A method and system for urban multi-modal passenger transport coordinated scheduling based on MPC and double-layer planning fusion framework

Abstract

The application discloses a kind of urban multimodal passenger transport collaborative deployment method and system based on MPC and double-layer planning fusion framework, belong to intelligent transportation technical field. Including: obtaining passenger selection characteristic data and each traffic mode transport capacity parameter;Adopting multinomial Logit model constructs passenger selection utility function, determines each traffic mode utility value;Build double-layer planning scheduling model that is integrated into model predictive control (MPC) strategy, and according to current number of people stranded, number of people arrived and evacuation number of people, predict next time period number of people stranded;Using NSGA-II algorithm to solve upper model, based on state transition equation rolling optimization, obtain each traffic mode scheduling scheme.The application realizes multimodal transport capacity dynamic collaborative scheduling, effectively reduces the number of people stranded in hub station, shortens the average waiting time of passenger and reduces operating cost.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, and more specifically to a method and system for coordinated dispatch of urban multimodal passenger transport based on an MPC and two-layer planning fusion framework. Background Technology

[0002] In recent years, with the continuous advancement of urbanization and the significant improvement in residents' quality of life, the travel demand of urban residents has continued to grow rapidly. Among these demands, the passenger dispersal needs of large transportation hubs are particularly pronounced, exhibiting clear dynamic fluctuations. Large integrated transportation hubs are crucial nodes in the urban transportation system, integrating multiple modes of transportation, organizing passenger transfers, and efficiently distributing passenger and freight traffic. Their operational efficiency directly impacts not only the travel experience of passengers but also significantly affects the operational stability of the entire urban transportation network.

[0003] However, the current transportation hub distribution system faces challenges such as the diversity of transportation modes, the dynamic nature of passenger flow demand, and insufficient collaborative management. On the one hand, the internal and external spaces of transportation hubs are limited, and the capacity and scheduling flexibility of various modes of transportation vary significantly. On the other hand, passenger travel demand exhibits strong temporal variability, especially during holidays, peak commuting periods, or emergencies, when passenger flow changes dramatically. This fluctuation makes it difficult for traditional static scheduling strategies to accurately match transportation resources with actual demand, often resulting in unreasonable allocation of transportation resources or untimely responses, easily leading to congestion and delays in and around the hub. Furthermore, most transportation hubs currently lack effective coordination between different modes of transportation, resulting in insufficient connections and low transfer efficiency, increasing the uncertainty of passenger travel and directly reducing travel efficiency and comfort.

[0004] Therefore, how to develop a system that can adapt to demand fluctuations in real time and achieve coordinated scheduling among different modes of transportation is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a method and system for coordinated dispatch of urban multimodal passenger transport based on the MPC and two-level planning fusion framework. It introduces a two-level planning model and combines the concept of model predictive control (MPC) to solve the limitation of some previous static optimization models that can only cope with fixed situations and are difficult to flexibly adapt to real-world changes.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: On the one hand, this invention provides a method for coordinated dispatching of urban multimodal passenger transport based on an MPC and two-layer planning fusion framework, including: Obtain passenger selection feature data and capacity parameters for each mode of transportation; Based on the passenger choice feature data, a multinomial Logit model is used to construct a passenger choice utility function and determine the utility value corresponding to each mode of transportation. A two-layer planning and scheduling model integrating model predictive control modeling strategy is constructed. The two-layer planning and scheduling model includes an upper-layer multi-objective optimization model and a lower-layer passenger selection and evacuation model. The upper-layer multi-objective optimization model aims to minimize the number of people stranded in the hub station, minimize the average passenger waiting time, and minimize the total operating cost of each mode of transportation. It uses the capacity parameters of each mode of transportation as decision variables and constructs a multi-objective optimization function and constraints. The lower-layer passenger selection and evacuation model calculates the selection probability of each mode of transportation in the current time period based on the capacity parameters and utility values ​​of each mode of transportation, and determines the number of people to be evacuated for each mode of transportation based on the selection probabilities. A state transition equation for the number of stranded people is constructed. The state transition equation predicts the number of stranded people in the next period based on the number of stranded people, the number of arrivals, and the number of evacuations in the current period. The NSGA-II genetic algorithm is used to solve the upper-level optimization model. Based on the state transition equation, rolling time-domain optimization is performed to obtain scheduling schemes for each mode of transportation that meet the predetermined optimization objectives.

[0007] Preferably, the expression for the passenger's choice utility function is:

[0008] in, U i Choose a mode of transportation for passengers The utility value is: A = passenger age, G = passenger gender, S = passenger income, B = passenger carrying large luggage, and D = passenger travel distance. To choose a mode of transportation Required travel time, To choose a mode of transportation The required costs, To choose a mode of transportation Required walking distance, W c P represents the weather conditions, and P represents the peak period conditions. , , , , , , , , , This represents the influence coefficient of the corresponding characteristic variable.

[0009] Preferably, the multi-objective optimization function and constraints are as follows:

[0010] Where, x (t) Let a be the number of people waiting inside the station during time period t. (t) The number of new arrivals at the station during time period t. Let I represent the number of people evacuated by mode i during time period t, and let I be the set of modes of transportation. For the fixed cost of mode i, Let θ represent the variable cost of mode i, and θ represent the time period length. Let be the scheduling frequency of traffic mode i during time period t. The total waiting time for passengers who did not leave the hub station during time period t. ρ represents the average waiting time for mode i during time period t; i For the full load factor constraint, λ i C represents the passenger arrival rate for mode i. i For the number of service counters, μ i For service rate.

[0011] Preferably, the evacuation model selected by the lower-level passengers specifically includes: Obtain the average waiting time for each mode of transportation mentioned in the previous time period; The average waiting time is weighted using the waiting time penalty value, and the weighted result is added to the utility value to obtain the set utility value of each mode of transportation in the current time period; The selection probability is determined using the Logit function based on the set utility value. The number of people to be evacuated for each mode of transportation is determined based on the chosen probabilities.

[0012] Preferably, the formula for calculating the utility value is:

[0013] in, It is the waiting time penalty value. Transportation mode for time period (t-1) Average waiting time; The formula for calculating the probability of selection is:

[0014] In the formula: Choose a mode of transportation for time period t The probability of.

[0015] The number of people evacuated by mode i at each time period is as follows:

[0016] in, For transportation Capacity conversion factor; Transportation mode during time period t Scheduling frequency, For transportation Single transport capacity, Select transportation mode for passengers during the specified time period The probability of.

[0017] Preferably, the state transition equation for the number of stranded people is as follows:

[0018] in, The predicted number of stranded people in the (t+1) period. Let t be the initial number of people remaining in the area. The number of newly arriving passengers during time period t. This represents the sum of the actual number of people evacuated from all modes of transportation during time period t.

[0019] Preferably, the NSGA-II genetic algorithm is used to solve the upper-level optimization model, including: Randomly generate the initial population within the scheduling frequency constraint; For each individual in the population, calculate the objective function values ​​for the number of stranded individuals, total operating costs, and average waiting time, and determine the fitness value. A non-dominated ranking strategy is used to hierarchically divide the fitness values ​​of all individuals in the population. Calculate the crowding distance between individuals within the same non-dominated hierarchy; Based on non-dominant hierarchy and crowding distance, a tournament selection strategy is used to select individuals for crossover and mutation operations to generate offspring populations. The parent and offspring populations are merged, and the non-dominated sorting and crowding distance calculations are performed again to select the next generation population. Repeat the above iterative process until the termination condition is met, and output the Pareto optimal solution set.

[0020] On the other hand, the present invention provides an urban multimodal passenger transport collaborative dispatch system based on an MPC and two-layer planning fusion framework, comprising: The data acquisition module is used to acquire passenger selection feature data and capacity parameters of each mode of transportation; The utility function construction module is used to construct passenger choice utility functions based on the passenger choice feature data using a multinomial Logit model, and to determine the utility values ​​corresponding to each mode of transportation. The upper-level optimization module is used to construct an upper-level multi-objective optimization model. The upper-level multi-objective optimization model aims to minimize the number of people stranded in the hub station, minimize the average waiting time of passengers, and minimize the total operating cost of each mode of transportation. It uses the capacity parameters of each mode of transportation as decision variables and constructs a multi-objective optimization function and constraints. The lower-level evacuation module is used to construct a lower-level passenger selection evacuation model. The lower-level passenger selection evacuation model calculates the selection probability of each mode of transportation in the current time period based on the capacity parameters and utility values ​​of each mode of transportation, and determines the number of people to be evacuated for each mode of transportation based on the selection probability. The state prediction module is used to construct the state transition equation for the number of stranded people. The state transition equation predicts the number of stranded people in the next period based on the number of stranded people, the number of arrivals, and the number of evacuations in the current period. The solution module is used to solve the upper-level optimization model using the NSGA-II genetic algorithm, and to perform rolling time-domain optimization based on the state transition equation to obtain scheduling schemes for each mode of transportation that meet the predetermined optimization objectives.

[0021] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for coordinated dispatching of urban multimodal passenger transport based on the MPC and two-layer planning fusion framework. By constructing a two-layer planning framework that incorporates model predictive control strategy, the upper-layer multi-objective optimization model achieves a Pareto optimal trade-off between the number of stranded passengers, passenger waiting time, and operating costs. The lower-layer evacuation allocation model dynamically selects and simulates based on passenger characteristics, environmental information, and real-time waiting conditions, realizing interactive coordination between supply and demand. The state transition equation for the number of stranded passengers incorporates the time dimension into the optimization process, enabling the scheduling scheme to predict the evolution trend of passenger flow in advance and perform rolling optimization, overcoming the deficiency of static schemes lacking time adaptability. The use of a multi-objective evolutionary algorithm to solve the model can provide decision-makers with a set of optional scheduling schemes under different objective weights, providing a scientific basis for capacity allocation in actual operation. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0023] Figure 1 A schematic diagram of the overall technical route of the scheduling method provided by the present invention.

[0024] Figure 2 A diagram illustrating alternative travel options for passengers.

[0025] Figure 3 This is a plot of the MNL regression coefficients.

[0026] Figure 4 This is a heatmap of variable coefficients.

[0027] Figure 5 This is a heatmap of the coefficients of another variable.

[0028] Figure 6 The curve showing the optimal operating cost as a function of iteration generations.

[0029] Figure 7 The curve shows the optimal average waiting time as a function of the number of iterations.

[0030] Figure 8 The curve shows the final number of people remaining as a function of the number of iterations.

[0031] Figure 9 To optimize the Pareto optimal frontier distribution for multi-objective purposes.

[0032] Figure 10 To predict the number of people using each mode of transportation at a given time step.

[0033] Figure 11 To predict changes in the number of stranded people. Detailed Implementation

[0034] 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.

