constructing the adjacency matrix: Define the adjacency matrix of the road network. ,in The total number of nodes; if nodes With nodes There are directly connected road sections. ,but ;otherwise, ;

[0147] S212. Calculate topological indices based on matrices: using the aforementioned adjacency matrix Based on relevant algorithms, the following three indicators were selected for quantitative evaluation.

[0148] Then, the topological index is calculated based on the matrix, as follows:

[0149] S213. Computational Degree Centrality: This indicator assesses the hub-like nature of a road segment in network connectivity. For any road segment... Connecting nodes and Calculate the degree centrality of each road segment;

[0150] S214. Calculate Local Efficiency: This indicator assesses whether the communication efficiency of the surrounding local network remains good after a road segment fails. Calculate the local efficiency of the road network;

[0151] S215. Calculate the clustering coefficient: This indicator assesses the ability of a road segment's area to form a closed loop, reflecting the redundancy of the path. Calculate the clustering coefficient of the road segment;

[0152] Finally, the above indicators will be used for subsequent comprehensive resilience calculations.

[0153] S22. Calculate the functional resilience of each road segment, that is, based on real-time rainstorm data, monitor the evolution of the traffic performance of the road segment under the impact of rainstorm, construct a resilience triangle model, and quantitatively evaluate the real-time service efficiency loss of the road segment in the waterlogged environment.

[0154] S23. Calculate the comprehensive resilience based on structural resilience and functional resilience, that is, use the degree centrality, local efficiency, clustering coefficient and resilience triangle area as evaluation indicators, and weighted aggregate to obtain the comprehensive resilience index of each road section under the current rainstorm environment.

[0155] S3. Construct a nonlinear integer programming model with the objective of minimizing the sum of vehicle operating costs, passenger waiting time costs, system penalty costs, and electricity consumption costs. The constructed nonlinear integer programming model is as follows:

[0156]

[0157] In the formula, the first term represents the time window. Passenger waiting time costs within the premises The overall objective function; This represents the set of all time windows, dividing continuous time into time windows of equal length. This is a collection of all road segments in the area. This represents the cost per unit of waiting time for passengers. Indicates time window Inner section The number of newly added passengers, Indicates time window Inner section The number of passengers who were not served. This represents the duration of a time window. The second term in the formula represents the previous time window. The waiting time cost for unserved passengers This indicates the first time window. This indicates that the first time window is excluded from the set of all time windows. The third term in the formula represents the travel time cost for a passenger from the origin to the destination. A collection of all modular vehicles; Indicates time window Inner vehicle Passing through the section The actual time Modular vehicles The unit time operating cost. The fourth term in the formula represents the startup cost of the modular vehicle. This refers to a modular vehicle consisting of a modular carriage. Fixed startup costs for vehicle departure; Indicates by Modular vehicles composed of carriages In the time window Whether the internal network is scheduled to enter the road network, a value of 1 indicates that it is... Modular vehicles composed of carriages In the time window If the value is 0, it indicates that the network is being dispatched internally. Modular vehicles composed of carriages In the time window It was not dispatched into the road network. The index represents the number of carriages. The fifth term in the formula represents the cost of the modular vehicle's travel route. For the set of the number of carriages, Modular vehicles The unit operating cost Indicates by Modular vehicles composed of carriages In the time window Is the road section within the vehicle's driving route? A value of 1 indicates Modular vehicles composed of carriages In the time window The section of road that was driven inside , 0 indicates Modular vehicles composed of carriages In the time window Unused road sections ; Indicates road segment The length of the term. The sixth term in the formula represents the situation where the penalty waiting time significantly exceeds the limit. This represents the unit penalty cost for passengers waiting longer than the maximum allowed waiting time. Indicates time window Inner section The number of passengers exceeding the maximum allowed waiting time. The seventh term in the formula represents the penalty cost for passengers stranded on the last train. It is an infinitely large positive number. Indicates the last time window Inner section The number of passengers who have not been served. The eighth item in the formula represents the penalty for passengers who have requests but the system fails to dispatch a vehicle. Indicates the penalty coefficient for passengers who are not served; Indicates time window Inner section Whether passenger travel demand is responded to by the system is indicated by a value of 1, which means that demand exists on the road segment and has been met, and a value of 0, which means that demand exists on the road segment but no vehicle has been assigned. The ninth term in the formula represents the penalty cost for violating the principle of prioritizing service for low-resilience road segments under heavy rain conditions. This represents the penalty coefficient for not prioritizing service to low-resilience road sections. Indicates time window Within the formula, the difference in service levels between high-resilience road sections and low-resilience road sections is used to quantify the deviation of the system from the "low-resilience road section priority principle" when allocating resources. The tenth term in the formula represents the cost of electricity consumption by the modular vehicle during operation. This indicates the unit price of electricity. Indicates time window Internally Vehicles composed of carriages On the road section The amount of electricity consumed during driving; Indicates by Modular vehicles composed of carriages In the time window Does it stop and serve the road section? A value of 1 indicates that it is generated by Modular vehicles composed of carriages In the time window Internal parking and service sections A value of 0 indicates that... Modular vehicles composed of carriages In the time window There are no stops or service areas within the area. .

