A bus departure interval optimization system and method based on waiting negative emotion accumulation and perceived time expansion

Abstract

The application relates to the field of bus management and discloses a bus departure interval optimization system and method based on waiting negative emotion accumulation and perceived time expansion, wherein the system comprises a perceived waiting time quantization module, a data acquisition module, a parameter fitting module and a bus departure plan optimization module. The subjective emotional experience of passengers is deeply fused with an actual scheduling model for the first time, the change of negative emotions of different passengers in the waiting process and the expansion phenomenon of perceived waiting time are quantized, the emotional experience target of passengers can be considered on the mathematical level and the operation target at the same time, the travel satisfaction of passengers is improved, and double balance is realized on the cost structure. Meanwhile, the method has strong adaptability and generalizability and can be applied to different cities, different bus line types and even other operation optimization existing waiting scenes.

Description

Technical Field

[0001] This invention relates to the field of bus management, specifically to a system and method for optimizing bus departure intervals based on the accumulation of negative emotions while waiting for buses and perceived time dilation. Background Technology

[0002] In the daily operation of public transportation systems, the passenger experience while waiting for buses significantly impacts their satisfaction with public transportation services. However, bus stops frequently face negative emotions such as boredom and anxiety caused by excessively long wait times. As wait times increase, passengers' anxiety and frustration gradually rise, leading to a subjective perception that the wait time is slower than the actual wait time. Furthermore, the perceived wait time increases further with the accumulation of actual wait time; the gradual accumulation of negative emotions makes time feel even slower, resulting in perceived wait time inflation, which reduces passengers' overall travel experience. On the other hand, ignoring the perceived wait time inflation caused by negative emotions during the waiting process fails to effectively reduce passengers' psychological costs, thereby lowering passenger satisfaction and further reducing the overall service efficiency of the public transportation system.

[0003] Although there is a certain research foundation in the field of public transport optimization, existing technologies still have significant shortcomings: (1) There is a lack of effective measurement methods for negative emotions and perceived waiting time during passenger waiting. Existing studies generally calculate passenger waiting time costs in a static way, evaluating only based on actual waiting time and ignoring the phenomenon of perceived waiting time inflation caused by the accumulation of negative emotions among service passengers; (2) Existing optimization models do not fully consider the impact of passenger perceived waiting time on the effectiveness of optimization strategies. Effectively measuring and incorporating passenger perceived time costs can significantly improve the accuracy and effectiveness of public transport optimization schemes, but existing methods often fail to achieve this goal, resulting in limited optimization effects. Summary of the Invention

[0004] To address the aforementioned technical challenges, developing a bus route optimization system and method that comprehensively considers both public transport operating costs and passenger perceived waiting time costs is of great significance for improving public transport service levels, reducing passenger waiting burdens, and enhancing the overall efficiency of the transportation system. This system should be able to dynamically assess passengers' perceived waiting costs and provide precise vehicle scheduling and departure interval optimization strategies to achieve more accurate resource allocation and overall system efficiency improvement, meeting the ever-changing passenger demands and traffic environment challenges.

[0005] To achieve the above objectives, this invention provides a bus departure interval optimization system and method based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, thereby overcoming the limitations of existing technologies in terms of passenger experience and system efficiency.

[0006] The specific plan is as follows:

[0007] A bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation includes: a perceived waiting time quantification module, a data acquisition module, a parameter fitting module, and a bus departure scheme optimization module.

[0008] The perceived waiting time quantification module is used to construct a first mathematical model representing the relationship between passengers' actual waiting time and passengers' negative emotions; at the same time, based on the first mathematical model, a second mathematical model representing the relationship between passengers' negative emotions and passengers' perceived waiting time is constructed.

[0009] The data acquisition module is used to obtain multi-dimensional data on the waiting process of passengers on the target bus route through a display preference survey. The multi-dimensional data includes: actual waiting time, subjectively perceived waiting time, passenger negative emotion score, and travel demand per unit time.