[0035] This invention discloses a method for coordinated dispatching of urban multimodal passenger transport based on a fusion framework of MPC and two-layer planning, such as... Figure 1 As shown, it includes: Obtain passenger selection feature data and capacity parameters for each mode of transportation; Based on the passenger choice feature data, a multinomial Logit model is used to construct a passenger choice utility function and determine the utility value corresponding to each mode of transportation. A two-layer planning and scheduling model integrating model predictive control modeling strategy is constructed. The two-layer planning and scheduling model includes an upper-layer multi-objective optimization model and a lower-layer passenger selection and evacuation model. The upper-layer multi-objective optimization model aims to minimize the number of people stranded in the hub station, minimize the average passenger waiting time, and minimize the total operating cost of each mode of transportation. It uses the capacity parameters of each mode of transportation as decision variables and constructs a multi-objective optimization function and constraints. The lower-layer passenger selection and evacuation model calculates the selection probability of each mode of transportation in the current time period based on the capacity parameters and utility values ​​of each mode of transportation, and determines the number of people to be evacuated for each mode of transportation based on the selection probabilities. A state transition equation for the number of stranded people is constructed. The state transition equation predicts the number of stranded people in the next period based on the number of stranded people, the number of arrivals, and the number of evacuations in the current period. The NSGA-II genetic algorithm is used to solve the upper-level optimization model. Based on the state transition equation, rolling time-domain optimization is performed to obtain scheduling schemes for each mode of transportation that meet the predetermined optimization objectives.

[0036] Furthermore, the landside transportation service system of large railway hubs comprises various forms of transportation, including buses, subways, taxis, and ride-hailing services. In actual travel, the travel environment upon arrival at a large railway hub can influence a passenger's travel decisions, such as weather conditions and whether it is peak season. In addition, differences in passenger attributes are also significant factors influencing travel mode selection, such as age, income level, luggage carrying capacity, and affordability, all of which affect passengers' weighing of factors like travel efficiency, economic cost, and comfort to varying degrees. Therefore, it is evident that the choice behavior of different types of passengers among various transportation modes exhibits significant individual heterogeneity in different scenarios, and their choice probabilities and preference structures may vary considerably. Thus, it is necessary to conduct an in-depth analysis of passenger travel mode selection behavior based on multi-source factors to more accurately understand demand-side characteristics and predict passenger choices.

[0037] The embodiments of the present invention aim to determine the passenger choice utility function, design a questionnaire combining SP and RP surveys, analyze the collected questionnaire data to analyze the passenger choice tendency on the demand side, and explore the degree of influence of different influencing factors on passenger choices under different travel scenarios.

[0038] Specifically, in characterizing passenger transportation mode selection behavior, the utility function is a core component of discrete choice models, used to quantify passengers' subjective preferences for each option. The utility function is generally considered a potential evaluation mechanism; when weighing multiple transportation modes, passengers tend to choose the option with the highest utility value. This embodiment constructs the passenger choice utility function from three aspects: environmental characteristics, passenger characteristics, and transportation mode characteristics.

[0039] Environmental characteristics include weather conditions and peak-hour conditions. Weather conditions are categorized into good weather and severe weather. Peak-hour conditions are categorized into peak and off-peak periods. In severe weather conditions such as heavy rain, strong winds, or low visibility, the risk of road traffic accidents increases, vehicle speeds decrease, and traffic efficiency is significantly reduced. During morning and evening rush hours, traffic congestion and long queues are common on main urban roads and around transportation hubs, further exacerbating traffic congestion. In such environments, taxi and ride-hailing drivers are typically less willing to operate, resulting in fewer vehicles available for service. Passengers may experience higher fares for ride-hailing services, and waiting times and journey times may also increase, potentially reducing the likelihood of passengers choosing ride-hailing or taxi services.

[0040] Passenger characteristics include gender, age, income, carrying large luggage, and travel distance. Men and women may have different travel preferences; men may have a wider acceptable walking distance, and women are less likely to choose options requiring long walks. Different age groups have different cognitive levels, which may also affect their choice of transportation. For example, minors may not have mobile phones, and the elderly may not use ride-hailing apps, so both age groups are less likely to choose ride-hailing services. Different income groups also significantly influence their choice of transportation. Low-income individuals may adjust their travel budgets based on their circumstances. For instance, in good weather, with short distances and fewer passengers at hubs during off-peak hours, they are more likely to choose public transportation (buses or subways), while with large luggage or longer distances, they may prefer ride-hailing services or taxis.

[0041] The characteristics of a mode of transportation include the travel time, cost, and walking distance required for that mode of transport. Travel time and cost vary depending on environmental conditions and the travel distance within the passenger's own characteristics. For example, both travel time and cost increase in inclement weather compared to good weather. The walking distance for each mode of transport primarily varies based on changes in the passenger's own travel distance. For instance, when a passenger's travel distance increases, taking a bus or subway requires more transfers, thus increasing the walking distance.

[0042] Based on the various features described above, the passenger choice utility function is constructed as follows:

[0043] In the formula: Select transportation mode for the set passengers Utility value For the passenger's own characteristic function, For the characteristic function of the mode of transportation, For environmental characteristic functions, This is a collection of various modes of transportation.

[0044] The passenger's own characteristic function is specifically composed as follows:

[0045] In the formula: For passenger age, For passenger gender, For passenger revenue, Information on whether passengers are carrying large luggage (whether they are carrying it or not). For passenger travel distance, These are the coefficients corresponding to each category.

[0046] The specific components of the transportation mode characteristic function are as follows:

[0047] In the formula: To choose a mode of transportation Required travel time To choose a mode of transportation Required fees To choose a mode of transportation Required walking distance Corresponding coefficients for each category The environmental characteristic function is specifically composed as follows:

[0048] In the formula: Weather conditions (good or bad) This refers to peak period conditions (peak or off-peak period). In summary, passengers choose their mode of transportation. The utility function is specifically structured as follows:

[0049] In travel behavior research, there are two commonly used survey methods for analyzing passengers' choice tendencies and preferences. Based on the authenticity of the survey situation, they are divided into Revealed Preference (RP) surveys and Stated Preference (SP) surveys.

[0050] RP surveys are a method of reflecting individuals' preferences and decision-making logic by obtaining their actual choices during travel. RP surveys are typically based on travelers' past travel activities, collecting information such as travel modes, routes, times, and costs under specific circumstances through questionnaires, movement trajectory data, and other means. Because the data comes from real-world behavior, RP surveys can accurately reflect individuals' behavioral responses under real-world constraints and have strong behavioral authenticity. However, due to limitations imposed by the real-world transportation supply structure and travel environment, they cannot cover unexplored options or extreme scenarios.

[0051] SP (Special Purpose) surveys present respondents with several travel options through a series of simulated travel scenarios, requiring them to choose under simulated conditions. This allows the survey to understand their preferences regarding factors such as travel cost, time, comfort, and weather conditions. Unlike RP (Responsible Purpose) surveys, SP does not rely on respondents' existing travel experiences. Instead, it constructs scenario combinations by controlling variables to explore potential behavioral responses. The advantage of this method is its ability to analyze response mechanisms to new service models, policy adjustments, or extreme travel conditions, contributing to policy prediction and forward-looking research. However, because it is based on subjective judgment, it may be influenced by respondents' level of understanding or psychological expectations. Therefore, it is crucial to ensure reasonable question design and clear variable descriptions during the design phase to enhance the credibility of the survey results.

[0052] Passengers face many different scenarios when choosing a mode of transportation after leaving a transportation hub. Weather conditions and peak hours are uncertain, and the passenger's own travel distance is also uncertain. Therefore, the design of the questionnaire requires the use of SP (Special Purpose) surveys. By setting clear travel environments and travel distances, and providing clear information on four modes of transportation, passengers can make their choices.

[0053] The transportation mode selection scenarios faced by travelers after leaving a transportation hub are highly uncertain, including the diversity and unpredictability of factors such as weather conditions, peak traffic hours, and distance to their destination. Therefore, this embodiment uses the Stated Preference (SP) survey method in its questionnaire design. By constructing several scenarios with clearly defined travel environments (such as weather type and travel time) and travel distances, and providing attribute information (including cost, travel time, and price) for four transportation modes in each scenario, respondents are guided to make choices under simulated conditions, thereby obtaining their potential preferences and behavioral tendencies in different travel scenarios.

[0054] In this embodiment, the questionnaire design first includes a basic information collection section, covering passengers' gender, age, and income. Gender is divided into "male" and "female," age is divided into four levels based on age stage, and income level is also divided into four tiers, categorized by monthly income range, to identify differences in travel preferences among different economic groups. The specific ranges are shown in Table 1.

[0055] Table 1. Passenger Basic Attribute Survey

[0056] In the travel scenario setting section, based on the influencing factors of actual traffic behavior, scenario attributes were set up consisting of three variables: weather conditions, peak period conditions, and travel distance. As shown in Table 2 below, weather conditions are divided into "good" and "bad" categories; peak period conditions are divided into "peak period" and "off-peak period"; and travel distance is set as four typical scenarios, namely 5 kilometers, 10 kilometers, 15 kilometers, and 20 kilometers.

[0057] Table 2 Travel Situation Categories

[0058] For each travel scenario, the questionnaire provides detailed information on four modes of transportation, including estimated travel time, cost, and walking distance for each mode, presented graphically on the page, such as... Figure 2 As shown, this helps respondents make a choice based on a clear understanding of the attributes of the options.

[0059] To reduce the workload and improve respondent efficiency while ensuring representativeness of the scenarios, an orthogonal experimental design was used for the scenario combination section. Three travel scenario variables were orthogonally paired to obtain 16 representative travel scenarios, requiring a total of 16 scenario-based questions. Considering the time required for the questionnaire survey and the authenticity of the data, the 16 questions were divided into two questionnaires, A and B, each with 11 questions: three questions collecting basic passenger information and eight travel scenario-based questions. Questionnaires were distributed, and the data was collected to provide efficient and well-structured data support for subsequent preference modeling.

[0060] The questionnaires were distributed and collected online, with 160 questionnaires of each type (A and B) collected. The data were integrated according to the travel scenario of each question. Eight data points were extracted from each returned questionnaire, as shown in Table 3 below, for a total of 2560 data points.

[0061] Table 3 Example of integrated data

[0062] The meanings of the corresponding values ​​for each variable are shown in Table 4 below: Table 4 Explanation of the meaning of variable values

[0063] First, data preprocessing and variable setting were carried out. The six attributes of "gender", "weather conditions", "peak season", "luggage", "age" and "income" were converted into categorical variables. At the same time, the four continuous variables of "travel time", "cost", "walking distance" and "travel distance" were numerically processed and standardized to eliminate the influence of the difference in variable units and ensure that the regression coefficients are comparable.

[0064] Subsequently, to accommodate the structural requirements of the input data in the multinomial Logit model, dummy variables were used to expand the categorical variables, and a baseline class was set to prevent the dummy variables from falling into perfect collinearity. The processed data contains a large number of 0-1 type variables and standardized numerical variables, forming the model input matrix X.

[0065] Secondly, multicollinearity testing and variable selection were conducted. Before formal modeling, to improve model stability and ensure the reliability of parameter estimation, multicollinearity testing was performed on all explanatory variables. By calculating the variance inflation factor (VIF), variables with VIF values ​​exceeding 10 were identified and removed to avoid redundant information interfering with the model's fitting accuracy and significance assessment.

[0066] The values ​​of the variable VIF are shown in the following table (5 tables): Table 5 VIF values

[0067] The decision to retain a variable is based on whether its VIF value is greater than 10. The variables to be removed are travel distance and cost. The processed variable set is then used as the final regression input.

[0068] Next, model specification and parameter estimation were performed. The model was constructed using the MNL Logit model module from the statsmodels library, with the mode of transportation chosen by passengers as the response variable Y, and the standardized and dummy variable processed X as the explanatory variables. The model used maximum likelihood estimation for parameter fitting, and the Newton-Raphson optimization method was selected to accelerate the convergence process. The maximum number of iterations was set to 2000 to ensure that the model could still converge stably when the sample size was large or the variable dimensionality was high.