[0158] S4. Construct a constraint system, including passenger demand response constraints, modular bus dynamic formation consistency constraints, environmental adaptive spatiotemporal constraints, and energy endurance safety constraints, to ensure the feasibility of the scheduling scheme in the spatiotemporal, capacity, and energy dimensions. The constraint system includes:

[0159] (1) Constructing passenger demand response constraints. The passenger demand response constraints include demand coverage and service matching constraints, vehicle passenger capacity constraints, capacity demand matching constraints, passenger number conservation constraints, maximum passenger waiting time constraints, and overdue passenger quantification constraints.

[0160] (2) Constructing consistency constraints for modular bus dynamic formation. The consistency constraints for modular bus dynamic formation include the upper limit constraint on the number of coupled carriages, the number of coupling and decoupling times and prerequisite constraints, the single coupling constraint of a single carriage, and the carriage state continuity constraint.

[0161] (3) Constructing environmental adaptive spatiotemporal constraints. The environmental adaptive spatiotemporal constraints include road segment resilience-based travel time constraints, maximum number of departures within the scheduling cycle constraints, safe interval constraints between adjacent vehicle departures, vehicle node arrival time constraints, and upper and lower bound constraints on road segment safe speeds;

[0162] (4) Constructing energy range safety constraints. The energy range safety constraints include vehicle remaining power state transition constraints, minimum safe power constraints throughout operation, range constraints for a single charging cycle, and power reserve constraints for returning to the site after the mission; the vehicle remaining power state transition constraints introduce a rainstorm energy consumption correction coefficient; the rainstorm energy consumption correction coefficient is obtained by linear regression fitting based on road section resilience and historical energy consumption data.

[0163] The process of step S4 specifically includes:

[0164] S41. Construct passenger demand response constraints. These constraints include demand coverage and service matching constraints, vehicle passenger capacity constraints, capacity-demand matching constraints, passenger quantity conservation constraints, maximum passenger waiting time constraints, and excess passenger quantification constraints. The specific steps for constructing these passenger demand response constraints are as follows:

[0165] S411. Construct demand coverage and service matching constraints to ensure that road segments with passenger demand are covered by at least one modular vehicle. Specific constraints are as follows:

[0166] Constraint 1 ,

[0167] in, Indicates time window Inner section Is there passenger demand? A value of 1 indicates passenger demand, otherwise there is no passenger demand. Constraint 1 represents the service coverage constraint, which specifies the necessity of the service, meaning that in the current time and space, the system must access all available vehicles. and all grouping forms In this process, at least one modular bus should be dispatched to stop on the section of road to prevent situations where passengers have needs but no bus is available.

[0168] S412, Constructing Modular Vehicles in Arbitrary Spacetime The number of passengers must not exceed the actual total passenger capacity of the modular vehicle, as constrained as follows:

[0169] Constraint 2 ,

[0170] in, Indicates by Vehicle composed of carriages In the time window Driving section The actual number of passengers at that time This indicates the maximum passenger capacity of a single modular carriage. This constraint mandates that at any time and on any road segment, the total number of passengers inside the modular vehicle must not exceed the current physical total capacity, fundamentally eliminating overloading and ensuring operational safety.

[0171] S413, Modular Vehicle Construction The carrying capacity should meet the actual needs of passengers, subject to the following constraints:

[0172] Constraint 3 ,

[0173] in, This represents the passenger demand amplification factor under severe weather conditions. This constraint forces the scheduling model to reserve additional capacity redundancy during the planning stage, preventing severe passenger congestion and station overcrowding caused by dispatching vehicles only according to normal weather demand, thereby significantly improving the system's robustness under extreme weather conditions.

[0174] S414. Construct the passenger quantity conservation constraint as follows:

[0175] Constraint 4 ,

[0176] Constraint 5 ;

[0177] Constraint 4 is used to calculate the start of the scheduling cycle, i.e., the first time window. The number of passengers stranded, since there are no passengers left over from the previous moment, the initial stranded number. Based solely on initial travel demand The number of passengers is determined by subtracting the capacity invested in the current period. The upper constraint of the fifth equation constructs the time recursive relationship of the number of passengers stranded, following the law of conservation of flow. The inequality of the lower constraint of the fifth equation ensures that the physical meaning of the model holds, that is, the number of passengers stranded at the station cannot be negative. This forces the model to assume that the number of passengers carried by the vehicle cannot exceed the actual total number of people on the platform when calculating, thus ensuring the logical correctness of the numerical calculation.