[0010] The parameter fitting module is used to fit the first mathematical model and the second mathematical model;

[0011] The bus departure scheme optimization module is used to construct a mixed integer nonlinear optimization model based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, with the goal of minimizing the sum of passenger perceived waiting time cost and bus operating cost. The module then uses the generalized Benders decomposition algorithm to solve the established mixed integer nonlinear optimization model and outputs a bus departure scheme that satisfies operational constraints and service quality.

[0012] Preferably, the constructed first mathematical model includes:

[0013] ,

[0014] in, Passengers wait continuously Real-time intensity of negative emotions at any given time unit; It is a continuous time variable calculated from the starting point of the wait; , This is the first parameter to be estimated.

[0015] Preferably, the constructed second mathematical model includes:

[0016] ,

[0017] in, Passengers wait continuously Instantaneous perceived waiting time within a unit of time; This is the second parameter to be estimated.

[0018] Preferably, the perceived waiting time accumulates continuously as the actual waiting time increases, and the passenger's perceived waiting time throughout the entire waiting process is:

[0019] ,

[0020] The perceived waiting time cost per passenger is:

[0021] ,

[0022] in, For each individual passenger, the perceived cost of waiting time; This represents the economic cost of perceived waiting time per unit.

[0023] Preferably, passengers arrive evenly while waiting for the vehicle, and the perceived waiting time for all passengers is:

[0024] ,

[0025] in, Indicates time window The interval between bus departures within the city; This represents the perceived waiting time for all passengers. Indicates time window Passengers inside the station Arrive at the station The travel demand; Indicates time window Length; Indicates time window Arrival time at the station per unit of time Waiting to be sent to the station The number of passengers on the bus; Indicates the bus arrival station within the time window. The number of times; The integral variable represents the passenger's... Arrival time; This indicates the actual waiting time for passengers;

[0026] The arrival time of each passenger will affect their actual waiting time. The outer integral iterates through all waiting passengers within the time window, while the inner integral calculates the perceived waiting time for each passenger.

[0027] Preferably, the workflow of the parameter fitting module includes:

[0028] First mathematical model parameter fitting:

[0029] Parameters are determined by nonlinear least squares optimization. and The optimization objective is to minimize the observed negative sentiment values. and predicted value Sum of squared residuals:

[0030] ,

[0031] The predicted value is defined by the integral model:

[0032] ,

[0033] in, The model predicts passengers The negative emotion value; For passengers Observations of accumulated negative emotions; Passengers The actual waiting time; and These are the parameters that need to be fitted;

[0034] Second mathematical model parameter fitting:

[0035] Parameters are determined by nonlinear least squares optimization. The optimization objective is to minimize the observed perception wait time. and predicted value Sum of squared residuals:

[0036] ,

[0037] The predicted value models include:

[0038] ,

[0039] in, The predicted value of passengers' perceived waiting time; The observed value of passengers' perceived waiting time; Passengers The actual waiting time; This is the ratio of the intensity of negative emotions to perceived waiting time.

[0040] Preferably, the bus operating costs include:

[0041] One-way bus departure frequency, within the time window Inside, the line The frequency of departures in one direction is:

[0042] ,

[0043] in, Indicates time window Length; Indicates time window Internal lines Frequency of departures in one direction; Indicates time window Internal lines Bus departure intervals; Indicates time window After the departure interval scheduling is completed, there is not enough time to schedule the next bus. The calculation formula is:

[0044] ,

[0045] The required frequency of bus departures for a given route, considering two-way operation, is calculated using the following formula:

[0046] ,

[0047] in, Indicates the line Bus departure frequency;

[0048] Operating fixed costs, routes The fixed operating cost model for public transportation operations is expressed as follows:

[0049] ,

[0050] in, Indicates the line Fixed costs of public transportation operation; Indicates the line Fuel costs for the distance covered by the bus operating unit; Indicates the line The fixed costs incurred by a bus operating for one day; This represents the labor costs incurred by a bus operator in one day. Indicates the length of the line; Indicates the line The number of buses in operation;

[0051] Fuel costs for bus operating units The calculation formula is:

[0052] ,

[0053] in, Indicates the line Fuel consumption per unit distance for bus operation, unit: liters; This indicates the price of oil.