[0069] Finally, significance analysis and result visualization were performed. After model fitting, the regression coefficients, standard errors, Z-statistics, and corresponding p-values ​​of each explanatory variable were extracted for different modes of transportation to further determine the statistical significance of each variable. A p-value less than 0.05 was used as the criterion to select variables that significantly influenced individual choice behavior in at least one mode of transportation. To improve the interpretability of the results, a heatmap of the regression coefficients of significant variables was plotted to show the marginal effect strength of each variable across all alternatives.

[0070] Model execution results: 1) A summary of the basic model is shown in Table 6: Table 6 Summary of MNL Models

[0071] Interpretation of key statistical indicators: The dependent variable (Dep.Variable) is "mode", which represents the types of travel modes available to passengers. It includes four categories of categorical response variables: bus, taxi, ride-hailing, and subway.

[0072] The sample size (No. Observations) is 2560, indicating that the model is estimated based on 2560 valid observation samples, and the data size is representative.

[0073] The residual degrees of freedom (Df Residuals) are 2524, representing the degrees of freedom after deducting the 33 parameters used for estimation in the model. This indicates that the number of model parameters is within a reasonable range compared to the sample size, avoiding the risk of overfitting.

[0074] The model method is Maximum Likelihood Estimation (MLE), which is the standard estimation method for multinomial Logit models. It estimates the marginal effects of each variable by maximizing the probability of the observed data occurring.

[0075] The pseudo-determination coefficient (Pseudo R-squared) was 0.5376, indicating the degree of improvement of the model compared to the empty model (without explanatory variables). While it cannot be compared to the traditional R-squared in linear regression... 2 While a direct comparison is not possible, this numerical value already demonstrates the model's strong explanatory power for individual choice behavior. According to McFadden's judgment criteria (pseudo-R...),... 2 A score >0.2 indicates a good fit, meaning the current model is performing at a high level.

[0076] The log-likelihood value is -1628.0, which indicates how well the model fits the sample data under the current parameters. The larger the value (the closer to 0), the closer the model is to the true data distribution.

[0077] The log-likelihood value (LL-Null) of the empty model is -3520.8, which corresponds to the model without any explanatory variables. The improvement in explanatory power can be observed by comparing it with the current model.

[0078] The significance level p-value (LLR p-value) of the log-likelihood ratio test is 0.000. A p-value less than 0.05 indicates that the model is significant. Therefore, the model is statistically significantly better than the empty model without explanatory variables, which verifies that the overall model fit is statistically significant. The null hypothesis (the explanatory variables have no effect on the dependent variable) is rejected.

[0079] The convergence status is displayed as True, indicating that the model has successfully completed the estimation process under the specified number of iterations and convergence conditions, demonstrating that the algorithm runs stably and the estimation results are reliable.

[0080] 2) Significance coefficient heatmap

[0081] In a heatmap, the intensity of colors reflects the direction and significance of a variable's influence across different categories, making it easy to visually identify dominant variables. Below is an analysis of the main influencing variables using a heatmap: The variable "time" mainly reflects its impact on the choice of subway mode. Data shows that when travel time increases, passengers' tendency to choose the subway decreases significantly (coefficient of -4.25), while the coefficient for ride-hailing services is close to 0, and the coefficient for taxis is 0.21. This indicates that passengers are less likely to choose the subway when they need to travel for a long time, which may be related to the comfort and ease of transfer of the subway.

[0082] "Walking distance" is one of the variables with the greatest impact. Figure 3 As can be seen, the regression coefficients for "walking distance" for ride-hailing and taxi are -5.08 and -5.48, respectively, showing a strong negative relationship. This indicates that increasing walking distance will significantly inhibit passengers' choice of these two modes of transportation, meaning that passengers who choose taxis and ride-hailing are less willing to walk longer distances than those who choose buses and subways.

[0083] In the "gender" variable, only "gender_1" (male) is significant, and its impact on each mode of transportation is relatively limited. Based on the values ​​of transportation modes corresponding to gender, it can be found that men are slightly more likely to choose to take a taxi than to choose a bus or subway.

[0084] In the "Weather Conditions" variable, only "Weather Condition_1" (severe weather) has a significant impact on the choice of the four modes of transportation. Specifically, it has a positive incentive effect on the choice of ride-hailing services and taxis, with a coefficient of 1.76 for ride-hailing services and 1.65 for taxis. This indicates that in severe weather, passengers are more inclined to choose transportation modes that reduce outdoor exposure and improve travel comfort. In contrast, the impact of the subway on this variable is weaker, with a coefficient of only 0.13. This may be because its transfers still require walking and entering the station hall, limiting its attractiveness to passengers in severe weather.

[0085] In the "Peak Hour Situation" variable, only the "Peak Hour_1" (Peak Hour) variable is significant. Specifically, it shows a significant inhibitory effect on ride-hailing services, with coefficients of -1.39 and -1.77 for ride-hailing and taxis respectively, reflecting that passengers are more inclined to avoid these modes of transportation when faced with potential road congestion and difficulty in hailing a taxi during peak hours. In contrast, the subway, due to its independent tracks and high operating frequency, maintains better traffic efficiency during peak hours, thus its coefficient under this variable is positive (+0.33), indicating its substitutive advantage.

[0086] To analyze the collected questionnaire data and examine passengers' travel mode selection behavior after exiting railway transportation hubs, this embodiment constructs a multi-class prediction model based on multinomial logistic regression, implemented using the scikit-learn toolkit in Python. The model uses the passenger's chosen mode of transportation as the response variable and their individual attributes and travel environment variables as explanatory variables to characterize the influence of different factors on travel decisions.

[0087] First, the raw data was imported and missing values ​​were cleaned to ensure the integrity of the sample data. In terms of data structure, the feature variables to be fitted by the model were divided into two categories: one category is categorical variables, including "weather conditions", "whether luggage is carried", "whether it is peak season", "age" and "income level"; the other category is continuous variables, including four indicators: "travel distance", "travel time", "travel cost" and "walking distance".

[0088] In the preprocessing stage of modeling, categorical and numerical variables are encoded and standardized respectively. Categorical variables are converted into 0-1 indicator variables using a One-Hot Encoder to avoid the class order misleading the model structure; numerical variables are standardized using a Standard Scaler to ensure that each feature dimension has a similar numerical scale, which helps improve model stability and estimation efficiency. All of the above preprocessing processes are encapsulated in a Column Transformer and integrated with the classifier through a pipeline mechanism, enabling coordinated operation of feature engineering and modeling processes.

[0089] For model selection, considering that the target variables are multi-class and mutually exclusive, a logistic regression classifier under the One-vs-Rest strategy was chosen, and a maximum number of iterations was set to ensure model convergence. To evaluate the model's generalization ability on the overall sample, a Repeated Stratified K-Fold strategy was adopted, repeating the 10-fold cross-validation three times, and the average accuracy of the model was calculated.

[0090] After model training, the classifier coefficients for each category are extracted, the feature-category two-dimensional coefficient matrix is ​​reconstructed, and the variable names and transportation modes are re-labeled to facilitate result interpretation. Subsequently, a heatmap is drawn to visualize the degree and direction of influence of each explanatory variable on the preference for different transportation modes, providing intuitive support for behavioral explanation.

[0091] The final model fitting results are shown in Table 7: Table 7 Results of the Multinomial Logistic Regression Model

[0092] The model was evaluated using repeated stratified 10-fold cross-validation, achieving an average accuracy of 99.9%, indicating high prediction accuracy in multi-category travel mode identification tasks. Furthermore, its accuracy standard deviation was only 0.2%, demonstrating stable performance across different data partitions and exhibiting good generalization ability and robustness.

[0093] As shown in Table 8 and Figure 4 Here is a table of influence coefficients and a heatmap for each variable: Table 8. Variable Influence Coefficient Table

[0094] Analysis of regression coefficient results for model variables: Figure 2 The image shows the influence of each variable on different travel mode choices in a multinomial logistic regression model (measured by standardized regression coefficients), visualized using a heatmap. Darker colors indicate a more significant impact of the variable on the corresponding travel mode; red represents a positive effect, and blue represents a negative effect. The results are analyzed below for different variable categories.

[0095] 1) Passenger's own characteristics

[0096] Among the passenger's own characteristic variables, only travel distance has a significant impact on travel mode selection. The other characteristic variables have a smaller impact and lower coefficient values, but certain trends can still be observed: Analyzing the "gender" variable, the coefficients for women choosing taxis and ride-hailing services are -0.05 and -0.13 respectively, both negative, while the coefficients for choosing buses and subways are 0.02 and 0.16 respectively, both positive. In contrast, the coefficients for men choosing ride-hailing services and taxis are -0.04 and 0.09 respectively, while the coefficients for choosing buses and subways are 0.00 and -0.13 respectively, both negative. This indicates that men are more likely than women to choose taxis and less likely to choose public transportation.

[0097] Analyzing the "age" variable reveals that the younger group (under 25 years old) has the highest coefficients for taxis and ride-hailing services compared to other age groups (0.06 and 0.05), indicating a preference for convenient and personalized travel options. Meanwhile, the group over 36 years old has a slightly higher probability of using public transportation than the group under 36 years old.

[0098] Analyzing the "income" variable reveals that the coefficient for high-income groups (income over 10,000 yuan) on ride-hailing services is the highest at 0.07 compared to other income groups, indicating that economic capacity can enhance the willingness to choose high-cost travel options. In contrast, the coefficient for low-income groups (income 0-3,000 yuan / month) on ride-hailing services is the lowest at -0.08, which aligns with expected economic adaptive behavior.

[0099] Analyzing the "luggage" variable reveals that the coefficient for taxis increases from -0.06 to 0.05 when passengers are carrying large luggage, which aligns with the expectation that passengers carrying large luggage are more willing to choose convenient and fast travel methods.

[0100] Analyzing the "travel distance" variable, the coefficient for subway is 4.31, for bus it is -3.70, and for taxi and ride-hailing services it is -1.06 and 0.45 respectively. This indicates that as travel distance increases, passengers are more inclined to choose subway and ride-hailing services, while the likelihood of choosing bus and taxi decreases. This aligns with the common understanding that buses are suitable for short to medium distances, while rail transit has a greater efficiency advantage for long distances, and that ride-hailing services have a price advantage over taxis for long-distance travel.

[0101] 2) Characteristics of the travel environment

[0102] Analyzing the "weather conditions" variable reveals that severe weather significantly impacts the choice between ride-hailing and taxis. The coefficient for passengers choosing ride-hailing services increased from -0.38 in normal weather to 0.34, while the coefficient for taxis decreased from 0.59 in normal weather to -0.60. This may be because, in normal weather, taxi waiting times are shorter than ride-hailing services, while the costs are similar, leading passengers to prefer taxis. However, in severe weather, the increase in taxi fares is much greater than that of ride-hailing services, thus increasing the probability of choosing ride-hailing services.

[0103] Analyzing the variable "peak hour conditions," compared to off-peak hours, under peak conditions, the coefficients for ride-hailing and taxis decreased from 0.21 and 0.34 to -0.22 and -0.38, respectively, while the coefficient for the subway increased from -0.58 to 0.61. This change in values ​​may be due to increased road congestion during peak hours, which diminishes the speed advantage and amplifies the cost disadvantage of ride-hailing and taxis, while the subway, being more punctual and economical, becomes more popular with passengers.

