Demand response bus scheduling optimization method based on man-vehicle cooperation under time-varying road network

Abstract

The invention discloses a demand response bus scheduling optimization method based on man-vehicle cooperation under a time-varying road network, and the method comprises the following steps: constructing a man-vehicle cooperation scheduling mode after introducing space-time flexibility, obtaining data used for the parameter calibration of a utility function, and evaluating the structure of the utility function, so as to support the decision of the man-vehicle cooperation scheduling mode; the method comprises the following steps: in a human-vehicle cooperative scheduling mode, constructing a demand response bus scheduling model, and converting a demand response bus scheduling optimization problem into a plurality of constraint sub-problems based on a rolling time domain optimization framework; establishing an objective function of a demand response bus scheduling model of human-vehicle cooperation, determining constraint conditions of the demand response bus scheduling model, and defining decision variables of the demand response bus scheduling model; and designing an improved dynamic multi-objective optimization algorithm based on a memory search strategy, and solving a demand response bus scheduling optimization problem of human-vehicle cooperation by adopting a local search and elite selection strategy. Based on a man-vehicle cooperative scheduling mode, cost reduction and benefit increase are realized for demand response buses.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of demand response bus scheduling, in particular, to a demand response bus scheduling optimization method based on a man-vehicle cooperative scheduling mode. BACKGROUND

[0002] The public transportation system has made remarkable achievements as the main thread of ensuring the healthy development of China's transportation. However, times have changed, and the traditional public transportation is difficult to meet the increasing customized travel demand with the development of economy and society. On the other hand, due to the high threshold for opening routes, it is difficult to radiate the low passenger flow density areas on the edge of urban expansion. Under this background, a new public transportation system that provides on-demand services, demand response bus (DRT), has emerged. Its operating mode is between traditional public transportation and network car-hailing, providing quasi-door-to-door services at a relatively low price, combining flexibility and economy, and effectively making up for the shortcomings of fixed traditional public transportation routes.

[0003] In recent years, various places have been committed to promoting the marketization of demand response buses, but its development still faces severe challenges. The main problems are as follows: First, the traditional scheduling system is mostly based on static or semi-dynamic optimization models, and its path planning is difficult to adapt to the dynamic characteristics of time-varying road networks, resulting in response lag and scheduling distortion. The lack of dynamic response capability leads to vehicle detours, empty driving, and prolonged passenger waiting time, significantly increasing operating costs and weakening service reliability. Second, the existing scheduling mode mostly only focuses on one-way configuration of transport resources. Under this principle, the utilization rate of transport resources is limited by the time and space rigidity of demand, making it difficult to take advantage of the intensification of demand response buses. Although some studies attempt to introduce demand guidance, there is still no applicable systematic mode to effectively integrate the coordination between passenger behavior flexibility and scheduling decisions.

[0004] Thirdly, from the functional positioning, demand response buses fill the service gap in low-density areas, respond to fragmented demand, make up for the lack of flexibility of traditional public transportation, and meet the "differentiated and precise public transportation service" direction proposed in the "National Comprehensive Three-dimensional Transportation Network Planning Outline". As a supplement to "rail" and "regular public transportation" systems, it can theoretically improve the hierarchical level of urban composite public transportation networks, but its economic unsustainability seriously restricts the large-scale promotion. This high-cost rigidity and low-revenue flexibility financial feature leads DRT to fall into the "subsidy-driven" development dilemma, and effective cost reduction and efficiency improvement measures are urgently needed to achieve a self-sufficient and virtuous development model.

[0005] Although the demand-responsive bus operation mode has advantages, it still faces certain challenges in the process of popularization and application. Weak profitability is the main factor restricting the further development of demand-responsive buses. Combined with its operation characteristics, if passengers can be guided to adjust the boarding station or time appropriately to achieve trip integration, the problem can be alleviated to some extent. This supply-demand coordination mechanism that realizes capacity optimization by introducing passenger time-space flexibility is called passenger-vehicle collaborative scheduling. To realize the sustainable development of demand-responsive buses and further improve the comprehensive public transportation system, it is urgent to enrich the theory and technology system of scheduling optimization based on market-oriented operation demand and around cost reduction and efficiency improvement. SUMMARY

[0006] The present application aims to overcome the defects and deficiencies of the prior art, and provides a demand-responsive bus scheduling optimization method based on passenger-vehicle collaboration in a time-varying road network. By considering the properties of the time-varying road network, the scheduling mode is optimized based on the passenger-vehicle collaboration idea under dynamic demand, which reduces the cost of demand-responsive buses and promotes the healthy development of the comprehensive public transportation system.

[0007] To achieve the above-mentioned purpose, the technical solution adopted by the present application is as follows:

[0008] A demand-responsive bus scheduling optimization method based on passenger-vehicle collaboration in a time-varying road network, comprising the following steps:

[0009] S1: After introducing time-space flexibility, a passenger-vehicle collaborative scheduling mode is constructed to obtain data for utility function parameter calibration, evaluate the utility function structure, and support the decision-making of the passenger-vehicle collaborative scheduling mode;

[0010] S2: Under the passenger-vehicle collaborative scheduling mode, a demand-responsive bus scheduling model is constructed, and based on the rolling time domain optimization framework, the demand-responsive bus scheduling optimization problem is converted into multiple constraint sub-problems;

[0011] S3: The objective function of the demand-responsive bus scheduling model based on passenger-vehicle collaboration is established, the constraint conditions of the demand-responsive bus scheduling model are determined, and the decision variables of the demand-responsive bus scheduling model are defined;

[0012] S4: Based on the memory search strategy, an improved dynamic multi-objective optimization algorithm is designed, and local search and elite selection strategies are used to solve the demand-responsive bus scheduling optimization problem based on passenger-vehicle collaboration.

[0013] Further, in step S1, after introducing time-space flexibility, the passenger-vehicle collaborative scheduling mode is constructed, including:

[0014] In the demand side spatiotemporal flexibility, in the demand response bus scheduling, the boarding and alighting station and time window submitted by passengers are taken as an original scheme, a candidate scheme is generated by combining the spatiotemporal flexibility adjustment strategy, the utility levels of the two schemes are compared through an utility function, thereby a feasible option which is not worse than the original scheme in the passenger perspective is screened out, and the person-vehicle collaborative scheduling optimization is carried out accordingly; the utility of the original scheme and the utility of the candidate scheme are obtained; based on the existing subjective cognitive difference and perception uncertainty, a random disturbance term subject to a specific distribution is introduced, and the utility difference of the two schemes is obtained.

[0015] Further, after introducing the spatiotemporal flexibility, the person-vehicle collaborative scheduling mode is constructed, and further comprises:

[0016] In the supply side spatiotemporal flexibility, under the premise of meeting the scheduling task, the vehicle autonomously selects different road sections to avoid congestion according to the current or predicted traffic state, so as to save travel time; the essence is to refine the granularity of scheduling decision, that is, for any pair of stations, the platform no longer presets a unique shortest path, but dynamically selects a path scheme with the shortest predicted travel time in the current period from multiple candidate paths, and expands the scheduling decision to "whether to go from a station to a station through a path";

[0017] The person-vehicle collaborative scheduling mode is proposed, and the decision of the operation party in each time period is obtained.

[0018] Further, in step S1, data used for parameter calibration of the utility function is obtained, and the structure of the utility function is evaluated, comprising:

[0019] By designing a questionnaire based on a simulated situation, high-quality behavior data used for parameter calibration of the utility function is obtained; in order to comprehensively evaluate the fitting effect and behavior recognition ability of the utility function structure, a composite evaluation system including five classical classification indicators is constructed, covering three dimensions of prediction accuracy, discrimination ability and classification balance;

[0020] The accuracy Accuracy represents the proportion of samples predicted correctly by the person-vehicle collaborative scheduling mode in all samples, and measures the overall classification performance;

[0021] The precision Precision represents the proportion of samples actually accepting the candidate scheme in the samples predicted to accept by the person-vehicle collaborative scheduling mode;

[0022] The recall Recall represents the proportion of samples successfully identified by the person-vehicle collaborative scheduling mode in the samples actually accepting the candidate scheme;

[0023] The F1 score F1 Score is the harmonic mean of the precision and the recall, balancing the weights of the two in the performance of the person-vehicle collaborative scheduling mode;

[0024] The area under the curve (AUC) represents the probability that the human-vehicle collaborative scheduling mode will prioritize accepted samples over rejected samples. This indicator is calculated by sorting the samples according to the classification scores output by the human-vehicle collaborative scheduling mode, and then calculating the proportion of all positive and negative sample pairs that are correctly sorted.