[0178] S415. The constraint that passenger waiting time shall not exceed the maximum allowable waiting time is as follows:

[0179] Constraint 6 ,

[0180] in, Indicates the passenger's waiting time. This indicates the maximum allowed waiting time for passengers. This indicates whether the passenger waiting time exceeds the maximum allowed waiting time. This constraint uses the Big M method logic, where the actual passenger waiting time... Exceeding the maximum allowed duration When the inequality forces 0-1 state variables... The value is 1. This variable will directly activate the penalty term in the objective function of step S3, thereby guiding the scheduling scheme to minimize passenger waiting time.

[0181] S416. Based on sliding time window logic, dynamically identify and quantify the number of passengers whose waiting time exceeds the maximum allowed waiting time, as detailed below:

[0182] Constraint 7 ,

[0183] in, This indicates the number of time windows corresponding to the maximum allowed waiting time. This constraint defines the number of passengers who exceed the timeout limit. The calculation logic is as follows: First, the maximum allowed waiting time is converted into the corresponding number of time windows. Then, the current total number of stranded people is calculated. In, deduct the time allowed during the waiting window. The total number of newly arrived passengers.

[0184] S42. Construct consistency constraints for modular bus dynamic formation. These constraints include the upper limit constraint on the number of coupled carriages, the number of coupling / decoupling operations and prerequisites, single-carriage single-coupling constraints, and carriage state continuity constraints. The specific steps for constructing these consistency constraints are as follows:

[0185] S421, Modular Vehicle Construction The coupling length is not subject to the constraint that the maximum number of carriages shall not exceed the following:

[0186] Constraint 8 ,

[0187] in, Modular carriage In the time window Does the interior belong to modular vehicles? , Indicates the carriage In the time window Road section Is it coupled to the vehicle? middle, Indicates the carriage In the time window Road section Whether inside is from the vehicle Decoupling in the middle, This indicates the maximum number of wagons allowed to form a modular fleet. This constraint enforces the modularity of the vehicles. The actual number of carriages after dynamic formation will never exceed the physical safety limit. .

[0188] S422. The total number of coupling and decoupling operations for the modular vehicle and the preconditions and constraints are as follows:

[0189] Constraint 9 ,

[0190] Constraint 10 ,

[0191] Constraint 11 .

[0192] The inequality in constraint nine restricts the condition for any carriage unit. At the same time and place, the total number of times a carriage participates in coupling and decoupling operations must not exceed once. This ensures that the carriage cannot be split, meaning it cannot connect two carriages simultaneously, nor can it perform both connection and decoupling operations at the same time. Constraints 10 and 11 define the prerequisites for coupling and decoupling operations. Constraint 10 states that coupling and decoupling operations only occur when the carriage... The vehicle did not belong to it at the previous moment. Coupling operations are only allowed when [the specific conditions are met].

[0193] S423. The following constraints prohibit multiple couplings within the same time window for a single carriage:

[0194] Constraint 12 ,

[0195] Constraint 13 .

[0196] Constraint 12 represents any carriage Only one modular vehicle can be used at any given time. To perform coupling operations and prevent physical conflicts, constraint 13 represents any carriage. It can belong to at most one modular vehicle at any given time. This means that a carriage cannot serve two different lines or two different trains at the same time, ensuring the mathematical uniqueness of carriage ownership.

[0197] S424, Construction of the Carriage The state continuity constraints are as follows:

[0198] Constraint 14 .

[0199] This equation constructs the carriage. Modular vehicles The dynamic evolution logic of ownership relationships ensures that the ownership status of the carriage changes continuously over time and with operating instructions, preventing sudden changes in status without any operation.

[0200] S43. Constructing environmentally adaptive spatiotemporal constraints. These constraints include travel time constraints based on road segment resilience, maximum number of departures within a scheduling cycle, safe interval constraints between adjacent vehicle departures, vehicle node arrival sequence constraints, and upper and lower bound constraints on road segment safe speeds. The specific steps for constructing these environmentally adaptive spatiotemporal constraints are as follows:

[0201] S431. The adaptive travel time mapping constraints for the construction environment are as follows:

[0202] Constraint 15 ,

[0203] Constraint 16 ,

[0204] Constraint 17 ,

[0205] Constraint 18 ,

[0206] in, Indicates time window Vehicle passage sections in severe weather such as torrential rain Time, Indicates the road sections where vehicles pass under normal weather conditions within the time window. The lower quantile of velocity, Indicates time window Vehicle passage sections under normal weather conditions Time, Indicates time window Vehicles passing through sections of road during severe rainstorms The higher quantile of the velocity, Indicates road segment The normalized value of resilience, Indicates time window Inner section The resilience index, This represents the minimum resilience value among all road segments. This represents the maximum resilience value among all road segments. Constraints 15 and 16 define the travel time boundaries; Constraint 18 utilizes the resilience loss of road segments. As interpolation weights, the actual travel time of vehicles is dynamically calculated. The deeper the water accumulation on a road section, the more resilient it becomes. The lower the weight The larger the value, the closer the actual travel time will be to the maximum limit. It simulates the physical phenomenon of vehicles being forced to slow down in heavy rain.