[0104] 3) Characteristics of transportation modes

[0105] There are three variables related to transportation modes: "travel time," "transportation cost," and "walking distance." Since these three are interconnected, their coefficients need to be analyzed together. For taxis, the time coefficient is as low as -8.19, indicating that when the required travel time is long, the probability of passengers choosing ride-hailing services decreases significantly. This is consistent with the taxi cost coefficient being as high as 10.85, meaning that longer travel times correspond to higher costs compared to the other three transportation modes when choosing taxis. In contrast, the time and cost coefficients for buses are 8.05 and -4.37 respectively, indicating that for long-distance travel, passengers choose buses because they are less expensive.

[0106] Model Comparison

[0107] From the results perspective, the MNL Logit model demonstrates good performance in statistical tests, with a pseudo-determination coefficient of 0.5376, indicating that its explanatory power is more than 50% higher than that of the empty model without explanatory variables. The p-value of the log-likelihood ratio test (LLR p < 0.001) further validates the overall significance of the model. Furthermore, the Z-statistic and p-value identify the most significant factors influencing travel choices under different modes of transportation, contributing to a deeper understanding of passenger behavior mechanisms. However, when applied to large-scale, multi-scenario travel mode prediction tasks, the model's out-of-sample prediction accuracy and stability are somewhat limited. In contrast, the multinomial logistic regression model shows significant advantages in classification accuracy and generalization ability. Through repeated stratified 10-fold cross-validation, its average accuracy reaches 99.9%, with a standard deviation of only 0.2%, demonstrating excellent predictive stability. In confusion matrix analysis, the precision and recall of most classes both exceed 95%, further confirming the model's superior identification ability.

[0108] In terms of application selection, if the research objective focuses on in-depth analysis of passenger preferences, the effects of policy interventions, or the interactions between variables, the MNL Logit model is more suitable due to its rigorous utility theory and parameter significance testing capabilities. However, for systems that require rapid iteration and real-time prediction, and for engineering scenarios with high requirements for classification accuracy and stability, the multinomial logistic regression model undoubtedly has advantages in terms of development efficiency, computational cost, and prediction performance.

[0109] Considering the significant difficulties in accurately obtaining specific characteristic data for different modes of transportation during subsequent practical case calculations, this invention addresses the challenges of accurately determining pricing for ride-hailing and taxi services. For example, their pricing mechanisms are typically complex, involving not only basic mileage costs but also dynamic pricing and platform dispatch fees. Furthermore, given the lack of precise descriptions of weather and peak-hour conditions in this invention, accurately calibrating specific pricing for ride-hailing services under different environmental characteristics is challenging. Similarly, the actual calculation of travel time for passengers using different modes of transportation faces numerous uncertainties, such as difficulties in accurately quantifying factors like bus delays and slow travel due to traffic congestion. Moreover, according to the statistical results of the VIF test in the MNL logit model (see Table 1), the multicollinearity of the variables "travel time," "cost," and "walking distance" for each mode of transportation is significantly high. Therefore, considering the above practical conditions and statistical analysis results, this embodiment of the invention reasonably simplifies the passenger choice utility function, discarding the original transportation mode characteristic variables and retaining only two categories of variables: passenger personal characteristics (such as gender, age, income, and luggage) and environmental characteristics (such as weather conditions, peak period conditions, and travel distance). The adjusted passenger choice utility function is expressed as follows:

[0110] Based on the preceding analysis, this invention continues to use a multinomial logistic regression model to determine the parameters of the simplified utility function. The data still comes from a questionnaire survey, but in this analysis, the variables "time," "cost," and "walking distance" were removed, retaining only passenger personal attributes (gender, age, income, luggage carrying) and travel environment factors (weather conditions, peak period conditions, travel distance) for modeling. Subsequently, following the basic process of multinomial logistic regression modeling, the filtered data underwent missing value processing, variable format adjustment, and standardization. Finally, the model fitting and parameter estimation were completed to determine the specific degree of influence of each variable on passengers' choice of different modes of transportation.

[0111] The final model fitting results are shown in Table 9: Table 9 Results of the Multinomial Logistic Regression Model

[0112] The model, evaluated using repeated stratified 10-fold cross-validation, achieved an average accuracy of 36.0%, indicating that even with simplified utility function selection and retention of only passenger and environmental characteristics, the model still possesses a certain predictive ability for multiple travel modes. Furthermore, its accuracy standard deviation of 2.7% demonstrates relatively stable performance across different data partitioning scenarios, exhibiting reasonable generalization ability. In summary, the current model has a simple structure and readily available variables, providing a valid reference basis for practical applications. Future research could further optimize variable selection or expand the data sample to continuously improve the model's predictive performance.

[0113] Table 10 and Figure 5 Here is a table of influence coefficients and a heatmap for each variable: Table 10 Variable Influence Coefficient Table

[0114] Subsequent research will use the above variable parameters to construct the passenger evacuation selection function of the lower-level model in the bi-level programming model, providing effective feedback and support for the upper-level resource scheduling decision.

[0115] The bi-level programming model incorporating Model Predictive Control (MPC) strategy provided by this invention comprises four parts: upper-level model construction, lower-level model construction, MPC strategy fusion, and model solving. First, the upper-level model construction clarifies the objective function to be optimized and its corresponding constraints, primarily guiding the dynamic allocation and scheduling strategies of traffic resources. Second, the lower-level model construction, based on passenger behavior, constructs a traffic mode selection and evacuation allocation mechanism, characterizing demand-side selection behavior at a micro-level. Then, the embedding method of the MPC mechanism in the model is introduced, achieving real-time response and feedback adjustment to the dynamic evolution of passenger flow through the construction of state transition functions and a rolling prediction framework. Finally, the NSGA-II genetic algorithm is outlined, and how to use this model for solving provides technical support for subsequent case studies and application deployment.

[0116] The construction of the upper-level model mainly includes setting the objective function and defining the constraints. Regarding the objective function, considering both operational efficiency and service costs within the transportation hub, a multi-objective optimization function is constructed from multiple dimensions, specifically covering: minimizing the average passenger waiting time, minimizing the number of passengers stranded within the station, and minimizing the operating costs of all transportation modes. Regarding constraints, based on the capacity and cost limits of various urban transportation modes, specifically considering the service capabilities of four modes of transportation—subway, bus, taxi, and ride-hailing—an operational capacity constraint set is constructed.

[0117] The dynamic changes in the number of people stranded within the station reflect the changing characteristics of the transportation hub's operational status and are also an important indicator for measuring the hub's evacuation efficiency. In this embodiment, the evolution of the number of people stranded within the station is defined as a time-series updated state transition relationship during the modeling process. Its basic calculation formula is as follows:

[0118] In the formula: The number of people waiting inside the station during time period t. The number of new arrivals at the station during time period t. The total number of people evacuated from the station by all modes of transportation during time period t, of which It is derived from the passenger evacuation model of the lower level, as shown in formula (42).

[0119] In this embodiment, the average passenger waiting time refers to the time interval from when a passenger enters the transportation hub until they actually board and leave. This embodiment uses time steps as the unit of study; therefore, passengers within a time step are divided into two categories: passengers who have already boarded and left within that time step, whose waiting time is calculated based on the queuing model of the corresponding transportation mode; and passengers who did not board and leave within that time step, whose waiting time is equal to the entire time step length. Finally, the average waiting time for all passengers is calculated by weighting the number of passengers.

[0120] The formula for calculating the waiting time of passengers who have not left the hub within a set time period t is as follows:

[0121] In the formula: The total waiting time for passengers who did not leave the hub station during time period t. This represents the length of the time period.

[0122] For passengers who have completed their journey within the set time period, their waiting time is calculated based on the queuing model corresponding to their chosen mode of transportation. In urban evacuation scenarios, buses, taxis, and ride-hailing services are affected by road conditions and vehicle scheduling uncertainties, and their arrival and departure intervals can be considered as stochastic processes; therefore, the M / M / C model is used to characterize them. The subway system, however, operates strictly according to a timetable, with relatively fixed service intervals, making the M / D / C model more suitable for its description. The following sections will introduce the basic components of the M / M / C and M / D / C models and their queuing time calculation formulas.

[0123] (1) M / M / C model

[0124] 1) Model Overview

[0125] The M / M / C queuing model is a classic multi-server model widely used in queuing theory to describe systems where both arrival and service processes are stochastic. In urban evacuation systems at transportation hubs, modes of transportation such as buses, taxis, and ride-hailing services exhibit significant uncertainty due to factors such as traffic flow, road conditions, and temporary scheduling. Therefore, using a capacity-constrained M / M / C queuing model can more realistically reflect the dynamic characteristics of passenger queuing.

[0126] The three letters in the model name have the following meanings: the first M means that the arrival time interval follows an exponential distribution (the arrival process is a Poisson process); the second M means that the service time follows an exponential distribution (the service process is a random and independent exponential distribution); and C means that there are C parallel service stations in the system, which can provide services to multiple customers at the same time.

[0127] 2) Introduction to Model Parameters Customer arrival rate (average arrival rate of the Poisson process); Service rate of each service counter; Number of service counters; The system's maximum capacity (i.e., the maximum number of passengers it can accommodate, including those currently being served and those waiting). The system happens to have The probability of a customer being served; Utilization (load per server); The formula for calculating utilization rate is:

[0128] 3) Waiting time calculation formula

[0129] When the number of passengers in the system does not exceed hour:

[0130] In the formula: The average number of passengers in the queue. The average passenger waiting time.

[0131] When the number of passengers in the system exceeds hour:

[0132] In the formula: For the number of arrivals that the system could not accommodate, This represents the length of the time period.

[0133] Considering the real-world capacity limitations, bus stops, taxi / ride-hailing waiting areas all have capacity restrictions. When a platform reaches its capacity limit, passengers will consider choosing other modes of transportation. Therefore, it is assumed that once the capacity limit is reached, subsequent passengers will no longer choose that mode of transportation. Thus, the waiting times for buses, taxis, and ride-hailing services are calculated separately based on the scenario before the capacity limit is reached.

[0134] In actual transportation hub operations, bus stops, taxi waiting areas, and ride-hailing pick-up areas all have clearly defined capacity limitations. Once the platform reaches its capacity, the system cannot accept any more waiting passengers. Considering this practical constraint, this paper makes the following assumptions during the modeling process: When the waiting area for a particular mode of transportation reaches its capacity limit, newly arriving passengers will no longer choose that mode of transportation, but will instead switch to other modes of transportation that still have available capacity.

[0135] Based on this assumption, the waiting times for buses, taxis, and ride-hailing services are calculated under the premise that the capacity limit is not reached, and the average waiting time of each mode of transportation under normal load conditions is estimated using a steady-state queuing model (M / M / C).

[0136] (2) M / D / C model

[0137] 1) Model Overview

[0138] The M / D / C queuing model is an important multi-server model in queuing theory, suitable for describing queuing systems where arrival processes are random but service times are fixed. In the urban evacuation system of the transportation hub examined in this study, the subway, as a typical timetable operation system, has relatively fixed and controllable train departure intervals and is less affected by external random interference. Therefore, using the M / D / C model to model passenger waiting times in the subway system can more accurately reflect its high-frequency and punctual operation characteristics.

[0139] The three letters in the model name have the following meanings: the first M indicates that the arrival time interval follows an exponential distribution (the arrival process is a Poisson process); the second D indicates that the service time is a constant D; and C indicates that there are C parallel service stations in the system, which can provide services to multiple customers simultaneously.