[0025] Furthermore, obtaining data for utility function parameter calibration and evaluating the utility function structure also includes:

[0026] In terms of capturing time-varying travel time features, a data-driven historical mean method is adopted as the benchmark prediction strategy for future travel time. That is, for a certain target time, the predicted travel time is the average travel time observed in the past few days. On this benchmark, an adaptive mean correction mechanism based on residual weighting is introduced, which adaptively allocates weights by measuring the similarity between historical samples and current road condition trends.

[0027] Furthermore, in step S2, under the human-vehicle collaborative scheduling mode, a demand-response bus scheduling model is constructed. Based on the rolling time-domain optimization framework, the demand-response bus scheduling optimization problem is transformed into multiple constrained sub-problems, specifically:

[0028] Based on the rolling time-domain optimization framework, the system divides the time into several equal-length time slices at fixed intervals. At the end of each time slice, a short-cycle decision update is performed, called the decision phase. At this time, the scheduling plan is recalculated and optimized based on the position and status of each vehicle in the current time slice, previously assigned but not yet completed orders, and new orders with service time windows in the next time slice. After entering a time slice, the scheduling decision from the previous round is executed in the initial phase, called the execution phase. The alternation between decision and execution allows the scheduling results to be continuously iterated and optimized based on the latest environmental conditions and predictions of travel time in the next time slice, achieving forward-looking correction.

[0029] At the same time, a scheduling behavior continuation mechanism is established between time slices to help the continuation of decision-making by introducing inter-slice consistency. For tasks that have entered the execution stage, they are regarded as immutable information and are directly treated as fixed variables in the demand response bus scheduling model, thereby avoiding interference with the established service in path reconstruction. Tasks that have been assigned but have not yet started execution are naturally inherited into the next round of optimization and continue to participate in path construction or as scheduling constraints.

[0030] Furthermore, in step S3, the objective function of the demand-response bus scheduling model for human-vehicle collaboration is established. Objective functions for maximizing profitability and minimizing average spatiotemporal displacement are constructed from both the supply and demand sides, specifically:

[0031] In terms of profitability, ticket revenue depends on the base fare and the fare discounts offered to passengers to leverage time and space flexibility. The base fare uses a distance-based pricing method; the fare discounts are determined by the utility of alternative travel options; and the final discount is obtained.

[0032] The operating costs for each time slot consist of the mileage costs incurred within that time slot, the fixed costs of using newly deployed vehicles, and the labor costs of providing services.

[0033] In terms of spatiotemporal displacement, the spatiotemporal migration amount generated by the current decision in the next stage consists of the average spatial displacement amount and the average time window change amount caused by the order adjustment. The spatial offset is obtained by the average passenger boarding position offset caused by the alternative schemes optimized in the next stage, and the time offset is obtained by the average passenger boarding time window offset caused by the alternative schemes optimized in the next stage. The time scale is unified by converting the walking distance from the original boarding station to the new boarding station after adjustment into walking time.

[0034] Construct a bi-objective optimization function for a demand-response bus scheduling model that integrates human and vehicle collaboration.

[0035] Furthermore, the constraints of the demand response bus scheduling model are determined.

[0036] Furthermore, the decision variables for the demand response bus scheduling model are defined.

[0037] Furthermore, in step S4, an improved dynamic multi-objective optimization algorithm is designed based on a memory search strategy. This algorithm employs local search and elite selection strategies to solve the demand-response bus scheduling optimization problem involving human-vehicle collaboration. Specifically:

[0038] The dynamic multi-objective Memetic algorithm is designed based on the memory search strategy. It integrates centralized scheduling in the static stage with rolling optimization in the dynamic stage. By utilizing spatiotemporal flexibility and historical plan inheritance mechanism, it achieves fast response while ensuring solution quality.

[0039] At the end of the static phase, all reservation order information to be served is known; the order boarding and alighting behavior is expressed as chromosomes using a gene encoding mechanism. After population initialization, the algorithm selects parent and mother generations from the current population for crossover operation. The complete vehicle scheduling path is used as the granularity of the exchange. The non-covering crossover strategy is adopted to improve the utilization rate of vehicle resources, avoid order overlap or omission, and improve the integration of solutions.

[0040] Based on this, the algorithm optimizes and adjusts the current scheduling scheme through a spatiotemporal flexible local search operator. After the local search is completed, the solution sets of the offspring and the parent generation are merged, and the superior solutions are selected from them based on the heterogeneous elite selection strategy, retaining the candidate solutions that achieve a good trade-off between revenue and passenger experience. The algorithm repeats the above iterative process until the set termination condition is reached. After the static phase iteration is completed, the completed order assignment scheme and the corresponding vehicle path and status are used as the environmental benchmark. The optimal combination method and service path set of each order are recorded, and the PM algorithm is used to filter non-dominated solutions. The output is used as the scheduling execution scheme in the early stage of operation.

[0041] After the dynamic multi-objective Memetic algorithm enters the dynamic phase, it processes new orders and responds to vehicle status updates in each rolling time slice. The algorithm compares the current order and vehicle status with the environmental features in the static phase and historical time slices. If a highly similar state structure is identified, the existing scheduling scheme can be inherited to reduce redundant computation. If the difference is large, the algorithm decides whether to perform incremental insertion or reconstruct the scheduling scheme including incomplete orders based on the state deviation. For the scheme that needs optimization, a local search and elite selection mechanism is used for iterative updates, continuously re-evaluating the objective function performance after new orders are included until the phase termination condition is met. Finally, the optimal scheduling result under the current rolling cycle is output as the input for the next time slice execution phase.

[0042] Compared with existing technologies, this invention, by considering the time-varying characteristics of urban road networks and using the spatiotemporal flexibility of both passengers and vehicles as a link, proposes a demand-response bus scheduling mode that integrates human and vehicle operations, effectively improving capacity utilization efficiency and reducing total scheduling costs. This invention employs a multi-objective dynamic Memetic algorithm framework based on a memory search mechanism, reducing redundant computation and accelerating convergence through a de-inheritance mechanism to meet real-time requirements. This invention introduces a heterogeneous elite retention mechanism to alleviate the problem of premature convergence in dynamic scenarios. This invention combines the principle of diminishing marginal utility to construct an executability-oriented scheduling selection mechanism, achieving a balance between revenue and average spatiotemporal displacement, and improving the applicability and economy of the joint scheduling strategy at different stages. Attached Figure Description

[0043] Figure 1 This is a flowchart of a demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks.

[0044] Figure 2 A schematic diagram of the interactive decision-making process for a human-vehicle collaborative scheduling mode that introduces spatiotemporal flexibility.

[0045] Figure 3 This is a schematic diagram of the rolling time domain framework.

[0046] Figure 4This is a schematic diagram of the overall framework of the DMOMA algorithm.

[0047] Figure 5 This is a schematic diagram of the encoding scheme.

[0048] Figure 6 This is a diagram illustrating the cross operation.

[0049] Figure 7 A diagram of the local search operator.

[0050] Figure 8 A diagram illustrating strategies for selecting heterogeneous elites.

[0051] Figure 9 A diagram illustrating the insertion and reconstruction rules.

[0052] Figure 10 Performance metrics for different dynamic order ratios.

[0053] Figure 11 Performance indicators under different spatiotemporal displacement weights. Detailed Implementation

[0054] The following description, in conjunction with the accompanying drawings and specific embodiments, further illustrates the demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks of the present invention.