[0054] This invention discloses a method for optimizing bus departure intervals based on the accumulation of negative emotions while waiting for a bus and perceived time dilation. The method is applied to the aforementioned system and includes the following steps:

[0055] A first mathematical model is constructed to characterize the relationship between passengers' actual waiting time and passengers' negative emotions; at the same time, based on the first mathematical model, a second mathematical model is constructed to characterize the relationship between passengers' negative emotions and passengers' perceived waiting time.

[0056] Multi-dimensional data on passenger waiting processes for target bus routes were obtained through a display preference survey. The multi-dimensional data included: actual waiting time, subjectively perceived waiting time, passenger negative emotion rating, and travel demand per unit time.

[0057] Fit the first mathematical model and the second mathematical model;

[0058] Based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, a mixed-integer nonlinear optimization model is constructed with the goal of minimizing the sum of passenger perceived waiting time cost and bus operating cost. The generalized Benders decomposition algorithm is used to solve the established mixed-integer nonlinear optimization model, and the bus departure scheme that satisfies operational constraints and service quality is output.

[0059] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0060] Traditional bus route optimization models often focus on improving operational efficiency, neglecting the differences in passengers' subjective experiences while waiting for the bus, especially the phenomenon that "perceived waiting time" is longer than "actual waiting time" under negative emotions. This invention, for the first time, deeply integrates passengers' subjective emotional experience with the actual dispatching model, allowing passenger emotional experience goals to be considered alongside operational goals at the mathematical level. This shift improves passenger travel satisfaction and achieves a dual balance in cost structure.

[0061] Secondly, this invention proposes for the first time the concept of "nonlinear expansion of perceived time under negative emotions". By modeling the relationship between the negative emotions accumulated by passengers during the waiting process and the waiting time, modeling the negative emotional state and the instantaneous perceived waiting time, and then modeling the relationship between the actual waiting time and the perceived waiting time, the perceived time in the waiting scenario can be scientifically measured.

[0062] Finally, this invention has strong adaptability and scalability. Since the key parameters in the model can be fitted with localized survey data, this method is applicable to different cities and different bus route types (such as Bus Rapid Transit (BRT), feeder buses, etc.), and can even be further extended to the quantification of perceived time in other scenarios (such as waiting scenarios such as train station ticket halls and airport security checks), and then used for the operational optimization of different systems (bus departure intervals, queuing windows, etc.), demonstrating high portability and practicality. Attached Figure Description

[0063] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a schematic diagram of the system structure according to an embodiment of the present invention;

[0065] Figure 2 This is a schematic diagram illustrating a specific implementation of an embodiment of the present invention;

[0066] Figure 3 This is a schematic diagram illustrating the actual waiting time in an embodiment of the present invention;

[0067] Figure 4 This is a schematic diagram of the perceived waiting time according to an embodiment of the present invention;

[0068] Figure 5 This is a schematic diagram of bus route operation according to an embodiment of the present invention;

[0069] Figure 6 This is a flowchart illustrating the solution process of the generalized Benders decomposition algorithm in an embodiment of the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] Example 1:

[0073] like Figure 1The diagram shown is a schematic representation of the system structure of an embodiment of the present invention, including: a sensing waiting time quantification module, a data acquisition module, a parameter fitting module, and a bus departure scheme optimization module.

[0074] The following will describe in detail, with reference to this embodiment, how the present invention solves technical problems in real life, and the overall process is as follows: Figure 2 As shown.