[0140] 2) Introduction to Model Parameters Customer arrival rate (average arrival rate of the Poisson process); Service rate of each service counter; Number of service counters; The system happens to have The probability of a customer being served; Utilization (load per server); The formula for calculating utilization rate is:

[0141] 3) Formula for calculating queuing time

[0142] Then, the average queuing time for buses, taxis, ride-hailing services, and subways during time period t can be expressed as:

[0143] In the formula: Let t be the average waiting time for buses. Let t be the average waiting time for taxis during time period t. The average waiting time for ride-hailing services during time period t. Let t be the average waiting time for the subway during time period t.

[0144] The average waiting time for buses, taxis and ride-hailing services is calculated according to formula (12) (substituting the model parameters of different modes of transportation), while the average waiting time for subways is calculated according to formula (15).

[0145] In summary, the formula for calculating the average waiting time for all passengers during time period t is:

[0146] In the formula: Let t be the average waiting time for all passengers during time period t. The total waiting time for passengers who did not leave the hub station during time period t. The total number of people evacuated from the station by all modes of transportation during time period t.

[0147] This invention categorizes the operating costs of buses, taxis, ride-hailing services, and subways into two main categories: fixed costs and variable costs. Fixed costs primarily include vehicle purchase and depreciation costs, infrastructure construction and maintenance expenditures, fees related to road rights or operating permits, and fixed expenses for system management and operation. Variable costs cover fuel or electricity consumption, operator salaries, and routine maintenance and repair costs for vehicles or equipment. Different modes of transportation exhibit significant differences in their cost structures. Buses and subways, due to their large-scale infrastructure investment and high proportion of fixed assets, have a larger proportion of fixed costs; while taxis and ride-hailing services are primarily driven by variable costs based on operating volume, with relatively smaller overall fixed investments. A unified cost classification standard can effectively standardize the modeling and expression of cost parameters for each mode of transportation, enhancing the scientific rigor and applicability of comparing operating costs between different modes. The specific cost structure of each mode of transportation is described below.

[0148] (1) Bus operating costs :

[0149] In the formula: The time step length, This refers to the dispatch frequency of buses.

[0150] 1) Fixed costs

[0151] In the formula: For vehicle purchase and depreciation costs, For the construction and maintenance costs of site facilities, For right-of-way or operating permit fees, Fixed management costs (such as salaries of fixed management personnel, infrastructure maintenance, etc.).

[0152] 2) Variable Costs

[0153] In the formula: For fuel or electricity consumption costs, For staff salaries (drivers and operations staff, paid on a shift basis). Vehicle maintenance and repair costs (varying depending on usage frequency).

[0154] (2) Taxi operating costs

[0155] In the formula: The time step length, This refers to the dispatch frequency of taxis.

[0156] 1) Fixed costs

[0157] In the formula: For vehicle purchase and depreciation costs, For operating license or franchise permit fees, — Fixed administrative costs (such as salaries of fixed management personnel, infrastructure maintenance, etc.).

[0158] 2) Variable Costs

[0159] In the formula: For fuel or electricity consumption costs, For staff salaries (drivers and operations staff, paid on a shift basis). Vehicle maintenance and repair costs (varying depending on usage frequency).

[0160] (3) Ride-hailing operating costs (some taxi companies also offer ride-hailing services)

[0161] In the formula: The time step length, This refers to the dispatch frequency of ride-hailing services.

[0162] 1) Fixed costs

[0163] In the formula: For operating license fees, Fixed costs for platform operation and technical systems.

[0164] 2) Variable Costs

[0165] In the formula: For fuel or electricity consumption costs, For staff salaries (drivers and operations staff, paid on a shift basis). Vehicle maintenance and repair costs (varying depending on usage frequency).

[0166] (4) Subway operating costs :

[0167] In the formula: The time step length, This refers to the dispatch frequency of the subway.

[0168] 1) Fixed costs

[0169] In the formula: For the cost of purchasing and depreciating trains, For the construction and maintenance costs of the rail line and station facilities, For right-of-way or operating permit fees, This includes fixed management personnel costs and infrastructure operation and maintenance costs.

[0170] 2) Variable Costs

[0171] In the formula: For train energy consumption costs, Salaries for drivers, train dispatchers, station staff, and other personnel. Maintenance and repair costs for vehicles and lines (varying depending on usage frequency).

[0172] In summary, the total operating costs of buses, taxis, ride-hailing services, and subways... This can be expressed as:

[0173] In the model construction process, to better reflect the operational constraints of actual transportation hubs and management departments, this paper introduces several realistic and feasible constraints into the upper-level optimization model. First, considering the upper limit of capital investment for hub stations and operators of each mode of transportation, the total operating cost of the four modes of transportation is set to not exceed the prescribed budget limit to ensure that scheduling decision-making costs remain within the acceptable range of operating funds. The constraints are as follows:

[0174] Secondly, due to limited operational scheduling resources, an upper limit constraint is set on the scheduling frequency of each mode of transportation. This means that the number of departures or capacity allocation for each mode of transportation per unit time cannot increase indefinitely, reflecting the operational capacity boundary. Simultaneously, to meet basic passenger travel needs and prevent insufficient service supply due to excessively low scheduling frequencies, a lower limit constraint is also set for scheduling frequencies. The mathematical expressions for the scheduling frequency constraints of each mode of transportation are as follows:

[0175] Furthermore, to ensure the safety and service quality of transportation operations, the model incorporates a capacity constraint. Specifically, it stipulates that the actual number of passengers transported by each mode of transportation in each dispatch must not exceed the maximum single-trip capacity of that mode; that is, the passenger occupancy rate must be less than or equal to 1, thereby avoiding safety hazards and service degradation caused by overloading.

[0176] By setting the above constraints, the model can achieve a balance among financial, operational, and service aspects, ensuring the rationality and practical feasibility of the scheduling plan. The mathematical expression for the load factor constraint is as follows:

[0177] In summary, based on the dynamic evolution mechanism of the number of people stranded within the station, and combined with passenger evacuation needs and transportation mode scheduling resource constraints, this invention constructs an upper-level optimization model. The specific structure of the upper-level optimization model is as follows:

[0178] The lower-level model mainly constructs the decision-making process of passenger evacuation behavior and analyzes the probability of passengers leaving by different modes of transportation after arriving at the transportation hub. Based on the data analysis results above, this invention uses a multinomial logistic regression model to model passenger travel choice behavior. Based on the regression coefficients of each influencing factor obtained from the empirical analysis, the influence of different characteristic variables on travel mode selection is quantified. In the specific modeling process, the set utility value of each passenger in the four available modes of transportation (bus, taxi, ride-hailing, and subway) can be calculated using the coefficients in Table 5 and formula (5). Furthermore, considering that passengers may change their travel choices based on the current congestion levels of various transportation modes, a waiting time penalty is added to the utility value of each transportation mode. (per minute), the adjusted utility value calculation formula is as follows:

[0179] In the formula: Select transportation mode for passengers during time period t The calculated utility value, Choose a mode of transportation for passengers The set utility value, The penalty value is the waiting time. Transportation mode for time period (t-1) The average waiting time.

[0180] By adding a waiting time penalty value, the true passenger choice preference can be dynamically reflected. Then, based on the adjusted utility value, the probability of each mode of transportation being selected in time period t is calculated. The calculation formula is as follows:

[0181] In the formula: Choose a mode of transportation for time period t The probability, It is a collection of four modes of transportation.

[0182] After obtaining the formulas for calculating the probability of choosing each mode of transportation, the set probability of the first mode can be further calculated. The actual number of passengers evacuated by each mode of transportation during the specified time period. Specifically, for each mode of transportation, the number of passengers evacuated during the specified time period. The number of passengers successfully transported out during a given time period is the minimum value between the actual capacity of that mode of transport during that time period and the demand from passengers choosing that mode of transport. The calculation formula is as follows:

[0183] In the formula: For transportation Capacity conversion factor Transportation mode during time period t Scheduling frequency, For transportation Single transport capacity, Select transportation mode for passengers during time period t The probability of.

[0184] Ultimately, the four modes of transportation were selected in the [number]th [year]. The total number of passengers evacuated during each time period is summed to obtain the total number of passengers leaving the hub during that time period, providing basic data support for subsequent dynamic updates of the number of stranded passengers and optimization of scheduling strategies.

[0185] In the two-layer planning framework constructed in this invention, the core of the Model Predictive Control (MPC) strategy lies in introducing a state transition equation to dynamically describe the system evolution process. The number of people remaining in the station is defined as a key state variable of the system, reflecting the operational load of the transportation hub at different times. Specifically, the state transition equation is the evolution formula of the number of people remaining over time, which is also the calculation formula (7) for the number of people remaining in the upper-level model. It is dynamically updated based on the number of people remaining, arriving, and leaving through evacuation at the current time.

[0186] In the optimization process, the upper-level model aims to minimize the number of people stranded within the station, minimize passenger waiting time, and minimize the operating costs of each mode of transportation. It sets decision variables composed of the scheduling frequencies of each mode of transportation. The lower-level model then calculates the current... The actual number of passengers evacuated during the specified time period. Subsequently, the state transition equation is used to predict... The number of people remaining inside the station during a given time period.

[0187] Based on the predicted congestion status for the next time period, the model makes optimization decisions again, updates the scheduling frequency of each mode of transportation, and accordingly completes further passenger evacuation. This process, based on a certain rolling time window, follows a logical cycle of "prediction-optimization-implementation-update," forming a typical MPC rolling optimization strategy. By introducing state feedback and dynamic prediction mechanisms, the model can effectively capture the evolution characteristics of passenger flow at the hub, adjust scheduling strategies in real time, and achieve synchronous optimization of system operation status and scheduling resource allocation over multiple consecutive time periods, thereby improving the overall evacuation efficiency and service level of the transportation hub.

[0188] This invention employs the NSGA-II (Non-dominated Sorting Genetic Algorithm II) algorithm for model solving. Proposed by Deb et al. in 2002, the NSGA-II algorithm is one of the most widely used evolutionary algorithms in the field of multi-objective optimization. This algorithm simulates natural selection and genetic mechanisms to simultaneously optimize multiple objective functions in order to find a set of Pareto optimal solutions. Specifically, it iteratively optimizes the population as the basic unit by simulating the biological evolution process in nature. Each generation of the population is hierarchically sorted according to the non-dominated relationships of individuals on multiple objective functions, and individuals within the population are prioritized based on crowding distance. The algorithm preferentially retains individuals with higher non-dominated levels and lower density in the decision space, thereby achieving approximation and distribution control of the Pareto optimal front.

[0189] (1) Main features of the algorithm: Non-dominated sorting: NSGA-II employs a Pareto-dominant-based sorting mechanism, dividing the population into several different non-dominated layers. Individuals within the same layer do not have a dominant relationship with each other, while there are clear priorities between different layers. This ensures that the algorithm can correctly guide the population toward the Pareto optimal front during the optimization process.

[0190] Crowding distance calculation: To maintain the diversity of the solution set during population evolution, NSGA-II introduces the concept of crowding distance. It measures local density by calculating the distance between adjacent solutions of an individual in the objective function space. During the selection process, individuals with larger crowding distances are preferentially retained to avoid population concentration in local regions and improve the uniformity of solution distribution.

[0191] Elite Preservation Strategy: NSGA-II merges the parent and offspring populations, sorts them uniformly, and selects the best individuals to form the next generation, ensuring that high-quality solutions are not lost during evolution. This elite strategy effectively improves the algorithm's convergence speed and stability, ensuring that the population quality continuously improves during iteration.