[0055] Please see Figure 1 This invention discloses a demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks, comprising the following steps:

[0056] S1: After introducing spatiotemporal flexibility, construct a human-vehicle collaborative scheduling mode, obtain data for utility function parameter calibration, and evaluate the utility function structure to support human-vehicle collaborative scheduling mode decision-making;

[0057] S2: Under the human-vehicle collaborative scheduling mode, a demand response bus scheduling model is constructed. Based on the rolling time-domain optimization framework, the demand response bus scheduling optimization problem is transformed into multiple constrained sub-problems.

[0058] S3: Establish the objective function of the demand response bus scheduling model for human-vehicle collaboration, determine the constraints of the demand response bus scheduling model, and define the decision variables of the demand response bus scheduling model.

[0059] S4: An improved dynamic multi-objective optimization algorithm based on a memory search strategy is designed. It adopts local search and elite selection strategies to solve the demand response bus scheduling optimization problem of human-vehicle collaboration.

[0060] First, to facilitate the description of the mathematical model later, Table 1 lists the symbolic variables involved in this invention.

[0061] Table 1 Symbolic Variables

[0062]

[0063]

[0064]

[0065] Step S1: After introducing spatiotemporal flexibility, construct a human-vehicle collaborative scheduling mode, obtain data for utility function parameter calibration, and evaluate the utility function structure to support the decision-making of the human-vehicle collaborative scheduling mode.

[0066] In the demand-side spatiotemporal flexibility framework, under the human-vehicle collaborative scheduling model, the passenger-submitted boarding / alighting stations and time windows serve as the initial plan. Alternative plans are generated by combining spatiotemporal flexibility adjustment strategies. The utility levels of the two alternatives are compared using a utility function to select feasible options that are not inferior to the initial plan from the passenger's perspective. Based on this, human-vehicle collaborative scheduling is optimized. The utility of the initial plan... and the utility of alternative solutions The formula is:

[0067] (1)

[0068] (2)

[0069] in, , , These are utility parameters for ticket price, travel time, and delay, respectively. , Corresponding auxiliary variables , , representing the completion time and start time of the alternative plan. Equation (1) compares the original plan submitted by the passenger and divides the travel utility into ticket cost items. In-transit costs and delay costs Equation (2) is used to calculate the travel utility of alternative options, which includes three parts: discounted ticket price, new travel time and new delay.

[0070] When passengers accept alternatives with spatiotemporal adjustments, subjective cognitive differences and perceptual uncertainties make it difficult for a single deterministic model to accurately reflect real passenger decision-making behavior. To improve the model's behavioral fitting ability and real-world applicability, this paper combines chance constraint theory to characterize the probability of passengers accepting alternatives and introduces a random perturbation term following a specific distribution. To simulate unobservable preferences or perceived errors, the utility difference between the two options is as follows:

[0071] (3)

[0072] in, This indicates the degree of "advantage" of the original solution compared to the alternative solutions, as perceived by the passenger. This indicates that the alternative solution is no less effective than the original solution, and passengers are more inclined to accept the time and space migration.

[0073] Assumption It follows a logical distribution; based on this, ,in This represents the difference in expected utility. The distribution scale parameter determines the range of perceived fluctuations. To explicitly embed passenger acceptance of alternative options into the demand-response bus scheduling model, the following opportunity constraints are constructed:

[0074] , (4)

[0075] in , which represents the minimum probability threshold for a passenger to accept the alternative.

[0076] This constraint ensures that the offered alternatives are sufficiently attractive to passengers, thus encouraging them to relinquish decision-making power regarding the spatiotemporal attributes of orders for scheduling optimization to a certain extent. Transforming this opportunity constraint into a deterministic constraint can utilize the cumulative distribution function of the logistic distribution. :

[0077] , (5)

[0078] because The above constraints then further transform into:

[0079] , (6)

[0080] In supply-side spatial and temporal flexibility, vehicles, while fulfilling scheduling tasks, can autonomously choose different routes to avoid congestion and save travel time based on current or predicted traffic conditions. Essentially, this involves refining the granularity of scheduling decisions, that is, for any pair of stations... The platform no longer presets a single shortest path, but instead dynamically selects the path with the shortest estimated travel time for the current time period from multiple candidate paths, expanding the scheduling decision to "whether to allow travel by station". via path Go to the station ".

[0081] Further, a human-vehicle collaborative scheduling model is proposed, such as Figure 2 The diagram illustrates the interactive decision-making process of the spatiotemporally flexible human-vehicle collaborative scheduling mode, as shown in the figure. This allows for flexible scheduling in each time period. The decision is denoted as:

[0082] (7)

[0083] In the formula, For vehicle routes, For spatial offset, Adjust the time window.

[0084] Based on the quantification of the utility of the scheme according to equations (1) and (2), the parameters to be calibrated include the ticket price utility parameter. Trip time parameters Delay time parameters Utility perceptual fluctuation coefficient and minimum probability threshold A questionnaire based on simulated scenarios was designed to obtain high-quality behavioral data for calibrating utility function parameters. The questionnaire constructs a decision-making scenario faced by passengers when actually using DRT travel services, guiding them to choose between the "original solution" and "alternative solutions with temporal and spatial flexibility," thereby inferring their behavioral preferences and acceptance boundaries. The questionnaire structure is shown in Table 2 below.

[0085] Table 2 Questionnaire Structure

[0086]

[0087] To comprehensively evaluate the fitting effect of the utility function structure and its behavior recognition ability, a composite evaluation system was constructed, comprising five classic classification indicators, covering three dimensions: prediction accuracy, discriminative ability, and classification balance. The definition of each indicator is as follows:

[0088] Accuracy represents the proportion of correctly predicted data in all samples using the human-vehicle collaborative scheduling mode. It measures the overall classification performance and is calculated as follows:

[0089] (8)

[0090] Wherein, TP (True Positives) is the number of samples that were actually accepted and predicted as accepted, TN (True Negatives) is the number of samples that were actually rejected and predicted as rejected, and FP and FN are misjudged samples that were predicted as accepted but were actually rejected, and predicted as rejected but were actually accepted, respectively.

[0091] Precision represents the proportion of samples predicted as acceptable by the vehicle-human cooperative scheduling model that actually accept the alternative solution. It is calculated as follows:

[0092] (9)

[0093] Recall represents the proportion of samples that actually accept alternative solutions, where the human-vehicle collaborative scheduling mode is successfully identified. It is calculated as follows:

[0094] (10)

[0095] The F1 score is the harmonic mean of precision and recall, balancing their weights in the performance of the human-vehicle collaborative scheduling mode. It is calculated as follows:

[0096] (11)

[0097] The area under the curve (AUC) represents the probability that the human-vehicle collaborative scheduling mode will prioritize accepted samples over rejected samples. This metric is calculated by sorting the samples according to their classification scores and then calculating the proportion of all positive and negative sample pairs that are correctly sorted.

[0098] During the optimization process, the algorithm first randomly samples several sets of parameters and calculates their corresponding F1 scores. Then, it uses a Gaussian process regression surrogate model to determine the parameter combinations for the demand response bus scheduling model. In each iteration, the next most promising parameter combination is determined based on the sampling function and evaluated to continuously improve model performance until the maximum number of iterations or the convergence condition is met. A total of 20 rounds of optimization are performed, and the final optimal parameter combinations and evaluation results are shown in Table 3.

[0099] Table 3 Optimal Parameter Combinations and Index Results

[0100]

[0101] This optimal parameter combination not only performs well in terms of model performance metrics, but also has a high degree of rationality in terms of behavioral interpretation. It accurately reflects the sensitivity of passengers to price, service stability and tolerance for changes in reality, and can be used to determine whether the alternative DRT scheduling optimization scheme is acceptable.

[0102] Regarding the capture of time-varying travel time features, in order to improve the quality of route selection while ensuring real-time response, the scheduling system can rely on historical data to predict the changing trends of travel time for each road segment in the short term. First, travel time samples of the target area are obtained. Based on these samples, road segments are concatenated to construct the shortest path between station pairs, serving as the basic dataset to support the decision-making process of the human-vehicle cooperative mode. The overall structure of the samples is shown in Table 4.