[0075] Mechanisms by which passenger-perceived waiting time is generated:

[0076] (1) The extended waiting time stimulates negative emotions in passengers:

[0077] The Weber-Fechner Law, a fundamental principle in psychophysics, describes the relationship between the physical intensity of a stimulus and its perceived intensity. This law states that the perceived intensity of a stimulus increases logarithmically with increasing actual physical intensity. Mathematically, this can be expressed as:

[0078] ,

[0079] in, Indicates perceived intensity. Indicates the physical intensity of the stimulus. 0 is a constant.

[0080] (2) The accumulation of negative emotions leads to a slower perceived waiting time:

[0081] Depend on Figure 3 and Figure 4 It can be seen that as the waiting time increases, the perceived waiting time increases faster and faster, and the difference between the perceived waiting time and the actual time becomes larger and larger. In other words, the perceived waiting time inflates more and more, which shows that as the waiting time increases, the perceived waiting time seems to pass more slowly. At the same time, the perceived waiting cost increases more and more.

[0082] Based on the above, this embodiment utilizes the perceived waiting time quantification module to establish a first mathematical model characterizing the relationship between passengers' actual waiting time and passengers' negative emotions based on the Weber-Fechner law; based on the first mathematical model, a second mathematical model characterizing the relationship between passengers' negative emotions and passengers' perceived waiting time is established; based on the second mathematical model, the cost of passengers' perceived waiting time is determined; and a nonlinear optimization model is established with the objective function of minimizing the sum of the cost of passengers' perceived waiting time and the total operating cost of the public transportation system.

[0083] The first mathematical model representing the relationship between actual passenger waiting time and negative passenger emotions is:

[0084] ,

[0085] in, Passengers wait continuously Real-time intensity of negative emotions at any given time unit; It is a continuous time variable calculated from the starting point of the wait; , This is the first parameter to be estimated.

[0086] The second mathematical model representing the relationship between the intensity of passengers' negative emotions and their perceived waiting time is:

[0087] ,

[0088] in, Passengers wait continuously Instantaneous perceived waiting time within a unit of time; This is the second parameter to be estimated.

[0089] Since perceived waiting time accumulates as actual waiting time increases, the passenger's perceived waiting time throughout the entire waiting process is:

[0090] ,

[0091] The perceived waiting time cost per passenger is:

[0092] ,

[0093] in, For each individual passenger, the perceived cost of waiting time; This represents the economic cost of perceived waiting time per unit.

[0094] Subsequently, the data acquisition module obtains multi-dimensional data on the waiting process of passengers on the target bus route through the revealed preference survey method. The main process includes: recording the actual waiting time of passengers on site; obtaining passengers' subjective perception of the waiting time through a questionnaire survey; setting four categories of negative emotion items and scoring them using a Likert 5-point scale, which are used for parameter fitting of the first mathematical model and the second mathematical model.

[0095] The data collection module mainly includes the following dimensions:

[0096] (1) Actual waiting time record:

[0097] By combining observation and passenger self-reporting, the actual waiting time from the time a passenger arrives at the platform to the time they board the train is recorded. All time records are kept in the same unit of "minutes". Passengers' travel needs are also recorded.

[0098] (2) Perceived waiting time acquisition:

[0099] After passengers have finished waiting for and boarded the bus, a questionnaire was used to ask them about their "subjective feeling of waiting time". This perceived time is often higher than the actual waiting time, which is used to characterize the passenger's emotional regulation and psychological amplification effect.

[0100] (3) Design of negative emotion intensity rating:

[0101] To quantify the psychological burden experienced by passengers while waiting for a ride, this questionnaire includes four categories of typical negative emotions, covering the most common emotional reactions among passengers, including:

[0102] Anxiety (such as worrying about missing the bus or the bus being late);

[0103] Irritability (such as annoyance from a noisy environment or long waiting times for transportation);

[0104] Anxiety (such as worrying that there will be too many people to get on the bus);

[0105] Helplessness (such as psychological stress when encountering unexpected situations).