[0207] S432, the priority service constraints for constructing low-strength road sections are as follows:

[0208] Constraint 19 ,

[0209] in, This indicates road sections with resilience below the resilience threshold. This indicates road sections with resilience levels higher than or equal to the resilience threshold. Indicates time window Inner section Whether passage is permitted, with a value of 1 indicating passage is permitted and 0 indicating passage is prohibited.

[0210] The first equation of Constraint 19 constructs a relaxed constraint that allows for service defaults; the second equation of Constraint 19 defines the service surplus level of a road segment, and then the third equation compares low-resilience road segments through inequalities. High-resilience road sections Service level, variables This quantifies the degree of uneven resource allocation. If the system tends to accumulate capacity on high-resilience road sections while neglecting low-resilience road sections, then... The value will be forced to increase, resulting in huge penalty costs; this constraint is on the premise that traffic is allowed on the road segment. In such cases, priority should be given to allocating transportation resources to sections of roads with severe flooding and low resilience to ensure fair travel in vulnerable areas.

[0211] S433. The constraint that the number of times all modular vehicles added to the road network within any time window does not exceed the maximum allowed number of departures is as follows:

[0212] Constraint 20 ,

[0213] in, Indicates time window The maximum number of departures allowed within a given time window. This constraint defines the upper limit of the system's departure flow, specifying the maximum number of departures allowed within any given time window. Within that time period, the total number of modular vehicles in a specific formation that are dispatched into the network must not exceed the maximum departure threshold allowed for that time period. .

[0214] S434, Construction of Vehicles Reaching the node and leaving the node The timing and departure interval specifications are constrained as follows:

[0215] Constraint 21 ,

[0216] Constraint 22 ,

[0217] Constraint 23 ,

[0218] Constraint 24 ,

[0219] Constraint 25 ,

[0220] in, Nodes representing road segments Indicates vehicle Reaching the node Time window index, Indicates at node Time window Modular buses Whether the bus has departed is indicated by a value of 1 (1 indicates the bus has departed) and 0 (0 indicates the bus has not departed). Indicates vehicle Leave node Time window index, Indicates the road section through which modular vehicles pass. The number of time windows that need to be spanned. This represents the minimum time window interval between adjacent vehicles originating from the starting node. Indicates vehicle Index of the time window leaving the starting node. This represents the minimum time window interval between adjacent vehicles originating from the starting node. Constraints 21 to 23 form the time chain of vehicle operation; Constraints 24 and 25 form the inequalities used to regulate the operation order of the convoy.

[0221] S435. Construct a safe speed range constraint for vehicles based on statistical quantiles to limit the speed boundary of modular vehicles in heavy rain conditions, as follows:

[0222] Constraint 26 ,

[0223] Constraint 27 ,

[0224] Constraint 28 ,

[0225] Constraint 29 ,

[0226] in, This indicates the time window after considering road segment resilience indicators. Inner vehicle Passing through the section speed, Indicates road segment Maximum safe speed under severe weather conditions such as heavy rain. It is a quantile function. Indicates road segment Minimum safe speed in severe weather conditions such as heavy rain.

[0227] Constraint 26 calculates the actual speed of the modular vehicle, while constraints 27 and 28 use statistical quantile methods to process vehicle operation data under heavy rain conditions.

[0228] S44. Construct energy-range safety constraints. These constraints include constraints on vehicle remaining battery power state transition, minimum safe battery power throughout operation, range per charging cycle, and reserve battery power for return after mission completion. The vehicle remaining battery power state transition constraint incorporates a rainstorm energy consumption correction coefficient. This rainstorm energy consumption correction coefficient is obtained through linear regression fitting based on road resilience and historical energy consumption data. The specific steps for constructing these energy-range safety constraints are as follows:

[0229] S441. The state transition constraints for the remaining battery power of a modular vehicle, considering the rainstorm energy consumption correction coefficient, are as follows:

[0230] Constraint 30 ,

[0231] Constraint 31 ,

[0232] Constraint 32 ,

[0233] in, Modular vehicles In the time window The initial remaining battery power, Indicates time window Internally Vehicle composed of carriages On the road section The equation defines the recursive conservation relationship of battery energy over time: the energy consumed by the vehicle at the next moment. The remaining battery power is exactly equal to the current moment. The amount of electricity consumed minus the total energy consumption generated by all driving tasks at the current moment; constraint 31 reflects that energy consumption increases with the increase of the number of carriages and the number of passengers in the carriage at real time; constraint 32 defines The coefficients establish a mapping chain between road network resilience, water accumulation resistance, and additional energy consumption. When the road segment resilience... When reduced, the correction factor The increase leads to a higher calculated power consumption. The increase is significant, thus forcing the model to reserve more power when planning routes.