[0103] Table 4. Segment Travel Time Data Collection Structure Design

[0104]

[0105] Building upon this foundation, and leveraging the route planning service provided by the Gaode Maps Open Platform, automated data collection is achieved through web crawler scripts. The Gaode Open Platform's "Route Planning" API allows users to specify the coordinates of the starting and ending points to obtain the travel time between them. For coordinate acquisition, station-type nodes are converted from station names to latitude and longitude coordinates using Gaode's "Geocoding" interface; while road intersections are manually calibrated using developer tools, consistently retaining six decimal places for latitude and longitude accuracy to ensure spatial positioning consistency.

[0106] After acquiring historical travel time data for road segments, a data-driven historical average (HA) method is used as the baseline prediction strategy for future travel times. That is, for a given target time... The predicted travel time is the average travel time observed over the past few days at that moment, expressed as:

[0107] (12)

[0108] in Indicates predicted road segment At the point of time The travel time For the first Day, Time Point The actual travel time for this section of the road For historical reference days.

[0109] Based on this benchmark, an adaptive mean correction mechanism based on residual weighting is introduced. This mechanism adaptively assigns weights by measuring the similarity between historical samples and current road condition trends. The expression is as follows:

[0110] (13)

[0111] (14)

[0112] in, This is the revised predicted travel time. For each historical sample The weighting coefficients, Indicates the time span of the review. For historical data The mean at any given time.

[0113] Step S2: Under the human-vehicle collaborative scheduling mode, a demand response bus scheduling model is constructed. Based on the rolling time-domain optimization framework, the demand response bus scheduling optimization problem is transformed into multiple constrained sub-problems.

[0114] like Figure 3As shown in the rolling time-domain framework diagram, the scheduling process consists of a static phase and a dynamic phase. Before operations begin, all known orders are centrally decided at the end of the static phase, forming an initial scheduling plan that serves as input for the dynamic phase. After operations begin, at fixed intervals... Divide the time into several time slices of equal length , At the end of each time slice, a short-cycle decision update is performed, known as the decision phase. At this point, based on the location and status of each vehicle within the current time slice, previously assigned but not yet completed orders, and the service time window falling within the next time slice... The scheduling plan is recalculated and optimized based on new orders and other information. (Entering time slice) After that, the scheduling decision from the previous round is executed in the initial stage, which is called the execution stage. The alternating process of decision-making and execution allows the scheduling results to be continuously iterated and optimized based on the latest environmental conditions and predictions of the next time slice's travel time, thus achieving forward-looking correction.

[0115] Simultaneously, a scheduling behavior continuity mechanism is established between time slices, introducing inter-slice consistency to facilitate decision-making continuity. For tasks already in the execution phase, the system treats them as immutable information, directly processing them as fixed variables in the demand-response bus scheduling model, thus avoiding interference with established services during route reconstruction. Tasks already assigned but not yet executed are naturally inherited into the next round of optimization, continuing to participate in route construction or as scheduling constraints. The update frequency of travel time depends on the length of the time slice. Within any time slice, the travel time of all road segments is considered statically constant, with updates only occurring during time slice transitions. This setting is based on the realistic assumption that urban traffic fluctuates within a limited time scale, simplifying the route evaluation and ranking logic in the model solution process and reducing optimization oscillations caused by time-varying road networks.

[0116] Step S3: Establish the objective function of the demand response bus scheduling model for human-vehicle collaboration, determine the constraints of the demand response bus scheduling model, and define the decision variables of the demand response bus scheduling model.

[0117] The objective function for establishing a demand-response bus scheduling model that integrates human and vehicle operations is constructed by maximizing profitability and minimizing average spatiotemporal displacement from both the supply and demand sides, respectively:

[0118] In terms of profitability, the profits generated from making decisions on scheduling plans for any time slot are derived from the fare revenue of demand-response buses within that time slot. and operating costs The calculation shows that order rejection incurs no penalty cost; therefore, setting an order rejection cap can deter this behavior.

[0119] Ticket revenue depends on the base fare and the fare discounts offered to passengers to leverage time and space flexibility, where the base fare... Mileage-based pricing method:

[0120] , , (15)

[0121] in, Ticket price per unit distance for Euclidean distance between stations.

[0122] Ticket discount The travel utility of the alternative routes is determined by equations (1) and (2) relative to the travel utility of the original route. and the travel utility of alternative options Substituting the calculation method into equation (6), we can obtain:

[0123] (16)

[0124] (17)

[0125] Final Discount for:

[0126] , (18)

[0127] The operating cost of each time slice consists of the mileage cost generated within that time slice. Fixed costs of using newly commissioned vehicles and the human resource costs of providing services Composition, in which:

[0128] (19)

[0129] The cost of energy consumed per unit distance, Fixed costs for the use of company vehicles This refers to the cost of human resources per unit of time.

[0130] In terms of spatiotemporal displacement, the spatiotemporal migration amount generated by the current decision in the next stage consists of the average spatial displacement amount and the average time window change amount caused by the order adjustment, among which the spatial offset amount

[0131] ;

[0132] The time offset is obtained from the average passenger boarding position shift caused by the alternative solutions optimized in the next stage.

[0133] ;

[0134] The average passenger boarding time window shift is obtained from the alternative plans optimized in the next stage. The original boarding stations are then standardized on a time scale. Arrive at the new boarding station after adjustment Walking distance is converted to walking time:

[0135] (20)

[0136] In the formula, and These represent the spatial dimension offset and the temporal dimension offset weights when the alternative schemes are quantized for spatiotemporal displacement.

[0137] The bi-objective optimization function of the constructed human-vehicle collaborative demand-response bus scheduling model is expressed as:

[0138] ;(twenty one)

[0139] ;(twenty two)

[0140] Equation (21) is the objective function for maximizing total profit, determined by the difference between revenue and cost generated by the decision. Equation (22) is the objective function for minimizing the average spatiotemporal displacement of passengers, calculated by weighting time and spatial displacement. In the human-vehicle collaborative scheduling mode proposed in this invention, an increase in average spatiotemporal displacement indicates that orders will be more concentrated in terms of spatiotemporal attributes, which helps to save transportation resources and variable costs and improve total profit, but the service quality will decrease accordingly. Therefore, the two objective functions conflict with each other, and a balance point needs to be found.

[0141] Define constraints:

[0142] ;(twenty three)

[0143] ;(twenty four)

[0144] (25)

[0145] (26)

[0146] (27)

[0147] (28)

[0148] (29)

[0149] , (30)

[0150] (31)

[0151] (32)

[0152] (33)

[0153] (34)

[0154] (35)

[0155] (36)

[0156] (37)

[0157] (38)

[0158] (39)

[0159] Equations (23)–(26) are the order pick-up and drop-off point access constraints, ensuring consistency between the order acceptance status and the service path; Equation (27) is the intermediate node path balance constraint, ensuring that the number of entries and exits at all intermediate stations are equal; Equation (28) is the parking lot entry and exit path balance constraint, stipulating that each vehicle must depart from the parking lot and eventually return to the parking lot, forming a complete scheduling loop; Equation (29) is the vehicle capacity constraint, which tracks the number of passengers picking up and dropping off at each station. and Controlling the passenger load of vehicles at any point during the entire dispatching process Not exceeding the vehicle's maximum load capacity .

[0160] Equation (30) is the discount strength constraint, which should be applied to the order according to the system. Discount rate offered Equation (31) defines the logic for determining whether an order is delayed. Equations (32) and (33) together constitute the boarding time window constraint, controlling that the arrival time of the vehicle at the original or alternative pick-up and drop-off points must not exceed the specified tolerance range. Equations (34) and (35) respectively limit the overall delay rate and order rejection rate of the system. Equations (36) and (37) are the detour coefficient constraints for the service path, stipulating that the actual travel time of the order must not exceed the shortest path time between OD. Equations (38) and (39) are used to define the logical relationship between the arrival and departure times of a station.

[0161] Define the decision variables as:

[0162] (40)

[0163] (41)

[0164] (42)

[0165] , (43)

[0166] (44)

[0167] Step S4: Based on the memory search strategy, an improved dynamic multi-objective optimization algorithm (DMOMA) is designed. The algorithm uses local search and elite selection strategies to solve the demand response bus scheduling optimization problem of human-vehicle collaboration.

