Multi-objective optimization method for comprehensive passenger transfer system in metropolitan area

Abstract

This invention provides a multi-objective optimization method for integrated passenger transport transfer systems in urban agglomerations, relating to the field of passenger transport transfer analysis technology. The method includes: connecting the transfer structure information of the integrated passenger transport transfer system; constructing and analyzing a hierarchical structure model to obtain fuzzy hierarchical sub-models and non-fuzzy hierarchical sub-models; using fuzzy hierarchical analysis and analytic hierarchy process (AHP) to calculate the fuzzy and non-fuzzy hierarchical sub-models respectively, obtaining a first weight vector and a second weight vector; performing game-theoretic combination weighted optimization analysis; obtaining optimal solutions with combination coefficients; and scoring the transfer structure information. This invention solves the technical problems of existing integrated passenger transport transfer system evaluation methods, which suffer from single evaluation indicators and strong subjectivity, leading to low accuracy and reliability of evaluation results. It achieves the technical effect of improving the accuracy and reliability of evaluation results and enhancing the optimization effect of integrated passenger transport transfer systems in urban agglomerations.

Description

Technical Field

[0001] This invention relates to the field of passenger transport transfer analysis technology, specifically to a multi-objective optimization method for integrated passenger transport transfer systems in urban agglomerations. Background Technology

[0002] With the acceleration of urbanization and the continuous expansion of metropolitan areas, population mobility is becoming increasingly frequent. As a crucial node connecting various modes of transportation, the operational efficiency and service quality of integrated passenger transport transfer systems in metropolitan areas directly impact the overall effectiveness of the regional transportation network. However, existing evaluation methods for integrated passenger transport transfer systems often rely on single-objective optimization or subjective experience-based judgment. Single-objective optimization methods tend to focus only on one aspect of performance, such as transfer time or passenger flow, while neglecting other important factors, such as the convenience of transfer facilities and passenger comfort. This one-sided optimization can easily lead to transfer systems performing well in some aspects but exhibiting significant shortcomings in others, thus affecting overall operational efficiency and service quality. While subjective experience-based judgment can be combined with actual conditions, it lacks scientific rigor and repeatability. Different experts or decision-makers may provide different evaluations based on their own experience and preferences, leading to instability and uncertainty in the evaluation results, which is detrimental to systematic analysis and optimization.

[0003] In summary, existing technologies for evaluating integrated passenger transport transfer systems suffer from technical problems such as single evaluation indicators and strong subjectivity, leading to low accuracy and reliability of evaluation results and affecting the optimization effect of the transfer system. Summary of the Invention

[0004] The purpose of this application is to provide a multi-objective optimization method for integrated passenger transport transfer systems in urban agglomerations, in order to solve the technical problem that existing evaluation methods for integrated passenger transport transfer systems have single evaluation indicators and strong subjectivity, resulting in low accuracy and reliability of evaluation results and affecting the optimization effect of the transfer system.

[0005] In view of the above problems, this application provides a multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration. The method includes: connecting the transfer structure information of the integrated passenger transport transfer system; constructing a hierarchical structure model, wherein the hierarchical structure model includes a first-level objective layer, a second-level objective layer, and an indicator layer, wherein the second-level objective layer is a sub-objective of the first-level objective layer, and the indicator layer is a sub-objective of the second-level objective layer; parsing the hierarchical structure model to obtain a fuzzy hierarchical structure sub-model and a non-fuzzy hierarchical structure sub-model; using fuzzy hierarchical analysis to defuzzify the fuzzy hierarchical structure sub-model to obtain a first weight vector corresponding to the defuzzy hierarchical structure sub-model; using hierarchical analysis to calculate the non-fuzzy hierarchical structure sub-model to obtain a second weight vector; performing game-theoretic combination weighting optimization analysis on the first weight vector and the second weight vector to obtain a optimal solution with combination coefficients; using the optimal solution with combination coefficients to score the transfer structure information and obtain a scoring result.