[0234] S442. The minimum safe power supply constraints for the entire operation of modular vehicles are as follows: Constraint 33. ,

[0235] Constraint 34 ,

[0236] in, This indicates the minimum safe electrical threshold allowed for the operation of modular vehicles. This indicates the battery level at the start of the first time window. Modular vehicles Initial battery level.

[0237] Inequality 33 imposes a hard constraint on the battery discharge depth, mandating that the vehicle's remaining charge remain above a minimum threshold throughout the entire operational process. Constraint 34 defines the vehicle battery status at the start of the scheduling cycle, setting the initial battery level of all vehicles to a known value, such as leaving the depot fully charged, to provide a mathematical benchmark for the recursive calculation of battery levels in subsequent time windows.

[0238] S443. The feasibility constraints for constructing the vehicle's full-range driving capability based on a single charging cycle are as follows:

[0239] Constraint 35 ;

[0240] The left side of the inequality is accumulated with vehicles. The cumulative total energy consumption of all stops and trips throughout the entire scheduling cycle is defined on the right side of the inequality, which represents the upper limit of the effective available power, i.e., the initial full power. Excluding minimum safety reserves The net value after the constraint requires that the model's task allocation scheme must be within the physical range of the battery to ensure that the vehicle can run the entire distance without touching the safety red line.

[0241] S444. The return-to-base power reserve constraint after the completion of the modular vehicle construction mission is as follows:

[0242] Constraint 36 ,

[0243] Constraint 37 ,

[0244] in, Modular vehicles The battery level in the last time window This indicates the minimum electrical reserve required for a modular vehicle to return to the depot after completing its final mission. This represents the basic energy consumption per unit mileage for a single modular carriage. This indicates the number of carriages in the modular vehicle after the mission is completed. This indicates the energy consumption per unit passenger load. This indicates the distance of the modular vehicle from the last stop to the bus depot. This represents the energy consumption correction factor for heavy rain.

[0245] The inequality in constraint 36 mandates that the vehicle must [do something] at the end of its operation. Remaining battery power The required reserve power must be greater than or equal to the theoretically calculated minimum reserve power required for return. Constraint 37 quantifies the specific energy consumption requirements of the return trip, accurately reflecting the actual working conditions of empty vehicles returning to the depot after the end of operation. The calculation still incorporates a rainstorm energy consumption correction factor. This indicates that even if the return trip is empty, the model will reserve additional energy redundancy based on the water accumulation on the road section to ensure safe return to the depot in severe weather.

[0246] S5. Solve the model to obtain the optimal vehicle driving path, modular carriage quantity configuration, and coupling / decoupling nodes. Ensure that the optimal driving path, modular carriage quantity configuration, and coupling / decoupling nodes are obtained. Then, distribute the solution to the modular bus central control system to realize dynamic scheduling and coupled control of modular vehicles. The specific process is as follows:

[0247] S51. Model Instantiation and Solver Environment Construction: This involves transforming the multi-source heterogeneous data collected in the preceding steps into specific input parameters for the mathematical model, and configuring the solver environment. Specifically, this includes:

[0248] S511. Parameter calibration and assignment: Passenger demand, road network data, resilience index and energy consumption correction coefficient obtained from steps S1-S2 are used as input variables and substituted into the model constructed in steps S3-S4.

[0249] S512, Road Network Topology Matrix Construction: Construct the adjacency matrix and distance matrix based on the road network data. Use a commercial solver (such as Gurobi) or heuristic algorithm to solve the nonlinear integer programming model.

[0250] S52. Optimal Solution Decoding and Generation: Map the decision variables obtained from the solution to a physical scheduling scheme, including the specific driving routes of each vehicle, the number of carriages in each carriage group, and the specific nodes and times of coupling / decoupling.

[0251] S53. Closed-loop control execution: The generated scheduling plan is sent to the bus central control system through the communication network, and the system performs dynamic scheduling and formation control of vehicles on the road.

[0252] The above is an exemplary description of the invention. Obviously, the specific implementation of the invention is not limited to the above-described manner. Any non-substantial improvement made using the inventive concept and technical solution of the invention, or the direct application of the inventive concept and technical solution to other situations without modification, is within the protection scope of the invention.