[0168] like Figure 4 The overall framework diagram of the DMOMA algorithm is shown. The improved dynamic multi-objective Memetic algorithm (DMOMA algorithm) integrates centralized scheduling in the static stage with rolling optimization in the dynamic stage. It utilizes spatiotemporal flexibility and historical plan inheritance mechanism to achieve fast response while ensuring solution quality.

[0169] At the end of the static phase, all pending appointment order information is known. For example... Figure 5 As shown in the schematic diagram of the coding scheme, the order loading and unloading behavior is expressed as a chromosome using a gene coding mechanism. Figure 6 As shown in the crossover operation diagram, after the population is initialized, the algorithm selects the parent and mother generations from the current population for crossover operation. The complete vehicle scheduling path is used as the granularity of the exchange, and an over-coverage crossover strategy is adopted to improve the utilization rate of vehicle resources, avoid order overlap or omission, and improve the integration of solutions.

[0170] Based on this, such as Figure 7 As illustrated in the local search operator diagram, the algorithm optimizes and adjusts the current scheduling scheme through a spatiotemporally flexible local search operator. For example... Figure 8As illustrated in the diagram of the heterogeneous elite selection strategy, after the local search is completed, the solution sets of the offspring and parent generations are merged, and the superior solutions are selected based on the heterogeneous elite selection strategy, retaining the candidate solutions that achieve a good trade-off between revenue and passenger experience. The algorithm repeats the above iterative process until the set termination condition is reached. After the static phase iteration is completed, the completed order assignment schemes and corresponding vehicle routes and states are used as environmental benchmarks. The optimal combination method and service route set for each order are recorded, and the PM (Pareto Mapping) algorithm is used to filter non-dominated solutions, outputting the scheduling execution scheme for the initial stage of operation.

[0171] After the DMOMA algorithm enters the dynamic phase, it processes new orders and responds to vehicle status updates in each rolling time slice. For example... Figure 9 As illustrated in the insertion and reconstruction rule diagram, the algorithm compares the current order and vehicle status with environmental features from static stages and historical time slices. If a highly similar state structure is identified, the existing scheduling scheme can be inherited to reduce redundant computation. If the differences are significant, the algorithm determines whether to perform incremental insertion or reconstruct a scheduling scheme that includes incomplete orders based on the state deviation. For schemes requiring optimization, a local search and elite selection mechanism is used for iterative updates, continuously re-evaluating the objective function performance after new orders are included until the stage termination condition is met. Finally, the optimal scheduling result under the current rolling cycle is output as the input for the next time slice execution stage.

[0172] The following study uses a real-world demand-response bus dispatching project, specifically the Wanqingsha area of ​​Nansha District, Guangzhou, as the target region. It employs actual demand-response bus operation data from May 2023 as a case study to illustrate the optimization method for demand-response bus dispatching based on human-vehicle collaboration under a time-varying road network. Regarding bus infrastructure, statistics show that the maximum deployable fleet size is 9 vehicles. The area includes 35 passenger pick-up and drop-off points and 1 depot.

[0173] To quantify algorithm performance, the following metrics are used to construct an algorithm performance metric system:

[0174] Coverage is a commonly used performance metric to measure the relative merits of two non-dominated solution sets, used to compare the covering ability of algorithms in the solution space. Given two solution sets... and Coverage index Represents a set How many solutions dominate the set? The solution in the formula is:

[0175] (45)

[0176] in, Solution Dominant Solution That is, it is not inferior on all objectives, and is superior on at least one objective. .

[0177] The number of non-dominated solutions (Nps) on the Pareto front reflects the diversity and breadth of solutions that the algorithm can explore in a single optimization run. The more non-dominated solutions there are, the more fully the algorithm covers the objective space, and the more options it can provide for decision-makers.

[0178] Hypervolume (HV) is a comprehensive metric that measures the quality and distribution of the solution set in the objective space of a multi-objective optimization algorithm. It characterizes the volume of the objective space covered by the current non-dominated solution set, which is then truncated by a reference point. A larger hypervolume indicates a wider coverage of the objective space by the non-dominated solution set and a better overall objective value. The calculation method is as follows:

[0179] (46)

[0180] in, The solution is in the first... Values ​​in each target dimension It is the value of the reference point in this dimension. The target number.

[0181] The Pareto front nondominated solution dispersion degree (PSD) quantifies the uniformity of solution distribution in the Pareto front; a smaller value indicates better distribution performance of the algorithm. The calculation method is as follows:

[0182] (47)

[0183] in, The number of non-dominated solutions. For the first Euclidean distance between each Pareto solution and its neighboring solutions; Let be the average Euclidean distance between all adjacent solutions.

[0184] Solution time (CPUT) is the running time of an optimization algorithm in completing a full scheduling solution task, directly reflecting the algorithm's time efficiency and computational complexity.

[0185] Based on real-world operational data, six datasets with order sizes of 60, 120, 180, 240, 300, and 360 were constructed. The performance of DMOMA was compared with that of multi-objective genetic algorithm (NSGA-II), multi-objective simulated annealing algorithm (MOSA), multi-objective differential evolution algorithm (MODE), and multi-objective tabu search algorithm (MOTS). The results are shown in Table 5.

[0186] Table 5 Comparison of Algorithm Solving Performance

[0187]

[0188]

[0189] Regarding the total profitability metric, which is of utmost concern to operators, DMOMA outperformed the suboptimal algorithm by 16.61%, 17.12%, 21.28%, 37.79%, 40.86%, and 45.77% respectively across six sets of cases with different order sizes (60, 120, 180, 240, 300, and 360 orders). In terms of robustness, DMOMA exhibited smaller fluctuations in profitability and spatiotemporal displacement. Regarding the number of non-dominated solutions (Nps) and the dispersion of non-dominated solutions (PSD), DMOMA outperformed the other five comparison algorithms in both solution set diversity and convergence. Meanwhile, the total computation time of DMOMA increased relatively moderately with the problem size, growing by 95.8%, 80.92%, 28.18%, 29.14%, and 21.94% respectively, without showing a significant exponential expansion trend, indicating its good scalability. Under the same computational conditions, DMOMA consistently outperforms other comparative algorithms in computation time, especially in large-scale computational cases where its time-saving effect is more significant.

[0190] In summary, DMOMA demonstrates consistent performance advantages across various metrics by introducing a memory-based search strategy, an environment-matching mechanism, and inheritance operations. Particularly in medium- to high-scale tasks, these dynamic enhancement mechanisms significantly improve the guidance capability of local searches and the continuity of solution structures. In small-scale problems, DMOMA's main advantage lies in its operational efficiency, while in large-scale examples, it exhibits comprehensive superiority in solution quality, stability, diversity, and computational resource utilization. This also indicates that the introduction of dynamic mechanisms has greater marginal value in complex environments and is a key direction for improving the performance of multi-objective scheduling algorithms.

[0191] The results show that the proposed DMOMA solution algorithm has good characteristics and can be extended to practical applications. This invention, by considering time-varying road network attributes, optimizes the scheduling mode based on the concept of human-vehicle collaboration under dynamic demand, achieving cost reduction and efficiency improvement for demand-responsive public transport, promoting the healthy development of integrated public transport, and has strong practical application prospects.

[0192] The objective function of the model in this invention is: maximizing profitability based on the urgent needs of operators and the current state of DRT development; and minimizing average spatiotemporal displacement based on the impact on passenger travel experience. Furthermore, to ensure that the method proposed in this invention does not cause degradation of other dimensional indicators and to achieve multi-objective resilience, this invention additionally introduces indicators such as total profitability, number of dispatched vehicles, number of passengers served, response rate, mileage utilization rate, and carpooling rate.

[0193] Total profit records the profit value from the start of operation to different time points, calculated by summing the profits within each time slice. The number of vehicles called records the sum of vehicles in motion and vehicles parked at stations other than the parking lot. The number of passengers served represents the number of passengers served within each time slice, allowing observation of the temporal distribution characteristics of demand fulfillment under the spatiotemporal flexibility strategy.