[0006] Optionally, the source method, source object, and evaluation field of all indicators in the hierarchical model are parsed; quantitative confidence analysis of the indicators is performed according to the source method, source object, and evaluation field; indicators less than or equal to a preset confidence threshold are classified into fuzzy hierarchical sub-models, and indicators greater than the preset confidence threshold are classified into non-fuzzy hierarchical sub-models.

[0007] Optionally, a triangular fuzzy number is obtained by mapping according to a preset comparison scale; based on the triangular fuzzy number, pairwise comparisons are performed on the indicators in the fuzzy hierarchical sub-model to obtain P fuzzy judgment matrices; the P fuzzy judgment matrices are fuzzy averaged and fused to obtain a fused fuzzy judgment matrix; based on the fused fuzzy judgment matrix, defuzzification processing is performed to output a first weight vector.

[0008] Optionally, the fuzzy geometric mean of each row in the fused fuzzy judgment matrix is ​​calculated and normalized to obtain a fuzzy weight vector; the fuzzy weight vector is processed to obtain a scalar weight vector; the scalar weight vector of each index is hierarchically synthesized according to the hierarchical structure of the fuzzy hierarchical sub-model to output the first weight vector corresponding to the fuzzy hierarchical sub-model.

[0009] Optionally, after obtaining the fused fuzzy judgment matrix, a consistency check is performed on the fused fuzzy judgment matrix to obtain a consistency check result. The consistency check steps include splitting the fused fuzzy judgment matrix into a first corner matrix, a second corner matrix, and a third corner matrix; calculating the AHP consistency ratio for each of the first corner matrix, the second corner matrix, and the third corner matrix; if the AHP consistency ratio of any corner matrix is ​​greater than a set threshold, the consistency check result is output as failing; and the fused fuzzy judgment matrix is ​​corrected using the average of neighboring experts until the consistency check result passes.

[0010] Optionally, the indices of the non-fuzzy hierarchical sub-model are compared pairwise to obtain Q judgment matrices; each of the Q judgment matrices is used for vector calculation to output Q weight vectors; the Q weight vectors are then fused to obtain a second weight vector.

[0011] Optionally, a Nash equilibrium objective is defined, which is to maximize the product of the utility gain of the first weight vector and the utility gain of the second weight vector, wherein the utility gains of the first weight vector and the utility gains of the second weight vector are processed using the negative logarithmic distance; a regularization constraint is defined, which is a L2 penalty term for prior weight deviation; based on the regularization constraint and the Nash equilibrium objective, a game-theoretic combination weighting optimization analysis is performed on the first weight vector and the second weight vector to obtain the optimal solution of the combination coefficients.

[0012] Optionally, the first and second partial derivatives of the weight vector under the Nash equilibrium objective are obtained; a linear matrix equation is constructed based on the first and second partial derivatives of the weight vector, and the linear matrix equation is solved to obtain the optimal solution of the combination coefficients.

[0013] Optionally, the system connects to the transfer structure information of the integrated passenger transport transfer system; performs flow clustering analysis on the transfer structure information to obtain multiple transfer substructures; constructs multiple hierarchical structure models based on the multiple transfer substructures, and obtains multiple optimal solutions with combination coefficients using the multiple hierarchical structure models; scores the transfer structure information using the multiple optimal solutions with combination coefficients to obtain transfer substructures to be optimized, wherein the transfer substructures to be optimized are transfer substructures with scores below a first scoring threshold.

[0014] Optionally, connect the data entry module corresponding to the transfer structure information to obtain the hierarchical data model of the hierarchical structure model; use the optimal solution of the combination coefficients to score based on the hierarchical data model and obtain the scoring result.