[0192] Computational efficiency: Compared to earlier multi-objective genetic algorithms, NSGA-II has optimized the algorithm in the non-dominated sorting stage, reducing the overall time complexity to [missing value]. ,in The number of objective functions, This improvement significantly enhances the algorithm's computational efficiency and scalability when handling large-scale multi-objective problems, taking into account the population size.

[0193] (2) Basic flow of NSGA-II algorithm

[0194] Initialize the population: Randomly generate an initial population of fixed size, where each individual contains decision variables and the corresponding objective function value, serving as the starting point for the evolutionary search.

[0195] Fitness assessment: Multi-objective fitness calculation is performed on each individual in the population to evaluate its performance on each objective, which serves as the basis for subsequent non-dominated ranking and selection operations.

[0196] Non-dominated ranking: Individuals are divided into different non-dominated levels according to Pareto dominance, and individuals with lower dominance are prioritized to form the initial selection order of individuals in the population.

[0197] Crowding distance calculation: Within the same non-dominated layer, the degree of local crowding is assessed by calculating the distance between an individual and its neighboring solutions in the objective function space, which helps to maintain the balanced distribution of the solution set.

[0198] Generation of offspring population: A tournament selection strategy based on crowding distance and non-dominant hierarchy is applied to select individuals from the parent generation for crossover and mutation operations to generate offspring individuals and expand the search space.

[0199] Merging populations: The parent and offspring populations are merged and uniformly evaluated using non-dominated sorting and crowding distance to form a larger population containing more potential high-quality solutions.

[0200] Selecting a new generation of individuals: Based on the non-dominance level and crowding distance of individuals, select a fixed number of individuals from the merged population as the new parent population to enter the next iteration, ensuring convergence and diversity.

[0201] Termination condition determination: Repeat the above evolutionary operation until a preset termination condition is met, such as reaching the maximum number of iterations or the evolutionary change of the population being lower than the set convergence threshold. When the termination condition is met, output the approximate Pareto optimal solution set of the population as the optimization result for decision-making reference.

[0202] This invention chooses Python as the primary programming language, uses the DEAP framework to efficiently implement the NSGA-II algorithm logic, combines Pandas and NumPy to complete data processing and computation tasks, and uses the Matplotlib library to plot the results. Furthermore, SciPy is used for auxiliary computation to ensure the accuracy and efficiency of the model's solution, providing stable and reliable technical support for practical operational decisions. The specific implementation steps of the NSGA-II algorithm selected in this invention are described below: 1) Generating the Initial Population: Based on the bi-level optimization problem combining the MPC strategy proposed in this study, the upper-level decision variables are the scheduling frequencies of four transportation modes in the transportation hub: buses, subways, taxis, and ride-hailing services. Considering actual operational requirements, upper and lower bound constraints are set for the scheduling frequencies of each transportation mode. Within these constraints, a certain number of initial individuals are randomly generated. Each individual represents a specific combination of scheduling frequencies, forming the initial solution set for the subsequent optimization algorithm.

[0203] 2) Objective Function Definition and Individual Evaluation: The optimization objectives include minimizing the number of passengers stranded at the hub, minimizing the total operating cost of each mode of transportation, and minimizing the average passenger waiting time. The objective function is calculated for each individual in the population to determine their fitness value. Specifically, the number of passengers stranded at the hub is predicted using the MPC state transition equation; the total operating cost is obtained by summing the fixed and variable costs (dispatch frequency multiplied by unit cost) of each of the four modes of transportation, while also considering the budget constraint (setting an upper limit) on the total operating cost; the average passenger waiting time consists of two parts: for passengers who have completed their journey within the time step, their waiting time is calculated using the M / M / C model for buses, taxis, and ride-hailing services, and the M / D / C model for the subway; for passengers who have not completed their journey within the time step, their waiting time is equal to the length of the entire time step. Finally, the waiting times of the two types of passengers are weighted and summed according to their proportion in the total passenger population to obtain the overall average waiting time. Using these defined objective functions, the fitness value of each individual in the initial population is calculated and evaluated separately.

[0204] 3) Non-dominated ranking and congestion distance assessment: For the multiple objective functions (number of stranded people, operating costs, waiting time) involved in solving the hub evacuation scheduling optimization problem, this study employs a non-dominated ranking strategy to hierarchically divide the fitness values ​​of all individuals. During the ranking process, each individual is explicitly assigned to a specific non-dominated level; individuals with higher levels are closer to the overall optimization objective and are given priority. Furthermore, to avoid the optimization results being concentrated in a few specific areas, this study calculates the congestion distance of each individual within the same level to measure population diversity. Using the congestion distance index, the algorithm prioritizes retaining individuals located in sparse areas with higher congestion distances, ensuring the breadth of the solution set.

[0205] 4) Genetic Operator Design (Selection, Crossover, and Mutation): A tournament selection mechanism based on crowding and non-dominated sorting is adopted to select high-quality individuals from the current population for crossover and mutation operations. Specifically, the crossover operator uses two-point crossover for gene recombination, while the mutation operator uses a uniform integer mutation strategy to randomly adjust the values ​​of decision variables, increasing population diversity and global search capability.

[0206] 5) Elite Preservation and Population Update: After each genetic operation, the parent population is merged with the newly generated offspring population to form a larger set. Then, non-dominated sorting and crowding distance calculations are performed uniformly. From the merged large population, high-quality individuals with high non-dominated levels and large crowding distances are selected to form the next generation population, thus implementing an elite strategy. Through this method, the hub optimization model preserves and strengthens high-quality transportation mode scheduling schemes in each iteration, gradually achieving stable approximation of the model's objective, ensuring high quality of the final optimization results and the convergence of the algorithm.

[0207] 6) Algorithm Termination Criteria: The above optimization loop continues until a predetermined number of iterations is reached (100 in this study), or the change in the quality of the solution set during multiple consecutive iterations is lower than a predefined threshold, at which point the algorithm is considered to have converged. After the termination condition is met, the algorithm outputs an approximate Pareto optimal front solution set as the final optimization decision scheme, clarifying the trade-off between the number of stranded passengers, operating costs, and waiting times corresponding to different modes of transportation scheduling frequencies, and providing a scientific decision-making basis for the actual operation and management of transportation hubs.

[0208] Finally, using the Matplotlib library for plotting, we conducted a Pareto front visualization analysis on the final non-dominated solution set to explore the interrelationships and trade-offs among the objectives and clarify the practical feasibility and decision value of the final optimization scheme.

[0209] This invention also designs and optimizes a computational example based on relevant data from a transportation hub, and verifies the two-level programming model of the fusion model predictive control (MPC) strategy constructed in this invention by solving the example, thereby evaluating the feasibility and application effect of the model.

[0210] Parameter settings

[0211] (1) Setting basic parameters of the model

[0212] First, determine the basic parameters required for the bi-level programming model and MPC strategy, assuming the number of people stranded in the hub station at the start of optimization is 500; the time step... The MPC forecast rolling window is set to 15 minutes, with 6 time steps, predicting passenger flow changes over the next 90 minutes. Based on the station's main passenger arrival times (7:00–23:00) and operational data, the average daily passenger arrivals are estimated at approximately 120,000, translating to about 1,875 arrivals every 15 minutes. Considering the current operational status of the station's urban transportation system, it is estimated that approximately 1,000 passengers need to leave the hub every 15 minutes using other modes of transportation. Therefore, the estimated number of arriving passengers every 15 minutes during holidays or peak periods is approximately 4,000. The waiting time penalty value is set to -0.3 through comprehensive comparison. All parameter values ​​are set as shown in Table 11 below. It should be noted that in practical applications, the arrival volume can be adjusted based on real-time or more refined observation data to improve the accuracy and applicability of the model's predictions.

[0213] Table 11 Basic Model Parameters

[0214] (2) Setting of environmental variables and transportation mode parameters

[0215] The environmental variables that need to be set are "weather conditions" and "peak conditions". "Weather conditions" can be set to "normal" or "severe", and "peak conditions" can be set to "peak" or "off-peak". In order to test the scheduling ability of the model under extreme conditions, the environmental variables are set to "severe" and "peak" in this test case.

[0216] The parameters that need to be set for each mode of transportation include: single-trip capacity, dispatch frequency (vehicles / 15min), number of servers (the number of vehicles that can provide services simultaneously), service rate (x, y), representing the number of passengers that one server can serve in x minutes, fixed cost (calculated from monthly fixed cost to fixed cost per 15 minutes), and single-trip service cost. The values ​​used in this calculation are shown in Table 12: Table 12 Transportation Mode Parameters

[0217] (3) Passenger-related characteristics

[0218] The passenger-related characteristics that need to be set include gender ratio, age ratio, income ratio, proportion of passengers carrying large luggage, and proportion of passengers traveling by distance. In this case, the values ​​are selected based on the results of the questionnaire survey. The specific meanings of the numerical categories corresponding to each passenger characteristic are shown in Table 13.

[0219] Table 13 Passenger Characteristic Distribution Ratio

[0220] (4) NSGA-II algorithm parameter settings

[0221] The main parameters that need to be set for the algorithm are the initial population size, number of generations, crossover probability, and mutation rate (composed of the mutation operator and individual-level mutation probability). A smaller population size makes the model prone to premature convergence and a sparse frontier, while a larger population size leads to more evaluation function calls. To maintain diversity and controllable computational cost, a population size of 52 is chosen. Too small a number of generations can lead to insufficient convergence and an unstable frontier, while too large a number of generations results in longer processing time. Testing showed that the model converged efficiently when the number of generations was 500 in this test case. A crossover rate that is too small may lead to insufficient exploration, while a rate that is too high can disrupt good gene combinations. A commonly used range is 0.6-0.9, and a value of 0.7 is used in this test. A mutation rate that is too small may cause the solution to get stuck in a local optimum, while a mutation rate that is too high can lead to random walks. A value of 0.2 is used in this test case, which ensures continuous "perturbation" while avoiding getting stuck in a local optimum.

[0222] Test Results

[0223] (1) The NSGA-II algorithm is used to iteratively solve the bilevel programming model with the incorporated model predictive control (MPC) strategy. The solution results are as follows: Figure 6-9 .

[0224] from Figure 6 The optimal operating cost curve over time steps reveals a trend of "high level – fluctuation – decrease – stabilization" as time steps progress. In the initial stage (time steps 0–1), the operating cost remains at a high level (approximately 7000–8500 yuan), then gradually decreases to below 6000 yuan in time steps 2–5, and stabilizes in time step 6. While some fluctuations still exist between time steps, the overall fluctuation amplitude gradually decreases, indicating that the model rapidly reduces system costs through global optimization in the early stages, while later focusing on local fine-tuning to achieve stable convergence. This trend demonstrates that the algorithm combines exploratory and convergent aspects in dynamic scheduling, achieving superior cost control within a limited timeframe.

[0225] from Figure 7 The curve showing the change in average passenger waiting time over time steps reveals that the pattern is largely consistent with operating costs, exhibiting a pattern of "initial decline – mid-term fluctuation – later stabilization." In time steps 0–2, the waiting time decreased from approximately 5 minutes to around 1.8 minutes, reflecting that early scheduling optimization significantly improved passenger travel efficiency. A brief increase occurred in time step 3, indicating that the system faced short-term fluctuations due to localized congestion or capacity switching under specific operating conditions. In time steps 4–6, the waiting time remained stable at around 2 minutes, demonstrating that the model can maintain a good service level and resource allocation balance in the later stages.