[0106] Each emotion was scored using a five-point Likert scale, specifically:

[0107] 1 = None, 2 = Slight, 3 = Average, 4 = Strong, 5 = Very Strong.

[0108] Passengers were asked to rate their experience during the waiting process, item by item. The average of each passenger's four scores was then calculated to form a "negative emotion index," which served as the input parameter for the emotion-perception time transformation function in the subsequent model.

[0109] The systematic and structured data collection methods described above provide a solid empirical foundation for parameter fitting and algorithm design in this embodiment, and also ensure that the proposed optimization method has good practical applicability and scalability.

[0110] The first and second mathematical models are fitted using the parameter fitting module.

[0111] (1) Parameter fitting of the first mathematical model:

[0112] Parameters are determined by nonlinear least squares optimization. and The optimization objective is to minimize the observed negative sentiment values. and predicted value Sum of squared residuals:

[0113] ,

[0114] The predicted value is defined by the integral model:

[0115] ,

[0116] in, The model predicts passengers The negative emotion value; For passengers Observations of accumulated negative emotions; Passengers The actual waiting time; and These are the parameters that need to be fitted.

[0117] Fitting method: Nonlinear least squares method Because of the model Since this is a nonlinear function, it cannot be solved directly using simple linear algebra and requires an iterative optimization algorithm. A commonly used algorithm is the Levenberg-Marquardt (LM) algorithm, which combines the advantages of gradient descent and Gauss-Newton's method, handling nonlinear problems well and having a fast convergence speed. The algorithm requires a set of initial values. Then the algorithm will automatically adjust. and Simultaneously, it calculates the residual sum of squares at this point, continuing until the change in the residual sum of squares is less than a certain threshold or the maximum number of iterations is reached. At this point, it finds the residual sum of squares with the smallest value. and It is important to note that the choice of initial values ​​is crucial; poor initial values ​​may lead to convergence to a local minimum or failure to converge. You can set the initial values ​​based on the physical meaning of the problem or by trying several different sets of values.

[0118] (2) Parameter fitting of the second mathematical model:

[0119] Parameters are determined by nonlinear least squares optimization. The optimization objective is to minimize the observed perception wait time. and predicted value Sum of squared residuals:

[0120] ,

[0121] The predicted value model is shown below:

[0122] ,

[0123] in, The predicted value of passengers' perceived waiting time; The observed value of passengers' perceived waiting time; Passengers The actual waiting time; This is the ratio of the intensity of negative emotions to perceived waiting time.

[0124] Fitting method: Nonlinear least squares method , and Using the results fitted with the parameters of the first mathematical model, the Levenberg-Marquardt (LM) algorithm was also used to find the minimum sum of squared residuals. .

[0125] Finally, the bus departure scheme optimization module is used to construct a mixed integer nonlinear optimization model with the objective of minimizing the sum of passenger perceived waiting time cost and bus operating cost, based on the fitted first mathematical model, the fitted second mathematical model, and multi-dimensional data.

[0126] The perceived waiting time cost per passenger is:

[0127] ,

[0128] in, For each individual passenger, the perceived cost of waiting time; This represents the economic cost of perceived waiting time per unit.

[0129] Assuming passengers arrive at a uniform rate while waiting for the vehicle, the perceived waiting time for all passengers is:

[0130] ,

[0131] in, Indicates time window The interval between departures of internal public buses; This represents the perceived waiting time for all passengers. Indicates time window Passengers from the station to station The travel demand; Indicates the length of the time window; Indicates time window Arrival time at the station per unit of time Waiting to be sent to the station The number of passengers on the bus; Indicates the bus arrival station within the time window. The number of times; The integral variable represents the passenger's... Arrival time; Indicates the actual waiting time for passengers;

[0132] Passengers arrive at the station evenly while waiting for the bus. Each passenger's arrival time affects their actual waiting time. The outer integral iterates through all waiting passengers within the time window, while the inner integral calculates the perceived waiting time for each passenger.