[0015] One or more technical solutions provided in this application have at least the following technical effects or advantages:

[0016] The multi-objective optimization method for urban agglomeration integrated passenger transport transfer systems provided in this application constructs a hierarchical structure model by connecting the transfer structure information of the integrated passenger transport transfer system. The hierarchical structure model is analyzed to obtain fuzzy hierarchical sub-models and non-fuzzy hierarchical sub-models. The fuzzy hierarchical sub-models are defuzzified using fuzzy hierarchical analysis to obtain a first weight vector corresponding to the defuzzy hierarchical sub-model. The non-fuzzy hierarchical sub-models are then calculated using hierarchical analysis to obtain a second weight vector. A game-theoretic combination weighting optimization analysis is performed on the first and second weight vectors to obtain a optimal solution with combined coefficients. This optimal solution with combined coefficients is then used to score the transfer structure information to obtain a scoring result. This achieves a comprehensive and effective evaluation of the integrated passenger transport transfer system, improves the accuracy and reliability of the evaluation results, and ultimately enhances the optimization effect of the urban agglomeration integrated passenger transport transfer system.

[0017] The above description is merely an overview of the technical solution of this application. To enable a clearer understanding of the technical means of this application and to facilitate its implementation according to the description, and to make the above and other objects, features, and advantages of this application more apparent, specific embodiments of this application are described below. It should be understood that the content described in this section is not intended to identify key or important features of the embodiments of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent through the following description. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this application 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 merely exemplary. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 A flowchart illustrating the multi-objective optimization method for the integrated passenger transport transfer system in the metropolitan area provided in this application.

[0020] Figure 2 A flowchart illustrating the analytical hierarchical structure model in the multi-objective optimization method for the metropolitan area integrated passenger transport transfer system provided in this application. Detailed Implementation

[0021] This application provides a multi-objective optimization method for integrated passenger transport transfer systems in urban agglomerations. It addresses the technical problems of existing evaluation methods for integrated passenger transport transfer systems, which suffer from single evaluation indicators, strong subjectivity, and low accuracy and reliability of evaluation results, thus affecting the optimization effect of the transfer system. The method achieves a comprehensive and effective evaluation of the integrated passenger transport transfer system, improving the accuracy and reliability of evaluation results, and ultimately enhancing the optimization effect of the integrated passenger transport transfer system in urban agglomerations.

[0022] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. It should be understood that the present invention is not limited to the exemplary embodiments described herein. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. It should also be noted that, for ease of description, only the parts related to the present invention are shown in the accompanying drawings, not all of them.

[0023] like Figure 1 As shown, this application provides a multi-objective optimization method for an integrated passenger transport system in an urban agglomeration. The multi-objective optimization method for an integrated passenger transport system in an urban agglomeration includes:

[0024] Transfer structure information connecting the integrated passenger transport system.

[0025] Specifically, the system connects to the database of the metropolitan area's integrated passenger transport system via APIs, direct database connections, or file imports. This integrated passenger transport system includes, but is not limited to, geographic information systems (GIS), transportation operation databases, passenger flow monitoring systems, facility management systems, and public feedback systems. This connection allows access to the system's transfer structure information. Specifically, the GIS provides precise latitude and longitude coordinates, spatial layout, and physical path lengths of transfer corridors for transfer nodes such as high-speed rail stations, subway stations, bus hubs, and airports. The transportation operation database provides departure frequencies, first and last train times, fares, timetables, and real-time arrival and departure information for each route. The passenger flow monitoring system provides real-time and historical passenger flow, passenger flow direction, transfer passenger flow, and congestion levels for key nodes. The facility management system provides the quantity, status, and operational efficiency of facilities such as elevators, escalators, turnstiles, and security checkpoints. The public feedback platform provides textual reviews and ratings regarding the transfer experience. By connecting to this transfer structure information, a comprehensive analysis of the current status of the transfer system can be conducted, providing an accurate and reliable data foundation for optimizing the metropolitan area's integrated passenger transport system.