[0194] Response rate represents the proportion of orders that are responded to during operation out of the total number of orders. The calculation method is as follows:

[0195] (48)

[0196] Mileage utilization rate represents the ratio of the product of the number of passengers and the distance they travel during a vehicle's journey to the total distance the vehicle travels. It signifies the efficiency of resource utilization by the vehicle during operation. The calculation method is as follows:

[0197] (49)

[0198] The carpooling rate represents the proportion of all orders that involve carpooling.

[0199] (50)

[0200] To systematically evaluate the impact of spatiotemporal flexibility on the human-vehicle collaborative mode, this embodiment conducts a sensitivity analysis based on the characteristics of the Wanqingsha area. Due to its low-density characteristics, the Wanqingsha area has a sparse spatial distribution of stations, with an average of only 1.9 accessible stations within 1000m and only 4.8 within 2000m. To ensure that passengers have sufficient optional boarding stations within the variable spatial range, the experiment sets the upper limit of temporal flexibility at 20 minutes and the upper limit of spatial flexibility at 2000m. A case study is constructed based on 160 orders, and 20 repeated experiments are conducted to calculate the mean index and construct a three-dimensional response surface.

[0201] The results show that the overall profitability index exhibits a monotonically increasing trend with the increase in flexibility, and is more sensitive to spatial flexibility. Profitability increased by 220.8 yuan when time flexibility increased from 0 to 20 minutes, while it increased by 301.89 yuan when spatial flexibility increased from 0 to 2000 meters. This indicates that under the current order distribution structure, spatial flexibility is more conducive to reconstructing access sites and reducing empty runs, demonstrating its dominant role in the efficiency of capacity resource integration. The order service rate rapidly approaches and stabilizes at 100% after time flexibility reaches 15 minutes and spatial flexibility reaches 1500 meters, indicating that within the set threshold range, effective service can be achieved for almost all orders through joint scheduling. The saturation of the service rate reflects the carrying capacity limit of the scheduling system under the current regional structure and order density, further improving flexibility. Although no marginal improvement was achieved in service coverage, it still provides positive support for resource utilization efficiency.

[0202] In terms of mileage utilization, the improvement in flexibility also exhibits a diminishing marginal effect. The initial improvement phase shows a particularly significant increase in utilization, demonstrating a high degree of utilization of the initial flexibility release. However, as flexibility further expands, its marginal gain in resource matching gradually decreases, reflecting the path risks faced by the scheduling system beyond a certain degree of freedom.

[0203] The most structural change is in the group-buying rate. Without flexibility, the group-buying rate is only 19.71%, while with flexible opening hours and locations, it increases to 30.17% and 36.84%, respectively. This indicates that group-buying capability is limited by the distribution and matching characteristics of orders in the temporal and spatial dimensions, while the introduction of flexibility effectively widens the "matching window" between orders, greatly improving the success rate of order aggregation. The leap in the group-buying rate not only significantly improves the efficiency of operational resource utilization but also indirectly optimizes the average service waiting time for passengers and the consistency of scheduling.

[0204] In summary, spatiotemporal flexibility, as a key adjustable variable in the scheduling system, not only substantially improves profitability, service capacity, and route efficiency, but its mechanism also exhibits significant synergistic characteristics. Spatial flexibility enhances spatial coordination capabilities by expanding the set of accessible stations and reducing route overlap; temporal flexibility introduces a dynamic buffer into the scheduling process, alleviating execution rigidity and improving temporal operability. The synergistic effect of these two factors significantly expands the solution space of the scheduling system, providing empirical support and decision-making basis for flexible public transport services in low-density areas.

[0205] In addition to pre-booked orders, unscheduled requests frequently arise in actual operations. The randomness and suddenness of these requests can significantly disrupt existing scheduling plans. To systematically assess their impact, a sensitivity analysis was conducted on the proportion of unscheduled orders, and the results are presented below. Figure 10As the proportion of dynamic orders increased, various operational performance indicators declined to varying degrees. With the introduction of a time-space flexibility strategy, order service rate, mileage utilization rate, and group-buying rate decreased by 3.02%, 20.56%, and 28.29% respectively compared to the baseline. In the control scenario without a flexibility strategy, these three indicators decreased by 0.72%, 18.06%, and 29.66% respectively. Overall, the increase in the proportion of dynamic orders had a significant negative impact on scheduling performance, particularly in terms of group-buying efficiency and resource utilization.

[0206] The above phenomenon can be explained by the decision structure of rolling time-domain optimization. Before the start of each time slice, optimization calculations are performed based on the perceived pre-booked orders to determine the driving routes and service sequences to be executed in the next stage. This set of routes strictly satisfies constraints such as time windows and capacity. However, the introduction of subsequent ad-hoc orders will likely disrupt the feasibility of the original planned structure, and scheduling faces two response strategies: one is to directly reject services, leading to a decrease in the order service rate; the other is to dispatch vehicles separately for ad-hoc orders, which, while meeting service requirements, results in impaired order-sharing capabilities and reduced resource utilization. As can be observed from the data in the figure, under the condition of a high proportion of ad-hoc orders, the order service rate gradually approaches the set lower limit of the constraint (95%), confirming the frequency of order rejection; at the same time, the order-sharing rate shows a significant decline, reflecting the inability to effectively integrate multiple orders.

[0207] Mileage utilization did not decline monotonically; instead, it briefly increased during the initial rise in the proportion of dynamic orders before declining. This was because dynamic orders largely overlapped with sparsely distributed isolated orders, causing the initial task pool to exhibit some aggregation. Subsequent temporary orders could be inserted into existing trips without requiring additional vehicle dispatch, thus maintaining high resource utilization efficiency in the short term. However, this effect exhibits significant diminishing returns. As the proportion of dynamic orders further increases, more new demands from high-density areas are received, the insertion space tightens, requiring the dispatch of new vehicles to complete the tasks, leading to a decline in resource utilization efficiency.

[0208] While spatiotemporal flexibility strategies can mitigate the negative impact of uncertain demand on metrics, a longitudinal comparison of the difference between having and not having spatiotemporal flexibility under the same proportion of temporary demand reveals that the advantages of introducing spatiotemporal flexibility gradually diminish as the proportion of dynamic orders increases. The main reason is that the advantage of spatiotemporal flexibility lies in its holistic approach, adjusting passenger boarding stations and boarding time windows from an optimal perspective to achieve supply-demand coordination. When the proportion of dynamic orders is high, the initial perceptible information is incomplete, and orders appear sporadically hourly. Therefore, the scheduling plan tends to focus on meeting passengers' random needs, and the effect of globally coordinated spatiotemporal flexibility cannot be fully realized.

[0209] Meanwhile, passengers have varying levels of acceptance of spatial displacement caused by changes in boarding stations and temporal displacement caused by changes in service time windows among the alternative routes; therefore, a weighted approach is applied. To further explore the impact of weight ratios on scheduling strategies and operational indicators, this embodiment sets up two scenarios: full-time and spatial flexibility and path-only flexibility. Changes in weight ratios have no substantial impact on the latter and are only used to demonstrate the benchmark of operational indicators.

[0210] Different weighting ratios correspond to different scheduling philosophies. The relative importance of spatial and temporal displacements can be determined by... Adjusted by the ratio. Specifically, fixed. and change To simulate the different preferences of operators in terms of time and space adjustment: when At that time, time and spatial displacement are considered equally important, and it is assumed that the two adjustments cause the same degree of inconvenience to passengers. When spatial weight is higher, there is a greater emphasis on restricting spatial displacement. This means that operators believe that adjusting passenger boarding locations would cause greater inconvenience, and therefore are more inclined to adjust the time window. In this case, prioritizing the reduction of time displacement indicates that maintaining the original time window is more critical, while spatial adjustment is more acceptable.