[0133] The operating cost of public transportation is determined by both the frequency of vehicle use and the daily operating cost per vehicle. The operating cost of public transportation is as follows:

[0134] (1) Frequency of one-way bus departures, within the time window Inside, the line The frequency of departures in one direction is:

[0135] ,

[0136] in, Indicates time window Length; Indicates time window Internal lines Frequency of departures in one direction; Indicates time window Internal lines Departure intervals; Indicates time window After the departure interval scheduling is completed, there is not enough time to schedule the next bus. The calculation formula is:

[0137] .

[0138] (2) Bus departure frequency for the route: Considering two-way operation, the required bus departure frequency for the route is calculated using the following formula:

[0139] ,

[0140] in, Indicates the line Bus departure frequency.

[0141] (3) Fixed operating costs, routes The fixed operating cost model for public transportation operations is expressed as follows:

[0142] ,

[0143] in, Indicates the line Fixed costs of public transportation operation; Indicates the line Fuel costs for the distance covered by the bus operating unit; Indicates the line The fixed costs incurred by a bus operating for one day; This represents the labor costs incurred by a bus operator in one day. Indicates the length of the line; Indicates the line The number of buses in operation;

[0144] Fuel costs for bus operating units The calculation formula is:

[0145] ,

[0146] in, Indicates the line Fuel consumption per unit distance for bus operation, unit: liters; This indicates the price of oil.

[0147] The objective function of the final mixed-integer nonlinear optimization model is to minimize the total cost. The total cost Represented as:

[0148] ,

[0149] in, This represents the economic cost per unit of perceived waiting time. This represents the total perceived waiting time for all passengers. Indicates time window Length; Indicates time window Internal lines Bus departure intervals; Indicates bus routes The length.

[0150] The constraints of the mixed-integer nonlinear optimization model are:

[0151] ,

[0152] in, This indicates the time required for the bus to travel from departure to its return journey. Indicates the line Standard passenger capacity for public buses; Indicates time window Internal site Arrive at the station Maximum demand.

[0153] like Figure 5 As shown, the lower limit of the departure interval depends on the number of buses scheduled for the route. The number of buses departing at the specified interval within the time window is... The number of buses scheduled for a particular route should not be less than this number; the upper limit of the departure interval depends on the passenger capacity of the bus route, and the passenger capacity of the bus route within the time window is... Therefore, the maximum value of passengers' up and down demand should not exceed this value.

[0154] Considering the specific route conditions, the optimized objective function is integrated as follows:

[0155] ,

[0156] in, Indicates a certain time window Domestic passengers from Departure from station The travel needs of getting off at the station.

[0157] Regarding the aforementioned bus optimization problem, since the model contains integer variables... (Number of vehicles) and continuous variables (Departure interval) is a relatively difficult MINLP problem. To improve efficiency and scalability, this embodiment uses the generalized Benders decomposition algorithm for efficient iterative solution.

[0158] The core idea of ​​GBD is to decompose the original problem into two levels: the main problem and subproblems. Integer decision-making and continuous variable optimization are handled separately, and the optimal solution is continuously approximated through "Benders cut" during iteration. The specific solution process is shown below:

[0159] Step 1: Problem Breakdown

[0160] The decision variables are divided into: the main problem, i.e., integer variables (number of buses on the route). ) and auxiliary variables Sub-problems, namely continuous variables (bus departure intervals within each time window).

[0161] With a single time window For example, let's establish a hierarchical optimization framework:

[0162] (1) Main problem:

[0163] ,

[0164] (2) Subproblems:

[0165] ,

[0166] ,

[0167] in, This represents the operating cost of public transportation, while the other represents an approximate estimate of the perceived waiting cost for passengers. This represents the perceived cost of waiting time for passengers.

[0168] Step 2: Iterative solution core process:

[0169] The solution process flowchart is as follows: Figure 6As shown.

[0170] Step 3 Key Technical Features:

[0171] Cut generation mechanism:

[0172] When the subproblem is feasible, the optimal cut is generated:

[0173] ,

[0174] in, , These are dual variables.