[0026] A hierarchical structure model is constructed, which includes a first-level target layer, a second-level target layer, and an indicator layer. The second-level target layer consists of sub-targets of the first-level target layer, and the indicator layer consists of sub-targets of the second-level target layer.

[0027] Specifically, after connecting the transfer structure information of the integrated passenger transport transfer system, a primary objective layer is defined based on this information and actual needs. This primary objective layer represents the highest goal of the entire optimization problem, addressing the overall optimization objective of the transfer system, such as layout rationality. Then, the primary objective is decomposed into multiple secondary objectives. These secondary objectives are sub-objectives for achieving the primary objective, representing more specific optimization goals, such as a rational hub layout. For each secondary objective, specific evaluation indicators are determined, forming an indicator layer. This indicator layer is a sub-objective of the secondary objective layer. For example, for the secondary objective of a rational hub layout, the indicator layer includes quantifiable indicators such as the proportion of urban core areas reachable from the hub station via rail transit and the average time taken to reach each urban core area from the hub station. Table 1 shows the global evaluation indicators for the integrated passenger transport transfer system.

[0028] Table 1: Overall Evaluation Indicators of Integrated Passenger Transport Transfer System

[0029]

[0030]

[0031] By decomposing and refining layer by layer, and combining the actual data and features in the transfer structure information, a hierarchical structure model containing a first-level target layer, a second-level target layer, and an indicator layer is constructed.

[0032] The hierarchical model is analyzed to obtain fuzzy hierarchical sub-models and non-fuzzy hierarchical sub-models.

[0033] like Figure 2 As shown, the method for parsing the hierarchical structure model to obtain fuzzy hierarchical sub-models and non-fuzzy hierarchical sub-models includes: parsing the indicator source method, indicator source object, and indicator evaluation field of all indicators in the hierarchical structure model; performing indicator quantification confidence analysis according to the indicator source method, indicator source object, and indicator evaluation field; classifying indicators less than or equal to a preset confidence threshold into the fuzzy hierarchical sub-model; and classifying indicators greater than the preset confidence threshold into the non-fuzzy hierarchical sub-model.

[0034] Specifically, after obtaining the hierarchical structure model, the source methods, source objects, and evaluation fields of all indicators in the model are analyzed. The source method refers to the way the indicator data is obtained, such as collecting subjective evaluations through the Delphi method, real-time system monitoring, or historical statistical reports. The source object refers to the entity that generates the indicator data, such as the system or a person. People include experts and passengers, which are subjective. If the data comes from an automated system, such as real-time passenger flow counts in an intelligent transportation system, the data is more objective and has a higher confidence level. The evaluation field refers to the specific form of the indicator data, divided into quantitative and qualitative fields. Quantitative fields include numerical values ​​and percentages, while qualitative fields include textual descriptions or ratings such as "very good," "good," "average," and "poor." By analyzing the source method, source object, and evaluation fields of the indicators, weights are assigned to each, and weighted scores are calculated to determine the quantitative confidence level of each indicator. For example, the source method, source object, and evaluation field are assigned weights of 0.4, 0.3, and 0.3, respectively. Different situations under each attribute correspond to different scores. For example, in the source method, automatic collection by the system is worth 1 point, expert scoring is worth 0.6 points, and questionnaires are worth 0.4 points; in the source object, automated equipment is worth 1 point, experts are worth 0.6 points, and passengers are worth 0.4 points; in the evaluation field, quantitative fields are worth 1 point, and qualitative fields are worth 0.5 points. Then, for each indicator, the corresponding score is found according to its specific attribute, and the weighted sum is performed. The final weighted total score is the quantitative confidence score of that indicator. Based on the characteristics of multiple indicators and specific practical needs, a pre-set reliability threshold is established. Using this pre-set reliability threshold and the quantitative confidence score of the indicators, the indicator data is divided into subjective fuzzy indicators and objective precise indicators. Specifically, indicators less than or equal to the pre-set reliability threshold are assigned to the fuzzy hierarchical sub-model, while indicators greater than the pre-set reliability threshold are assigned to the non-fuzzy hierarchical sub-model. For example, analyzing the indicator data B21 (comfort in gatherings and dispersals), which originates from passenger questionnaires, focuses on passengers' subjective feelings, and uses general fuzzy text as the evaluation field, a weighted average quantitative confidence analysis yields a confidence score of 0.43. Compared to the pre-set reliability threshold of 0.7, this score is less than the pre-set reliability threshold, thus this indicator is explicitly assigned to the fuzzy hierarchical sub-model. Conversely, the indicator B12 (average travel time between platforms), whose data originates from an automatic timing system, uses sensor devices, and uses precise minute values ​​as the evaluation field, has a confidence score of 1, which is greater than the threshold of 0.7. Therefore, it is assigned to the non-fuzzy hierarchical sub-model. Specifically, weights, scores, and reliability thresholds can be flexibly set according to actual needs, thereby adjusting the tolerance for indicator ambiguity. Through quantitative confidence analysis, indicators are divided into fuzzy and non-fuzzy categories, improving the accuracy and reliability of data analysis, and thus enhancing the effectiveness and accuracy of optimization decisions for the metropolitan area integrated passenger transport transfer system.