Claims

1. A demand-responsive modular public transport route optimization method for rainstorm environments, characterized in that, Includes the following steps: S1. Collect passenger demand data, meteorological data, road network topology data, road section water accumulation information, and vehicle speeds before and after rainstorms. The passenger demand data includes: the passenger's origin and destination, the number of passengers, and the estimated time window for passengers to arrive at the origin. The meteorological data includes meteorological forecast data and real-time meteorological data; the meteorological forecast data includes: the time window of impending heavy rain, the area of ​​impending heavy rain, the duration of heavy rain, the expected rainfall, and the predicted evolution of water depth; the real-time meteorological data includes: rainfall per unit time and the real-time water depth of each road section; The road network topology data includes the physical length of each road segment, node data in the road network, and road segment connectivity; S2. Based on the meteorological data, road water accumulation information and vehicle speed, calculate the structural toughness and functional toughness of each road segment, and use the entropy weight method to obtain the comprehensive toughness; at the same time, construct an energy consumption correction model under rainstorm environment based on real-time meteorological data and vehicle operating conditions, and obtain the energy consumption correction coefficient of each road segment. S3. Construct a nonlinear integer programming model with the objective of minimizing the sum of vehicle operating costs, passenger waiting time costs, system penalty costs, and electricity consumption costs; S4. Construct a constraint system, including passenger demand response constraints, modular bus dynamic formation consistency constraints, environmental adaptive spatiotemporal constraints, and energy and range safety constraints. S5. Solve the nonlinear integer programming model to obtain the vehicle driving path, carriage configuration and coupling / decoupling nodes, and use them for dynamic scheduling and control of modular buses.

2. The demand-responsive modular public transport route optimization method for rainstorm environments according to claim 1, characterized in that, In step S4, the constraint system includes: Passenger demand response constraints include: a segment skipping rule based on real-time passenger flow to determine whether to stop on a segment, a low-resilience segment priority service principle based on the comprehensive resilience weight of the segment, and a timeout demand quantification rule based on the maximum allowable waiting time. The consistency constraints of the dynamic formation of modular buses include the uniqueness constraint of the coupling / decoupling state of the carriages in the same time and space, the spatiotemporal uniqueness and state continuity constraint of the ownership relationship of a single carriage, and the upper limit of the maximum number of carriages allowed in the operation of modular vehicles. Environmental adaptive spatiotemporal constraints include travel time constraints based on road segment resilience, maximum number of departures within the scheduling cycle, safe interval constraints between departures of adjacent vehicles, arrival sequence constraints of vehicle nodes, and upper and lower bound constraints of safe speed for road segments. Energy endurance safety constraints include capacity constraints (passenger capacity not exceeding the rated capacity of the train), energy state transition constraints, minimum safe energy constraints throughout the process, and minimum energy reserve constraints for returning to the depot.

3. The demand-responsive modular public transport route optimization method for rainstorm environments according to claim 1, characterized in that, Step S2 is as follows: S21. Calculate the structural resilience of each road segment, that is, based on the road network topology data, calculate the degree centrality of each road segment in the road network to evaluate its core position in the topology, calculate the local to evaluate the road network fault tolerance after the road segment failure, and calculate the clustering coefficient to evaluate the path redundancy of the area where the road segment is located. S22. Calculate the functional resilience of each road segment, that is, based on real-time rainstorm data, monitor the evolution of the traffic performance of the road segment under the impact of rainstorm, construct a resilience triangle model, and quantitatively evaluate the real-time service efficiency loss of the road segment in the waterlogged environment by calculating the area of ​​the triangle formed by the performance drop degree and recovery time. S23. Calculate the comprehensive resilience based on structural resilience and functional resilience, that is, use the degree centrality, local efficiency, clustering coefficient and resilience triangle area as evaluation indicators, objectively determine the weight of each indicator through entropy weight method, and weighted aggregate to obtain the comprehensive resilience index of each road section under the current rainstorm environment.