[0175] When a subproblem is infeasible, a feasible cut is generated:

[0176] ,

[0177] Convergence criterion:

[0178] ,

[0179] in, This is the preset tolerance.

[0180] Step 4: Solution Output

[0181] Generate an executable bus departure plan:

[0182] .

[0183] The optimized departure plan sets differentiated departure intervals for different time windows (such as the pre-morning rush hour window, the morning rush hour window, the daytime window, the evening rush hour window, and the nighttime window).

[0184] Through the complete modeling and algorithm solution process described above, we not only achieved a precise characterization of passenger demand changes for bus routes at different times, but also, by leveraging the close coupling between the mathematical model and actual data, accurately calculated the optimal number of buses and departure intervals required for each route within each time window. This result demonstrates clear engineering feasibility and provides a data-driven decision-making basis for dispatch management systems.

[0185] Compared to the traditional static scheduling method based on fixed departure intervals, the solution proposed in this invention not only ensures the economic benefits and resource utilization efficiency of public transportation companies, but also fundamentally improves passenger satisfaction and travel experience, thereby establishing a positive feedback mechanism between passengers and public transportation operators. In the future, this invention can also be extended to various scenarios such as subway connections, cross-line intermodal transport, and nighttime loop routes, and even to other scenarios with waiting time costs (such as train station ticket halls and airport security checks).

[0186] Example 2:

[0187] This embodiment also provides a method for optimizing bus departure intervals based on the accumulation of negative waiting emotions and perceived time dilation. The steps include: constructing a first mathematical model representing the relationship between passengers' actual waiting time and passengers' negative emotions; simultaneously, based on the first mathematical model, constructing a second mathematical model representing the relationship between passengers' negative emotions and passengers' perceived waiting time; obtaining multi-dimensional data on the waiting process of passengers on the target bus route through a revealed preference survey, including: actual waiting time, subjectively perceived waiting time, passengers' negative emotion scores, and travel demand per unit time; fitting the first and second mathematical models; based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, constructing a mixed-integer nonlinear optimization model with the objective of minimizing the sum of passengers' perceived waiting time cost and bus operating cost, and solving the established mixed-integer nonlinear optimization model using the generalized Benders decomposition algorithm to output a bus departure scheme that satisfies operational constraints and service quality.

[0188] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, characterized in that, include: The system includes a module for quantifying perceived waiting time, a data acquisition module, a parameter fitting module, and a bus departure plan optimization module. The perceived waiting time quantification module is used to construct a first mathematical model representing the relationship between passengers' actual waiting time and passengers' negative emotions; simultaneously, based on the first mathematical model, a second mathematical model representing the relationship between passengers' negative emotions and passengers' perceived waiting time is constructed; the constructed first mathematical model includes: ， in, Passengers wait continuously Real-time intensity of negative emotions at any given time unit; It is a continuous time variable calculated from the starting point of the wait; , This is the first parameter to be estimated; The second mathematical model constructed includes: ， in, Passengers wait continuously Instantaneous perceived waiting time within a unit of time; This is the second parameter to be estimated; The data acquisition module is used to obtain multi-dimensional data on passenger waiting processes for the target bus route through a display preference survey. This multi-dimensional data includes: actual waiting time, subjectively perceived waiting time, passenger negative emotion ratings, and travel demand per unit time. Perceived waiting time accumulates as actual waiting time increases, and the passenger's perceived waiting time throughout the entire waiting process is: ， The perceived waiting time cost per passenger is: ， in, For each individual passenger, the perceived cost of waiting time; This represents the economic cost per unit of perceived waiting time. Passengers arrive at a uniform rate while waiting for the vehicle, and the perceived waiting time for all passengers is: ， in, Indicates time window The interval between bus departures within the city; This represents the perceived waiting time for all passengers. Indicates time window Passengers inside the station Arrive at the station The travel demand; Indicates time window Length; Indicates time window Arrival time at the station per unit of time Waiting to be sent to the station The number of passengers on the bus; Indicates the bus arrival station within the time window. The number of times; The integral variable represents the passenger's... Arrival time; This indicates the actual waiting time for passengers; The arrival time of each passenger will affect their actual waiting time. The outer integral iterates through all waiting passengers within the time window, and the inner integral calculates the perceived waiting time for each passenger. The parameter fitting module is used to fit the first mathematical model and the second mathematical model; The bus departure scheme optimization module is used to construct a mixed integer nonlinear optimization model based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, with the goal of minimizing the sum of passenger perceived waiting time cost and bus operating cost. The module then uses the generalized Benders decomposition algorithm to solve the established mixed integer nonlinear optimization model and outputs a bus departure scheme that satisfies operational constraints and service quality.

2. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation as described in claim 1, characterized in that, The workflow of the parameter fitting module includes: First mathematical model parameter fitting: Parameters are determined by nonlinear least squares optimization. and The optimization objective is to minimize the observed negative sentiment values. and predicted value Sum of squared residuals: ， The predicted value is defined by the integral model: ， in, The model predicts passengers The negative emotion value; For passengers Observations of accumulated negative emotions; Passengers The actual waiting time; and These are the parameters that need to be fitted; Second mathematical model parameter fitting: Parameters are determined by nonlinear least squares optimization. The optimization objective is to minimize the observed perception wait time. and predicted value Sum of squared residuals: ， The predicted value models include: ， in, The predicted value of passengers' perceived waiting time; The observed value of passengers' perceived waiting time; Passengers The actual waiting time; This is the ratio of the intensity of negative emotions to perceived waiting time.

3. The bus departure interval optimization system based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, as described in claim 1, is characterized in that... The bus operating costs include: One-way bus departure frequency, within the time window Inside, the line The frequency of departures in one direction is: ， in, Indicates time window Length; Indicates time window Internal lines Frequency of departures in one direction; Indicates time window Internal lines Bus departure intervals; Indicates time window After the departure interval scheduling is completed, there is not enough time to schedule the next bus. The calculation formula is: ， The required frequency of bus departures for a given route, considering two-way operation, is calculated using the following formula: ， in, Indicates the line Bus departure frequency; Operating fixed costs, routes The fixed operating cost model for public transportation operations is expressed as follows: ， in, Indicates the line Fixed costs of public transportation operation; Indicates the line Fuel costs for the distance covered by the bus operating unit; Indicates the line The fixed costs incurred by a bus operating for one day; This represents the labor costs incurred by a bus operator in one day. Indicates the length of the line; Indicates the line The number of buses in operation; Fuel costs for bus operating units The calculation formula is: ， in, Indicates the line Fuel consumption per unit distance for bus operation, unit: liters; This indicates the price of oil.

4. A method for optimizing bus departure intervals based on the accumulation of negative emotions while waiting for a bus and perceived time dilation, the method being applied to the system described in any one of claims 1-3, characterized in that the steps... include: A first mathematical model is constructed to characterize the relationship between passengers' actual waiting time and passengers' negative emotions; at the same time, based on the first mathematical model, a second mathematical model is constructed to characterize the relationship between passengers' negative emotions and passengers' perceived waiting time. Multi-dimensional data on passenger waiting processes for target bus routes were obtained through a display preference survey. The multi-dimensional data included: actual waiting time, subjectively perceived waiting time, passenger negative emotion rating, and travel demand per unit time. Fit the first mathematical model and the second mathematical model; Based on the fitted first mathematical model, the fitted second mathematical model, and the multi-dimensional data, a mixed-integer nonlinear optimization model is constructed with the goal of minimizing the sum of passenger perceived waiting time cost and bus operating cost. The generalized Benders decomposition algorithm is used to solve the established mixed-integer nonlinear optimization model, and the bus departure scheme that satisfies operational constraints and service quality is output.

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