[0035] The fuzzy hierarchical sub-model is defuzzified using fuzzy hierarchical analysis to obtain the first weight vector corresponding to the defuzzified hierarchical sub-model.

[0036] Specifically, the indicators classified into the fuzzy hierarchical sub-model rely primarily on subjective human judgment, which introduces uncertainty. Fuzzy hierarchical analysis (AHP) is employed to analyze and process the fuzzy hierarchical sub-model. A fuzzy judgment matrix is ​​constructed based on pairwise comparisons of the indicators by experts. The comparison values ​​utilize triangular fuzzy numbers to quantify subjective uncertainty. Triangular fuzzy numbers are a mathematical tool used to quantify and express subjective uncertainty, describing the boundary and probability distribution of fuzzy concepts through three values ​​(lower limit, most likely value, and upper limit). The basic form of a triangular fuzzy number is (a, b, c), where a represents the minimum value, b represents the most likely value, and c represents the maximum value. Fuzzy numbers can more accurately reflect the subjective judgment of experts or decision-makers, addressing the uncertainty between indicators. Then, a fuzzy judgment matrix is ​​generated based on the comparison results, and a consistency check is performed to ensure logical rationality. Finally, the normalized eigenvector corresponding to the largest eigenvalue is calculated using the eigenvector method, yielding the first weight vector reflecting the relative importance of the indicators.

[0037] Fuzzy hierarchical analysis can effectively handle the uncertainty of indicators. By using fuzzy numbers and defuzzification, the weight calculation is made more consistent with the actual situation, thereby improving the reliability and accuracy of optimization analysis.

[0038] Furthermore, the fuzzy hierarchical sub-model is defuzzified using fuzzy hierarchical analysis. The method includes: obtaining triangular fuzzy numbers based on a preset comparison scale mapping; performing pairwise comparisons on the indicators in the fuzzy hierarchical sub-model based on the triangular fuzzy numbers to obtain P fuzzy judgment matrices; fusing the P fuzzy judgment matrices by fuzzy averaging to obtain a fused fuzzy judgment matrix; and performing defuzzification based on the fused fuzzy judgment matrix to output a first weight vector.