4. The demand-responsive modular public transport route optimization method for rainstorm environments according to claim 1, characterized in that, The nonlinear integer programming model constructed in step S3 is as follows: ， In the formula, The overall objective function; This represents the set of all time windows, dividing continuous time into time windows of equal length. This is a collection of all road segments in the area. This represents the cost per unit of waiting time for passengers. Indicates time window Inner section The number of newly added passengers, Indicates time window Inner section The number of passengers who were not served. The duration of a time window; This indicates the first time window. This means removing the first time window from the set of all time windows; A collection of all modular vehicles; Indicates time window Inner vehicle Passing through the section The actual time Modular vehicles The unit time operating cost, This refers to a modular vehicle consisting of a modular carriage. Fixed startup costs for vehicle departure; Indicates by Modular vehicles composed of carriages In the time window Whether the internal network is scheduled to enter the road network, a value of 1 indicates that it is... Modular vehicles composed of carriages In the time window If the value is 0, it indicates that the network is being dispatched internally. Modular vehicles composed of carriages In the time window It was not dispatched into the road network. An index representing the number of carriages; For the set of the number of carriages, Modular vehicles The unit operating cost Indicates by Modular vehicles composed of carriages In the time window Is the road section within the vehicle's driving route? A value of 1 indicates Modular vehicles composed of carriages In the time window The section of road that was driven inside , 0 indicates Modular vehicles composed of carriages In the time window Unused road sections ; Indicates road segment Length; This represents the unit penalty cost for passengers waiting longer than the maximum allowed waiting time. Indicates time window Inner section The number of passengers exceeding the maximum allowed waiting time; It is an infinitely large positive number. Indicates the last time window Inner section The number of passengers who were not served; Indicates the penalty coefficient for passengers who are not served; Indicates time window Inner section Whether the passenger's travel demand has been responded to by the system. A value of 1 indicates that there is demand on the road segment and it has been met, while a value of 0 indicates that there is demand on the road segment but no vehicle has been assigned. This represents the penalty coefficient for not prioritizing service to low-resilience road sections. Indicates time window Within this context, the difference in service levels between high-resilience road segments and low-resilience road segments is used to quantify the deviation of the system from the "low-resilience road segment priority principle" when allocating resources. This indicates the unit price of electricity. Indicates time window Internally Vehicles composed of carriages On the road section The amount of electricity consumed during driving; Indicates by Modular vehicles composed of carriages In the time window Does it stop and serve the road section? A value of 1 indicates that it is generated by Modular vehicles composed of carriages In the time window Internal parking and service sections A value of 0 indicates that... Modular vehicles composed of carriages In the time window There are no stops or service areas within the area. .

5. The demand-responsive modular public transport route optimization method for rainstorm environments according to claim 1, characterized in that, Step S4 specifically includes: S41. Construct passenger demand response constraints; the passenger demand response constraints include demand coverage and service matching constraints, vehicle passenger capacity constraints, capacity demand matching constraints, passenger number conservation constraints, maximum passenger waiting time constraints, and overdue passenger quantification constraints. S42. Construct a modular bus dynamic formation consistency constraint; the modular bus dynamic formation consistency constraint includes the upper limit constraint on the number of coupled carriages, the number of coupling and decoupling times and prerequisite constraints, the single coupling constraint of a single carriage, and the carriage state continuity constraint. S43. Construct environmental adaptive spatiotemporal constraints; the environmental adaptive spatiotemporal constraints include travel time constraints based on road segment resilience, maximum number of departures within the scheduling cycle constraints, safe interval constraints between departures of adjacent vehicles, arrival sequence constraints of vehicle nodes, and upper and lower bound constraints of safe speed for road segments. S44. Construct energy range safety constraints; the energy range safety constraints include vehicle remaining power state transition constraints, minimum safe power constraints throughout operation, range constraints for a single charging cycle, and power reserve constraints for returning to base after the mission; the vehicle remaining power state transition constraints introduce a rainstorm energy consumption correction coefficient; the rainstorm energy consumption correction coefficient is obtained by linear regression fitting based on road resilience and historical energy consumption data.

6. The demand-responsive modular public transport route optimization method for rainstorm environments according to claim 5, characterized in that, In step S41, the construction of passenger demand response constraints follows these steps: S411. Construct demand coverage and service matching constraints to ensure that road segments with passenger demand are covered by at least one modular vehicle. Specific constraints are as follows: Constraint 1 , in, Indicates time window Inner section Is there passenger demand? A value of 1 indicates that there is passenger demand, otherwise there is no passenger demand. S412, Constructing Modular Vehicles in Arbitrary Spacetime The number of passengers must not exceed the actual total passenger capacity of the modular vehicle, as constrained as follows: Constraint 2 , in, Indicates by Vehicle composed of carriages In the time window Driving section The actual number of passengers at that time This indicates the maximum passenger capacity of a single modular carriage; S413, Modular Vehicle Construction The carrying capacity should meet the actual needs of passengers, subject to the following constraints: Constraint 3 , in, This indicates the amplification factor of passenger demand under severe weather conditions; S414. Construct the passenger quantity conservation constraint as follows: Constraint 4 , Constraint 5 ; S415. The constraint that passenger waiting time shall not exceed the maximum allowable waiting time is as follows: Constraint 6 , in, Indicates the passenger's waiting time. This indicates the maximum allowed waiting time for passengers. This indicates whether the passenger's waiting time exceeds the maximum allowed waiting time; S416. Based on sliding time window logic, dynamically identify and quantify the number of passengers whose waiting time exceeds the maximum allowed waiting time, as detailed below: Constraint 7 , in, This indicates the number of time windows corresponding to the maximum allowed waiting time.