[0211] like Figure 11 As shown, the results indicate that order response rate, mileage utilization rate, and carpooling rate all exhibit a trend of change with... The ratio changes, showing a trend of first rising and then falling, and in It reaches its peak near the nearest point. This trend reflects the dynamic trade-off between time and spatial flexibility during scheduling. When the ratio is at either extreme (e.g., This means that scheduling excessively penalizes a certain type of displacement, essentially restricting the flexibility of that dimension and forcing reliance on another dimension for scheduling. When spatial displacement has a high weight, time windows are primarily adjusted to meet demand to avoid passenger transfers or walking, and vice versa. This single-dimensional scheduling approach limits the overall feasible solution space, making it difficult to flexibly respond to passenger demand, resulting in decreased response rates, fewer carpooling opportunities, and lower efficiency.

[0212] When the weight ratio gradually approaches a moderate level, it can be adjusted synergistically in both time and space dimensions. At this point, the scheduling algorithm can reasonably combine and balance the two types of flexibility, thereby expanding the matching range and improving path optimization capabilities. Especially in high-density demand areas, it is easier to form multiplication combinations and efficient paths, so multiple indicators also rise, showing a significant performance improvement.

[0213] The results of the examples prove that when At that time, all three key indicators generally reached their optimal values. This indicates that in real-world scheduling, spatial flexibility has greater optimization potential than temporal flexibility. Appropriately allowing adjustments to passenger boarding positions while maintaining the stability of their time windows is more conducive to achieving overall optimization. This result also aligns with real-world logic: compared to modifying time windows, passengers are more willing to accept small-scale spatial movements, and spatial flexibility plays a more direct role in promoting carpooling and route integration.

[0214] In summary, the "rise then fall" trend of the indicator reflects the nonlinear game relationship between temporal and spatial flexibility under the objective of "minimizing average spatiotemporal displacement". Both excessively high and low weight ratios will limit scheduling efficiency, while a moderate weight configuration, especially when spatial displacement is slightly advantageous (1:1.5), can significantly improve overall performance, providing a reference for the design of scheduling rules and strategies.

[0215] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit disclosed in the present invention should fall within the patent scope covered by the present invention.

Claims

1. A demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks, characterized in that, Includes the following steps: S1: After introducing spatiotemporal flexibility, construct a human-vehicle collaborative scheduling mode, obtain data for utility function parameter calibration, and evaluate the utility function structure to support human-vehicle collaborative scheduling mode decision-making; S2: Under the human-vehicle collaborative scheduling mode, a demand response bus scheduling model is constructed. Based on the rolling time-domain optimization framework, the demand response bus scheduling optimization problem is transformed into multiple constrained sub-problems. S3: Establish the objective function of the demand response bus scheduling model for human-vehicle collaboration, determine the constraints of the demand response bus scheduling model, and define the decision variables of the demand response bus scheduling model. S4: An improved dynamic multi-objective optimization algorithm based on a memory search strategy is designed. It adopts local search and elite selection strategies to solve the demand response bus scheduling optimization problem of human-vehicle collaboration.

2. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 1, characterized in that, In step S1, after introducing spatiotemporal flexibility, a human-vehicle collaborative scheduling mode is constructed, including: In demand-side spatiotemporal flexibility, during demand-response bus scheduling, the passenger-submitted boarding / alighting points and time windows serve as the initial plan. Alternative plans are generated by combining these with spatiotemporal flexibility adjustment strategies. The utility levels of the two alternatives are compared using a utility function to select feasible options that are not inferior to the initial plan from the passenger's perspective. Based on this, passenger-vehicle coordinated scheduling optimization is performed; the utility of the initial plan... The utility of alternative solutions The expression is: ； ； In the formula, This represents the utility value of a unit ticket price. Indicates order The initial ticket price; It represents the utility value per unit of travel time; Indicates order Actual time of disembarkation; Indicates order Actual departure time; Represents the utility value per unit of delay; Indicates order The earliest acceptable service time; Indicates order The actual discount received; Indicates alternative order Actual time of disembarkation; Indicates alternative order Actual departure time; This indicates the order among the alternative options provided by the platform. The time window variation; Indicates order The requested pick-up point; This indicates the order among the alternative options provided by the platform. The pick-up station; Indicates walking speed; express Euclidean distance between stations; Based on existing subjective cognitive differences and perceptual uncertainty, a random perturbation term following a specific distribution is introduced. The utility difference between the two options is: ； In the formula, This indicates the degree of "advantage" of the original solution compared to the alternative solutions, as perceived by the passenger.

3. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 2, characterized in that, Introducing spatiotemporal flexibility, the construction of a human-vehicle collaborative scheduling model also includes: In supply-side spatial and temporal flexibility, vehicles, while fulfilling scheduling tasks, autonomously select different routes to avoid congestion and save travel time based on current or predicted traffic conditions. Essentially, this involves refining the granularity of scheduling decisions, that is, for any pair of stations... The platform no longer presets a single shortest path, but dynamically selects the path with the shortest estimated travel time for the current time period from multiple candidate paths, expanding the scheduling decision to include "whether to dispatch by station". via path Go to the station ”; A human-vehicle collaborative scheduling model is proposed, whereby the operator schedules each time period... The decision is denoted as: ； In the formula, A variable that is 0-1 indicates that in Does the time slice dispatch a vehicle? via line By site Go to the station If so ,otherwise ; Indicates assembly at the station. , Representing the car park, Indicates bus stops; Indicates the actual operating site With the site A set of selectable routes between them. , ; Represents a set of orders. ; Represents a set of time slices. .

4. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks as described in claim 1, characterized in that, In step S1, data for utility function parameter calibration is obtained, and the utility function structure is evaluated, including: By designing a questionnaire based on simulated scenarios, high-quality behavioral data was obtained for the calibration of utility function parameters. In order to comprehensively evaluate the fitting effect of the utility function structure and the behavior recognition ability, a composite evaluation system containing five classic classification indicators was constructed, covering three dimensions: prediction accuracy, discriminative ability, and classification balance. Accuracy represents the proportion of correctly predicted human-vehicle collaborative scheduling modes across all samples, measuring overall classification performance. It is calculated as follows: ； In the formula, TP is the number of samples that were actually accepted and predicted to be accepted; TN is the number of samples that were actually rejected and predicted to be rejected; FP is the misjudged sample that was predicted to be accepted but was actually rejected; and FN is the misjudged sample that was predicted to be rejected but was actually accepted. Precision represents the proportion of samples predicted as acceptable by the vehicle-human cooperative scheduling mode that actually accept the alternative plan. It is calculated as follows: ； Recall represents the proportion of samples that actually accepted alternative solutions, where the human-vehicle collaborative scheduling mode was successfully identified. It is calculated as follows: ； The F1 score is the harmonic mean of precision and recall, balancing the weights of both in the performance of the human-vehicle collaborative scheduling mode. It is calculated as follows: ； The area under the curve (AUC) represents the probability that the human-vehicle collaborative scheduling mode will prioritize accepted samples over rejected samples. This indicator is calculated by sorting the samples according to the classification scores output by the human-vehicle collaborative scheduling mode, and then calculating the proportion of all positive and negative sample pairs that are correctly sorted.

5. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 4, characterized in that, Obtaining data for utility function parameter calibration, evaluating utility function structure, and also including: In terms of capturing time-varying travel time characteristics, a data-driven historical mean method is adopted as the benchmark prediction strategy for future travel time, that is, for a certain target time... The predicted travel time is the average travel time observed over the past few days at that moment, expressed as: ； In the formula, Indicates predicted road segment At the point of time Travel time; For the first Time of day The actual travel time for this section of the road; For historical reference days; Based on this benchmark, an adaptive mean correction mechanism based on residual weighting is introduced. This mechanism adaptively assigns weights by measuring the similarity between historical samples and current road condition trends. The expression is as follows: ； ； In the formula, This is the revised predicted travel time; For each historical sample Weighting coefficients; Indicates the time span of the review; For historical data The mean at any given time.

6. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 2, characterized in that, In step S2, under the human-vehicle collaborative scheduling mode, a demand-response bus scheduling model is constructed. Based on the rolling time-domain optimization framework, the demand-response bus scheduling optimization problem is transformed into multiple constrained sub-problems, specifically: Based on the rolling time-domain optimization framework, with fixed intervals Divide the time into several time slices of equal length , ; At the end of each time slice, a short-cycle decision update is performed, known as the decision-making phase. At this point, based on the location and status of each vehicle within the current time slice, previously assigned but not yet completed orders, and the service time window falling within the next time slice... The new order information is used to recalculate and optimize the scheduling plan; enter the time slice. After that, the scheduling decision from the previous round is executed in the initial stage, which is called the execution stage. The alternating and rolling decision-making and execution processes enable the scheduling results to be continuously iterated and optimized based on the latest environmental conditions and predictions of the next time slice's travel time, thus achieving forward-looking correction. At the same time, a scheduling behavior continuation mechanism is established between time slices to help the continuation of decision-making by introducing inter-slice consistency. For tasks that have entered the execution stage, they are regarded as immutable information and are directly treated as fixed variables in the demand response bus scheduling model, thereby avoiding interference with the established service in path reconstruction. Tasks that have been assigned but have not yet started execution are naturally inherited into the next round of optimization and continue to participate in path construction or as scheduling constraints.

7. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 6, characterized in that, In step S3, the objective function of the demand-response bus scheduling model for human-vehicle collaboration is established. Objective functions for maximizing profitability and minimizing average spatiotemporal displacement are constructed from both the supply and demand sides, specifically: In terms of profitability, ticket revenue depends on the base fare and the fare discounts offered to passengers to leverage time and space flexibility, with the base fare being the most significant factor. Mileage-based pricing method: ， ， ； In the formula, Ticket price per unit distance; for Euclidean distance between stations; Ticket discount The travel utility of alternative routes is determined, expressed as follows: ； ； In the formula, The distribution scale parameter; , representing the minimum probability threshold for a passenger to accept the alternative; Final Discount for: ， ； The operating cost of each time slice consists of the mileage cost generated within that time slice. Fixed costs of using newly commissioned vehicles and the human resource costs of providing services Composition, in which: ； In the formula, The cost of energy consumed per unit distance; Fixed costs for the use of a unit vehicle; The cost of human resources per unit of time; Indicates time slice Inside, vehicles pass through the track. By site Go to the station The actual travel time; Indicates a set of vehicles to be dispatched. ; express Inter-site paths The actual driving distance; Indicates in Time slice, whether to dispatch a vehicle via line By site Go to the station ; Indicates the actual operating site With the site A set of selectable routes between; In terms of spatiotemporal displacement, the spatiotemporal migration amount generated by the current decision in the next stage consists of the average spatial displacement amount and the average time window change amount caused by the order adjustment, among which the spatial offset amount ； The time offset is obtained from the average passenger boarding position shift caused by the alternative solutions optimized in the next stage. ； The average passenger boarding time window shift is obtained from the alternative plans optimized in the next stage; the original boarding stations are unified on the time scale. Arrive at the new boarding station after adjustment Walking distance is converted to walking time: ； In the formula, The weight of spatial dimension offset when weighting the spatiotemporal displacement of alternative schemes; The weight of the time dimension offset when weighting the spatiotemporal displacement of alternative schemes; This is a 0-1 variable, representing whether the passenger accepts the alternative option; if they accept, then... ,on the contrary ; Indicates order The number of passengers; A 0-1 variable, representing an order. Whether assigned to a vehicle In time slice Complete, if so ,otherwise ; The bi-objective optimization function for constructing a demand-response bus scheduling model that integrates human and vehicle operations is expressed as: ； ； In the formula, It is a 0-1 variable, indicating whether the platform responds to the order. The response is If you refuse ; A 0-1 variable, representing an order. Whether assigned to a vehicle In time slice Complete, if so ,otherwise .

8. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 7, characterized in that, The constraints of the demand-response bus scheduling model are determined as follows: ； ； ； ； ； ； ； ， ； ； ； ； ； ； ； ； ； ； In the formula, Indicates the actual operating site With the site A set of selectable routes between; Indicates in Time slice, whether to dispatch a vehicle via line By site Go to the station ; Indicates the actual operating site With the site A set of selectable routes between; Indicates in Time slice, whether to dispatch a vehicle via line By site Go to the station ; Indicates the actual operating site With the site A set of selectable routes between; Indicates in Time slice, whether to dispatch a vehicle via line By site Go to the station ; Indicates in Time slice, whether to dispatch a vehicle via line By site Go to the station ; Indicates in Time slice, whether to dispatch a vehicle via line By site Go to the station ; Indicates time slice vehicle to station The number of people in the vehicle at that time; Indicates vehicle Arrival Station The moment; Indicates vehicle Arrival Station The moment; Indicates vehicle Leave the station The moment; Indicates time slice Inside, vehicles depart from the station Go to the station The shortest travel time; Indicates time slice Inside, vehicles depart from the station Go to the station The shortest travel time; Indicates vehicle Arrival Station The moment; Indicates vehicle Leave the station The moment; Indicates vehicle Arrival Station The moment; Represents a maximum constant; Indicates the maximum vehicle capacity; This indicates the lower limit of the discount that the operator can accept; Indicates order Whether the actual service time is later than the time window, if This indicates that the vehicle is late; Indicates the length of the time window; This indicates the maximum allowed timeout for vehicle lateness. This indicates the maximum allowable percentage of vehicles to be late; This indicates the upper limit of the order rejection rate; Indicates the upper limit of the detour coefficient; Indicates time slice From vehicles On the site The number of people getting off the bus; Indicates time slice From vehicles On the site The number of people boarding the bus; This indicates the time taken for each passenger to complete the station service.

9. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 8, characterized in that, Define the decision variables for the demand-response bus scheduling model as follows: ； ； ； ， ； ； In the formula, This indicates the upper limit of the time displacement scale.

10. The demand-response bus scheduling optimization method based on human-vehicle collaboration under time-varying road networks according to claim 1, characterized in that, In step S4, an improved dynamic multi-objective optimization algorithm is designed based on the memory search strategy. This algorithm employs local search and elite selection strategies to solve the demand-response bus scheduling optimization problem involving human-vehicle collaboration. Specifically: The dynamic multi-objective Memetic algorithm is designed based on the memory search strategy. It integrates centralized scheduling in the static stage with rolling optimization in the dynamic stage. By utilizing spatiotemporal flexibility and historical plan inheritance mechanism, it achieves fast response while ensuring solution quality. At the end of the static phase, all pending appointment order information is known; The algorithm uses a gene coding mechanism to express order boarding and alighting behavior as chromosomes. After population initialization, the algorithm selects parent and mother generations from the current population for crossover operation. The algorithm uses the complete vehicle scheduling path as the granularity of the exchange and adopts a non-covered crossover strategy to improve the utilization rate of vehicle resources, avoid order overlap or omission, and improve the integration of solutions. Based on this, the algorithm optimizes and adjusts the current scheduling scheme through a spatiotemporal flexible local search operator. After the local search is completed, the solution sets of the offspring and the parent generation are merged, and the superior solutions are selected from them based on the heterogeneous elite selection strategy, retaining the candidate solutions that achieve a good trade-off between revenue and passenger experience. The algorithm repeats the above iterative process until the set termination condition is reached. After the static phase iteration is completed, the completed order assignment scheme and the corresponding vehicle path and status are used as the environmental benchmark. The optimal combination method and service path set of each order are recorded, and the PM algorithm is used to filter non-dominated solutions. The output is used as the scheduling execution scheme in the early stage of operation. After the dynamic multi-objective Memetic algorithm enters the dynamic phase, it processes new orders and responds to vehicle status updates in each rolling time slice. The algorithm compares the current order and vehicle status with the environmental features in the static phase and historical time slices. If a highly similar state structure is identified, the existing scheduling scheme can be inherited to reduce redundant computation. If the difference is large, the algorithm decides whether to perform incremental insertion or reconstruct the scheduling scheme including incomplete orders based on the state deviation. For the scheme that needs optimization, a local search and elite selection mechanism is used for iterative updates, continuously re-evaluating the objective function performance after new orders are included until the phase termination condition is met. Finally, the optimal scheduling result under the current rolling cycle is output as the input for the next time slice execution phase.

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