[0039] Specifically, based on a preset comparison scale, such as the 1-9 scale, expert evaluations such as "equally important," "slightly important," and "significantly important" are mapped to triangular fuzzy numbers to quantify the uncertainty boundary of subjective evaluations. Based on these triangular fuzzy numbers, all indicators in the fuzzy hierarchical sub-model are compared pairwise, generating P fuzzy judgment matrices, where P is a positive integer. Each element of the fuzzy judgment matrix is ​​a triangular fuzzy number, representing the fuzzy importance value of indicator i relative to indicator j. Using the geometric mean method, the arithmetic mean of each matrix element a, b, and c is directly calculated. The P fuzzy judgment matrices are then fused using fuzzy averaging to obtain a fused fuzzy judgment matrix. This fuzzy averaging fusion method combines multiple fuzzy judgment matrices into a single matrix, reducing individual differences and improving the stability of the judgments. Finally, defuzzification is performed based on the fused fuzzy judgment matrix. Using the centroid method, the fuzzy values ​​are converted into specific numerical values ​​by calculating the integral centroid of the fuzzy number membership function, thus outputting a first weight vector. This first weight vector reflects the relative importance of each indicator in the fuzzy hierarchical sub-model.

[0040] By quantifying subjective uncertainty through triangular fuzzy modeling and utilizing fuzzy fusion and defuzzification, the uncertainty of indicators in the fuzzy hierarchical sub-model is effectively addressed, improving the adaptability and reliability of the entire optimization scheme and thus enhancing the optimization effect of the metropolitan area integrated passenger transport transfer system.

[0041] Furthermore, the defuzzification process based on the fused fuzzy judgment matrix includes: calculating the fuzzy geometric mean of each row in the fused fuzzy judgment matrix and normalizing it to obtain a fuzzy weight vector; processing the fuzzy weight vector to obtain a scalar weight vector; and performing hierarchical synthesis of the scalar weight vector of each indicator according to the hierarchical structure of the fuzzy hierarchical sub-model to output the first weight vector corresponding to the fuzzy hierarchical sub-model.

[0042] Specifically, for the elements in the i-th row of the fusion fuzzy judgment matrix, each element is a triangular fuzzy number, representing the importance fuzzy value of index i relative to other indices. The geometric mean method is used to calculate its comprehensive fuzzy weight, obtaining the average fuzzy importance of that index relative to all other indices. The geometric mean preserves the boundary information of the fuzzy numbers, avoiding the fuzziness decay that may occur with the arithmetic mean. The fuzzy geometric mean of all rows is normalized, and the ratio of each fuzzy weight to the sum of all fuzzy weights is calculated to obtain a fuzzy weight vector representing the initial fuzzy weights of each index, ensuring that the sum of the weights is 1 while maintaining the form of fuzzy numbers. Then, the fuzzy weight vector is defuzzified to convert it into scalar weights. For example, the centroid method is used, mapping the fuzzy value to a sharp value by calculating the integral centroid of the membership function of the triangular fuzzy number. For the triangular fuzzy number (a, b, c), its center coordinates are w = (w... a+2w b +w c ) / 4, calculate the centroid coordinates of each triangular fuzzy number, and transform each fuzzy weight into a single scalar weight, obtaining a scalar weight vector. This scalar weight vector is the defuzzified result and represents the relative importance of each indicator. Then, according to the hierarchical structure of the fuzzy hierarchical sub-model, multiply the weights of lower-level indicators with the weights of upper-level sub-objectives, synthesizing them layer by layer upwards, ultimately obtaining the first weight vector corresponding to the fuzzy hierarchical sub-model.

[0043] By transforming the uncertainty information in the fuzzy judgment matrix into specific weight vectors, a precise quantitative basis is provided for the optimization decision of the transfer system. This not only improves the accuracy and reliability of the optimization decision, but also enables the fuzzy hierarchical structure to be effectively applied to practical optimization problems, thereby enhancing the effectiveness and adaptability of the entire scheme.

[0044] Furthermore, after obtaining the fused fuzzy judgment matrix, a consistency check is performed on the fused fuzzy judgment matrix to obtain the consistency check result. The consistency check steps include splitting the fused fuzzy judgment matrix into a first corner matrix, a second corner matrix, and a third corner matrix, calculating the AHP consistency ratio for each of the first corner matrix, the second corner matrix, and the third corner matrix, and outputting a consistency check result of failing if the AHP consistency ratio of any corner matrix is ​​greater than a set threshold. The fused fuzzy judgment matrix is ​​then corrected using the average of neighboring experts until the consistency check result passes.