7. The demand-responsive modular public transport route optimization method for rainstorm environments according to claim 6, characterized in that, In step S42, the construction of consistency constraints for modular bus dynamic formation follows these steps: S421, Modular Vehicle Construction The coupling length is not subject to the constraint that the maximum number of carriages shall not exceed the following: Constraint 8 , in, Modular carriage In the time window Does the interior belong to modular vehicles? , Indicates the carriage In the time window Road section Is it coupled to the vehicle? middle, Indicates the carriage In the time window Road section Whether inside is from the vehicle Decoupling in the middle, Indicates the maximum number of carriages allowed to form a modular convoy; S422. The total number of coupling and decoupling operations for the modular vehicle and the preconditions and constraints are as follows: Constraint 9 , Constraint 10 , Constraint 11 , S423. The following constraints prohibit multiple couplings within the same time window for a single carriage: Constraint 12 , Constraint 13 ; S424, Construction of the Carriage The state continuity constraints are as follows: Constraint 14 .

8. The demand-responsive modular public transport route optimization method for rainstorm environments according to claim 7, characterized in that, In step S43, the construction of the environment-adaptive spatiotemporal operational constraints is carried out in the following steps: S431. The adaptive travel time mapping constraints for the construction environment are as follows: Constraint 15 , Constraint 16 , Constraint 17 , Constraint 18 , in, Indicates time window Vehicle passage sections in severe weather such as torrential rain Time, Indicates the road sections that vehicles pass through under normal weather conditions within the time window. The lower quantile of velocity, Indicates time window Vehicle passage sections under normal weather conditions Time, Indicates time window Vehicles passing through sections of road during severe rainstorms The higher quantile of the velocity, Indicates road segment The normalized value of resilience, Indicates time window Inner section The resilience index, This represents the minimum resilience value among all road segments. This represents the maximum resilience value across all road segments; S432, the priority service constraints for constructing low-strength road sections are as follows: Constraint 19 , in, This indicates road sections with resilience below the resilience threshold. This indicates road sections with resilience levels higher than or equal to the resilience threshold. Indicates time window Inner section Whether passage is permitted; a value of 1 indicates passage is permitted, and a value of 0 indicates passage is prohibited. S433. The constraint that the number of times all modular vehicles added to the road network within any time window does not exceed the maximum allowed number of departures is as follows: Constraint 20 , in, Indicates time window The maximum number of trains allowed to depart within the specified area; S434, Construction of Vehicles Reaching the node and leaving the node The timing and departure interval specifications are constrained as follows: Constraint 21 , Constraint 22 , Constraint 23 , Constraint 24 , Constraint 25 , in, Nodes representing road segments Indicates vehicle Reaching the node Time window index, Indicates at node Time window Modular buses Whether the bus has departed is indicated by a value of 1 (1 indicates the bus has departed) and 0 (0 indicates the bus has not departed). Indicates vehicle Leave node Time window index, Indicates the road section through which modular vehicles pass. The number of time windows that need to be spanned. This represents the minimum time window interval between adjacent vehicles originating from the starting node. Indicates vehicle Index of the time window leaving the starting node. This represents the minimum time window interval between adjacent vehicles originating from the starting node. S435. Construct a safe speed range constraint for vehicles based on statistical quantiles to limit the speed boundary of modular vehicles in heavy rain conditions, as follows: Constraint 26 , Constraint 27 , Constraint 28 , Constraint 29 , in, This indicates the time window after considering road segment resilience indicators. Inner vehicle Passing through the section speed, Indicates road segment Maximum safe speed under severe weather conditions such as heavy rain. It is a quantile function. Indicates road segment Minimum safe speed in severe weather conditions such as heavy rain.

9. A demand-responsive modular public transport route optimization method for rainstorm environments according to claim 8, characterized in that, In step S44, the energy range safety constraints are constructed, and the specific steps are as follows: S441. The state transition constraints for the remaining battery power of a modular vehicle, considering the rainstorm energy consumption correction coefficient, are as follows: Constraint 30 , Constraint 31 , Constraint 32 , in, Modular vehicles In the time window The initial remaining battery power, Indicates time window Internally Vehicle composed of carriages On the road section The amount of electricity consumed during driving; S442. The minimum safe power supply constraints for the entire operation of modular vehicles are as follows: Constraint 33 , Constraint 34 , in, This indicates the minimum safe electrical threshold allowed for the operation of modular vehicles. This indicates the battery level at the start of the first time window. Modular vehicles Initial battery level; S443. The feasibility constraints for constructing the vehicle's full-range driving capability based on a single charging cycle are as follows: Constraint 35 ; S444. The return-to-base power reserve constraint after the completion of the modular vehicle construction mission is as follows: Constraint 36 , Constraint 37 , in, Modular vehicles The battery level in the last time window This indicates the minimum electrical reserve required for a modular vehicle to return to the depot after completing its final mission. This represents the basic energy consumption per unit mileage for a single modular carriage. This indicates the number of carriages in the modular vehicle after the mission is completed. This indicates the energy consumption per unit passenger load. This indicates the distance of the modular vehicle from the last stop to the bus depot. This represents the energy consumption correction factor for heavy rain.

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