[0226] from Figure 8 The curves showing the final number of stranded individuals over time steps reveal a segmented pattern: "high – sharp drop – rebound – further decline – stability." At time step 0, the number of stranded individuals was relatively high, around 500. This was followed by a rapid drop to near zero in time steps 1–2, demonstrating the model's strong early-stage immediate evacuation capability. In time step 3, the number of stranded individuals briefly rebounded by about 140, reflecting the pressure of concentrated arrival demands and resource reallocation encountered by the system at this stage. Subsequently, in time steps 4–6, the number of stranded individuals decreased significantly again and stabilized at a low level, indicating that the model can achieve continuous reduction in stranded individuals and system stability through cross-time-step optimization in dynamic environments.

[0227] from Figure 9 The Pareto optimal frontier distribution plot shows that the horizontal axis represents the final number of stranded passengers, the vertical axis represents the average waiting time, and the color of the dots indicates the level of operating costs. The overall distribution increases from the lower left to the upper right, meaning that operating costs gradually decrease as the number of stranded passengers and the waiting time increase. When the number of stranded passengers is low (0 to 200), the corresponding waiting time is short (approximately 2 to 3 minutes), but the cost is high (approximately 16,000 to 18,000 yuan). However, when the number of stranded passengers rises to 400 to 800, the waiting time extends to 4 to 6 minutes, and the cost drops to below approximately 8,000 yuan. This distribution clearly reflects the trade-off between cost and service quality in the system, providing managers with a set of optional scheduling schemes under different cost and efficiency trade-offs.

[0228] (2) After the model is solved, the passenger diversion of each mode of transportation at different time steps is as follows: Figure 10 .

[0229] from Figure 10As can be seen, under the current travel scenario of "severe weather and peak hours," the actual number of people choosing each mode of transportation exhibits significant phased changes over time. The subway consistently carries the largest passenger flow across all time steps, rising steadily from approximately 350 people in time step 1 to a peak of approximately 950 people in time step 4, before gradually declining to around 700 people in time step 6, showing a trend of "steady increase – peak – gradual decline." Buses are the second largest mode of transportation, gradually increasing from approximately 200 people in time step 1 to approximately 620 people in time step 4, indicating that they play a positive role in alleviating passenger flow during peak hours as an important supplement to the subway. Taxi passenger flow remains relatively stable throughout the process, fluctuating slightly between 400 and 600 people, demonstrating strong flexibility and continuous passenger diversion capabilities. In contrast, ride-hailing passenger flow fluctuates significantly, showing a clear trend of "first decrease, then increase, then decrease again," with the number of passengers varying between 100 and 500, reflecting that this mode of transportation is more sensitive to scheduling changes during peak hours. Overall, the passenger flow trends of the four modes of transportation are basically consistent with the phased fluctuations of the total arriving passenger flow, indicating that the model can dynamically allocate according to the capacity characteristics of different modes of transportation, making the dispersal and diversion among multiple modes more coordinated and efficient.

[0230] (3) After completing the model optimization solution, the passenger congestion situation in the hub station was further simulated and predicted based on the optimal scheduling scheme in the future prediction time steps. The final evolution results of the number of congested people in each time step are shown in Table 14: Table 14 Forecast Number of Stranded Persons

[0231] Depend on Figure 11 It can be seen that in the initial stage of model operation, the number of people stranded in the station was approximately 700, indicating that the initial concentrated arrival of passengers put significant pressure on the hub's capacity. After entering time step 1, the model effectively responded to changes in passenger flow through a dynamic scheduling strategy, and the number of stranded people quickly decreased to approximately 380. By time step 2, the number of stranded people further decreased to approximately 65, indicating that the scheduling scheme had achieved efficient evacuation capabilities at this stage. Subsequently, in time step 3, the number of stranded people rose slightly to approximately 100, indicating that the system was still affected by fluctuations in passenger arrivals or concentrated transfer demands in local periods. By time step 4, the number of stranded people briefly rebounded to approximately 620, the second peak in the entire process, reflecting the possibility of capacity switching or passenger congestion at this stage. However, in time steps 5 and 6, the model further optimized the scheduling frequency and capacity allocation, causing the number of stranded people to decrease to approximately 240 and 50 respectively, showing an overall fluctuating trend of "peak-decline-short rise-decline again". This demonstrates that the model can dynamically adjust the capacity of various modes of transportation based on real-time passenger flow during peak periods, enabling rapid response and recovery to sudden increases in passenger flow, and exhibiting strong time-varying adaptability and stable evacuation control capabilities.

[0232] (4) The comparison results before and after optimization are shown in Table 15.

[0233] Table 15 Comparison of key indicators before and after optimization of the bi-level programming model

[0234] A comparison of key indicators before and after optimization using the bi-level programming model reveals that the optimized scheme achieves dynamic adjustment among various modes in terms of scheduling frequency. Compared to the baseline scheme (15 buses, 20 subway vehicles, 200 ride-hailing vehicles, and 170 taxis), buses maintain high flexibility at each time step, with the number of vehicles fluctuating between 10 and 24, reflecting a strategy of proactively adding extra buses during peak passenger flow periods. The number of subway trips decreased from 20 to 8 and remained stable, indicating that the model uses the subway as a fixed capacity support. Ride-hailing vehicles maintained a high level of around 240 vehicles at each time step, serving as a flexible supplement to share short-term concentrated passenger flow. Taxis exhibited the characteristic of "increasing deployment during peak hours and withdrawing during off-peak hours," reaching 200 vehicles in the first and fourth time steps and decreasing to approximately 100 vehicles at the end.

[0235] In terms of operating costs, the total cost of the four methods decreased from RMB 132,760 before optimization to RMB 130,110, a reduction of approximately 2.0%. Although the reduction is relatively limited, the cost change is closely related to the structural optimization of capacity allocation. By reducing fixed high-cost capacity such as subways and adopting more flexible bus and ride-hailing scheduling during critical periods, the model has reduced the unit evacuation cost to a certain extent, reflecting the cost control capability under multi-objective optimization.

[0236] Regarding average passenger waiting time, the average number of stranded passengers decreased from 812 to 245, a reduction of nearly 70%. Specifically, the number of stranded passengers at the 2nd, 3rd, and 6th time steps decreased by 86.1%, 85.6%, and 92.9%, respectively, indicating that the model can quickly process backlogged passengers during both peak and closing periods. The average waiting time also decreased from 4.40 minutes to 2.84 minutes, a reduction of 35.5%, demonstrating that the optimized scheduling strategy not only improved evacuation speed but also effectively enhanced the passenger travel experience, making the overall operation of the hub system more efficient and stable.

[0237] When setting parameters, it was mentioned that there are two types of travel environment variables: weather conditions and peak period conditions. Therefore, there are four possible travel environments. This embodiment of the invention compares and analyzes the evacuation optimization effect of the two-layer planning model under the four conditions. The specific travel environment categories are shown in Table 16.

[0238] Table 16 Travel Environment Categories

[0239] To eliminate the randomness caused by the same number of future passenger arrivals, the number of passenger arrivals in the basic parameters of the model was modified. In addition, to better compare the optimization effects under different travel scenarios, the waiting time penalty value was also fine-tuned. The specific settings are shown in Table 17.

[0240] Table 17 Basic Model Parameters

[0241] The parameters of transportation mode, the proportion of passenger-related features, and the parameters of the NSGA-II algorithm are set in the same way as the case calculation in the previous section. The optimization results for the four travel environments are shown in Table 18 below.

[0242] Table 18 Optimization Results under Travel Environment Category 1

[0243] As shown in Table 18, under the conditions of "normal weather and off-peak hours," the number of buses dispatched at each time step after optimization remained between 19 and 27, an increase of approximately 20% to 50% compared to the baseline scheme, fully leveraging the backbone role of the public transportation system during regular periods. The number of subway trips decreased from 20 in the baseline scheme to 8 and remained stable, reflecting the reasonable constraints of the model on subway capacity supply. The number of ride-hailing and taxi dispatches showed a significant downward trend, with ride-hailing trips decreasing from 200 to 68-240 at each time step, and taxi trips decreasing from 150 to 50-200, with maximum reductions of 65% and 67% respectively. Overall, it can be seen that the optimized scheduling scheme, under normal weather conditions, prioritizes the allocation of capacity towards the public transportation and subway systems to achieve a balance between cost savings and efficiency improvement. In terms of operating costs, the total operating cost of all modes of transportation decreased from RMB 127,030 before optimization to RMB 103,830, a reduction of 18.26%, indicating that the optimized model effectively reduced system operating expenses while ensuring evacuation capacity. Meanwhile, passenger congestion levels improved significantly: the average number of passengers congested at each time step of the hub decreased from 889 to 309, an overall reduction of 65.21%. Specifically, in time steps 5 and 6, the reductions in congestion reached 80.02% and 87.76% respectively, indicating that the optimized scheduling had a significant effect on alleviating passenger congestion in the later stages. Regarding passenger travel experience, the average waiting time for all arriving passengers decreased from 5.59 minutes before optimization to 3.05 minutes, a reduction of 45.44%, indicating that the optimized scheduling frequency significantly improved passenger waiting efficiency and reduced congestion and waiting uncertainty within the station.

[0244] Table 19 Optimization Results under Travel Environment Category 2

[0245] As shown in Table 19, when the travel environment is "normal weather, peak period", the optimized scheduling scheme exhibits a clear dynamic adjustment characteristic in the allocation of multi-modal transport capacity. The number of bus departures increases from 18 in the baseline scheme to 21-27 in each time step, with 27 buses in time steps 1, 2, 4, and 5, significantly enhancing the main evacuation capacity during peak periods. The number of subway trains decreases from 20 to 8 and remains stable, reflecting the rigid constraints of transport capacity allocation. The dispatch volume of ride-hailing and taxis shows an alternating and complementary characteristic. Ride-hailing reaches a peak of 240 vehicles in time steps 1, 4, and 6, while taxis rise to 200 vehicles in time steps 3 and 5, reflecting the model's flexible response to passenger flow and road conditions at different times. Based on this, the total operating cost of the system decreased from RMB 127,030 to RMB 103,830, a decrease of 18.26%, the average number of stranded people decreased from 1,107 to 304, a decrease of 72.50%, and the average waiting time was shortened from 6.53 minutes to 3.01 minutes, a decrease of 53.91%. This fully demonstrates that the optimized two-level planning model has a significant effect on improving evacuation and scheduling efficiency under severe weather and peak conditions.

[0246] Table 20 Optimization results under travel environment category 3

[0247] Table 20 shows that when the travel environment is "severe weather and off-peak period," the number of bus departures is adjusted from 18 in the baseline scheme to 9–26 in each time step, reflecting the model's phased deployment strategy based on real-time passenger flow dynamics. The number of subway trains decreases from 20 to 8 and remains stable, reflecting the steady-state characteristics of the subway maintaining basic capacity under this scenario. Ride-hailing and taxis undertake the main task of supplementing the fleet. Ride-hailing reaches a peak of 240 vehicles in time steps 1, 2, and 4, while taxis maintain a high deployment level of 200 vehicles in time steps 1 and 4 to cope with the travel demand restricted by public transportation under severe weather conditions. After optimization, the total operating cost of the system decreased from 127,030 yuan to 105,835 yuan, a decrease of 16.69%. The average number of stranded passengers decreased from 534 to 442, a decrease of 70.08%, and the average waiting time was shortened from 4.34 minutes to 2.06 minutes, a decrease of 52.53%, indicating that the model can still maintain strong passenger flow dispersal and timeliness optimization capabilities during off-peak periods.

[0248] Table 21 Optimization results under travel environment category 4

[0249] Table 21 shows that when the travel environment is "severe weather, peak period," the bi-level programming model improves overall scheduling efficiency and passenger flow dispersal capacity under the "normal weather, peak period" scenario. The number of bus departures is dynamically adjusted from 18 in the baseline scheme to 13-27, reaching a peak of 27 at time step 2, effectively addressing the concentrated arrival of passengers during peak hours. The number of subway trains decreases from 20 to 8 and remains stable, indicating that the model can maintain the stability of subway capacity under normal supply conditions. The scheduling volume of ride-hailing and taxis alternates between different time steps: ride-hailing reaches a peak of 240 vehicles in time steps 1, 2, and 5, while taxis are deployed more in time steps 1, 4, and 6, reaching 200 vehicles in each step, demonstrating that the model can flexibly allocate resources according to the differences in demand at different times. Overall, the optimized system's operating cost decreased from 127,030 yuan to 109,655 yuan, a reduction of 13.68%. The average number of people waiting on the waiting list decreased from 564 to 305, a reduction of 46.04%, and the average waiting time was shortened from 4.24 minutes to 3.14 minutes, a reduction of 25.94%. This indicates that the optimization scheme achieved good results in most time steps. However, in time step 6, the number of people waiting on the waiting list increased slightly compared to before the optimization, indicating that the optimization effect was relatively weak. This suggests that there is still room for improvement in the model's resource reallocation at the end of the peak period.

[0250] Table 22 Comparison of Optimization Results for Different Travel Environments

[0251] Table 22 compares the optimization effects under four different travel environment conditions, leading to the following conclusions: The model's optimization performance varies significantly under different weather and peak conditions. Overall, weather factors have a more significant impact on the model's optimization results. During off-peak periods, the optimization performance differs considerably between normal and severe weather. Total operating costs are reduced by 18.26% and 16.69%, respectively; average number of stranded passengers is reduced by 65.21% and 70.08%, respectively; and average waiting time is shortened by 45.44% and 52.53%, respectively. This indicates that the model responds more effectively to passenger flow fluctuations and achieves better evacuation results under severe weather conditions. During peak periods, cost reductions are 18.26% and 13.68% under normal weather and 13.68% under severe weather, respectively; number of stranded passengers is reduced by 72.50% and 46.04%, respectively; and average waiting time is shortened by 53.91% and 25.94%, respectively. This suggests that the model's optimization performance weakens when peak passenger flow is combined with severe weather, and cost savings and evacuation efficiency are somewhat limited. Looking at the changes at each time step, the model generally performed well in time steps 2 to 4, with the number of stranded passengers decreasing by more than 60% in most scenarios. However, in some scenarios at time step 6, the number of stranded passengers showed negative growth, indicating that the model's scheduling adjustments still experienced local fluctuations during the passenger flow decline phase. Overall, the model could reduce operating costs, decrease the number of stranded passengers, and shorten waiting times under different travel environments, but the extent of optimization was affected by both weather and peak periods, showing phased differences.

[0252] On the other hand, the present invention provides an urban multimodal passenger transport collaborative dispatch system based on an MPC and two-layer planning fusion framework, comprising: The data acquisition module is used to acquire passenger selection feature data and capacity parameters of each mode of transportation; The utility function construction module is used to construct passenger choice utility functions based on the passenger choice feature data using a multinomial Logit model, and to determine the utility values ​​corresponding to each mode of transportation. The upper-level optimization module is used to construct an upper-level multi-objective optimization model. The upper-level multi-objective optimization model aims to minimize the number of people stranded in the hub station, minimize the average waiting time of passengers, and minimize the total operating cost of each mode of transportation. It uses the capacity parameters of each mode of transportation as decision variables and constructs a multi-objective optimization function and constraints. The lower-level evacuation module is used to construct a lower-level passenger selection evacuation model. The lower-level passenger selection evacuation model calculates the selection probability of each mode of transportation in the current time period based on the capacity parameters and utility values ​​of each mode of transportation, and determines the number of people to be evacuated for each mode of transportation based on the selection probability. The state prediction module is used to construct the state transition equation for the number of stranded people. The state transition equation predicts the number of stranded people in the next period based on the number of stranded people, the number of arrivals, and the number of evacuations in the current period. The solution module is used to solve the upper-level optimization model using the NSGA-II genetic algorithm, and to perform rolling time-domain optimization based on the state transition equation to obtain scheduling schemes for each mode of transportation that meet the predetermined optimization objectives.

[0253] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0254] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for coordinated dispatching of urban multimodal passenger transport based on a fusion framework of MPC and two-layer planning, characterized in that, include: Obtain passenger selection feature data and capacity parameters for each mode of transportation; Based on the passenger choice feature data, a multinomial Logit model is used to construct a passenger choice utility function and determine the utility value corresponding to each mode of transportation. A two-layer planning and scheduling model integrating model predictive control modeling strategy is constructed. The two-layer planning and scheduling model includes an upper-layer multi-objective optimization model and a lower-layer passenger selection and evacuation model. The upper-layer multi-objective optimization model aims to minimize the number of people stranded in the hub station, minimize the average passenger waiting time, and minimize the total operating cost of each mode of transportation. It uses the capacity parameters of each mode of transportation as decision variables and constructs a multi-objective optimization function and constraints. The lower-layer passenger selection and evacuation model calculates the selection probability of each mode of transportation in the current time period based on the capacity parameters and utility values ​​of each mode of transportation, and determines the number of people to be evacuated for each mode of transportation based on the selection probabilities. A state transition equation for the number of stranded people is constructed. The state transition equation predicts the number of stranded people in the next period based on the number of stranded people, the number of arrivals, and the number of evacuations in the current period. The NSGA-II genetic algorithm is used to solve the upper-level optimization model. Based on the state transition equation, rolling time-domain optimization is performed to obtain scheduling schemes for each mode of transportation that meet the predetermined optimization objectives.

2. The urban multimodal passenger transport collaborative dispatching method based on the MPC and two-layer planning fusion framework as described in claim 1, characterized in that, The expression for the passenger choice utility function is: in, U i Choose a mode of transportation for passengers The utility value is: A = passenger age, G = passenger gender, S = passenger income, B = passenger carrying large luggage, and D = passenger travel distance. To choose a mode of transportation Required travel time, To choose a mode of transportation The required costs, To choose a mode of transportation Required walking distance, W c P represents the weather conditions, and P represents the peak period conditions. , , , , , , , , , This represents the influence coefficient of the corresponding characteristic variable.

3. The urban multimodal passenger transport collaborative dispatching method based on the MPC and two-layer planning fusion framework as described in claim 1, characterized in that, The multi-objective optimization function and constraints are as follows: Where, x (t) Let a be the number of people waiting inside the station during time period t. (t) The number of new arrivals at the station during time period t. Let I represent the number of people evacuated by mode i during time period t, and let I be the set of modes of transportation. For the fixed cost of mode i, Let θ represent the variable cost of mode i, and θ represent the time period length. Let be the scheduling frequency of traffic mode i during time period t. The total waiting time for passengers who did not leave the hub station during time period t. ρ represents the average waiting time for mode i during time period t; i For the full load factor constraint, λ i C represents the passenger arrival rate for mode i. i For the number of service counters, μ i For service rate.

4. The urban multimodal passenger transport collaborative dispatching method based on the MPC and two-layer planning fusion framework as described in claim 1, characterized in that, The evacuation model selected by the lower-level passengers specifically includes: Obtain the average waiting time for each mode of transportation mentioned in the previous time period; The average waiting time is weighted using the waiting time penalty value, and the weighted result is added to the utility value to obtain the set utility value of each mode of transportation in the current time period; The selection probability is determined using the Logit function based on the set utility value. The number of people to be evacuated for each mode of transportation is determined based on the chosen probabilities.

5. The urban multimodal passenger transport collaborative dispatching method based on the MPC and two-layer planning fusion framework as described in claim 4, characterized in that, The formula for calculating utility value is set as follows: in, It is the waiting time penalty value. Transportation mode for time period (t-1) Average waiting time; The formula for calculating the probability of selection is: In the formula: Choose a mode of transportation for time period t The probability of. The number of people evacuated by mode i at each time period is as follows: in, For transportation Capacity conversion factor; Transportation mode during time period t Scheduling frequency, For transportation Single transport capacity, Select transportation mode for passengers during the specified time period The probability of.

6. The urban multimodal passenger transport collaborative dispatching method based on the MPC and two-layer planning fusion framework as described in claim 1, characterized in that, The state transition equation for the number of stranded people is as follows: in, The predicted number of stranded people in the (t+1) period. Let t be the initial number of people remaining in the area. The number of newly arriving passengers during time period t. This represents the sum of the actual number of people evacuated from all modes of transportation during time period t.

7. The urban multimodal passenger transport collaborative dispatch method based on the MPC and two-layer planning fusion framework as described in claim 1, characterized in that, The NSGA-II genetic algorithm is used to solve the upper-level optimization model, including: Randomly generate the initial population within the scheduling frequency constraint; For each individual in the population, calculate the objective function values ​​for the number of stranded individuals, total operating costs, and average waiting time, and determine the fitness value. A non-dominated ranking strategy is used to hierarchically divide the fitness values ​​of all individuals in the population. Calculate the crowding distance between individuals within the same non-dominated hierarchy; Based on non-dominant hierarchy and crowding distance, a tournament selection strategy is used to select individuals for crossover and mutation operations to generate offspring populations. The parent and offspring populations are merged, and the non-dominated sorting and crowding distance calculations are performed again to select the next generation population. Repeat the above iterative process until the termination condition is met, and output the Pareto optimal solution set.

8. A collaborative dispatching system for urban multimodal passenger transport based on an MPC and two-layer planning fusion framework, characterized in that, include: The data acquisition module is used to acquire passenger selection feature data and capacity parameters of each mode of transportation; The utility function construction module is used to construct passenger choice utility functions based on the passenger choice feature data using a multinomial Logit model, and to determine the utility values ​​corresponding to each mode of transportation. The upper-level optimization module is used to construct an upper-level multi-objective optimization model. The upper-level multi-objective optimization model aims to minimize the number of people stranded in the hub station, minimize the average waiting time of passengers, and minimize the total operating cost of each mode of transportation. It uses the capacity parameters of each mode of transportation as decision variables and constructs a multi-objective optimization function and constraints. The lower-level evacuation module is used to construct a lower-level passenger selection evacuation model. The lower-level passenger selection evacuation model calculates the selection probability of each mode of transportation in the current time period based on the capacity parameters and utility values ​​of each mode of transportation, and determines the number of people to be evacuated for each mode of transportation based on the selection probability. The state prediction module is used to construct the state transition equation for the number of stranded people. The state transition equation predicts the number of stranded people in the next period based on the number of stranded people, the number of arrivals, and the number of evacuations in the current period. The solution module is used to solve the upper-level optimization model using the NSGA-II genetic algorithm, and to perform rolling time-domain optimization based on the state transition equation to obtain scheduling schemes for each mode of transportation that meet the predetermined optimization objectives.

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