[0045] Specifically, after obtaining the fused fuzzy judgment matrix, a consistency check is performed on the matrix to ensure its rationality and reliability. During the consistency check, the fused fuzzy judgment matrix is ​​first split into three corner matrices: the first corner matrix, the second corner matrix, and the third corner matrix. Corner matrices are specific parts extracted from the original matrix and used to check the consistency of different parts of the matrix. The first corner matrix consists of all 'a' values, representing the minimum value matrix; the second corner matrix consists of all 'b' values, representing the most probable value matrix; and the third corner matrix consists of all 'c' values, representing the maximum value matrix. Then, the AHP (Aspect-Hyperbidic Hierarchy) method is used to calculate the AHP consistency ratio for each of the three corner matrices. The AHP consistency ratio measures the consistency of the judgment matrix. The maximum eigenvalue of each matrix is ​​calculated, and the formula CR = CI / RI is used, where CI is the consistency index, derived from the maximum eigenvalue of the judgment matrix, and RI is the random consistency index, whose value is related to the matrix order. If the AHP consistency ratio of any corner matrix is ​​greater than a set threshold of 0.1, the consistency of that corner matrix is ​​considered to have failed, and the consistency check result of the entire fused fuzzy judgment matrix is ​​also considered to have failed. Conversely, if the consistency test of the fused fuzzy judgment matrix is ​​passed, it is considered to have passed. When the output consistency test result fails, the elements in the fused fuzzy judgment matrix are adjusted using the average judgment value of neighboring experts. The original judgment matrix of the individual expert whose deviation from the fused matrix is ​​the furthest is identified, and the original value is replaced by the average of the fuzzy evaluations of its neighboring experts. After correction, the fused fuzzy judgment matrix is ​​regenerated, and the steps of splitting the corner matrices and the consistency test are repeated until the CR of all corner matrices is ≤0.1. Finally, the result of passing the consistency test is output.

[0046] Consistency checks can identify and correct inconsistencies in the fused fuzzy judgment matrix, avoiding erroneous decisions caused by inconsistent judgments. This ensures the rationality and reliability of the fused fuzzy judgment matrix, thereby improving the accuracy and reliability of the optimization decision scheme.

[0047] The second weight vector is obtained by calculating the non-fuzzy hierarchical sub-model using the analytic hierarchy process (AHP).

[0048] Furthermore, the analytic hierarchy process (AHP) is used to calculate the non-fuzzy hierarchical sub-model to obtain a second weight vector. The method includes: performing pairwise comparisons of the indices of the non-fuzzy hierarchical sub-model to obtain Q judgment matrices; performing vector calculations on each of the Q judgment matrices to output Q weight vectors; and fusing the Q weight vectors to obtain a second weight vector.

[0049] Specifically, the analytic hierarchy process (AHP) is used to calculate the non-fuzzy hierarchical sub-model. First, using the 1-9 scaling method, pairwise comparisons are performed on the indicators of the non-fuzzy hierarchical sub-model to obtain Q judgment matrices. Each matrix corresponds to the comparison result of a level or a set of indicators. Then, the eigenvector method is used to perform vector calculations on each of the Q judgment matrices. By calculating the maximum eigenvalue and its corresponding eigenvector of each matrix, the eigenvectors are normalized to obtain the corresponding weight vectors, forming Q weight vectors. After calculating the Q weight vectors, a geometric mean is applied to the Q weight vectors to obtain a second weight vector. The second weight vector reflects the importance of the objective and logical indicators.

[0050] By calculating the weights of indicators in a non-fuzzy hierarchical sub-model using the analytic hierarchy process (AHP), non-fuzzy indicators can be processed accurately and effectively, thereby improving the accuracy of evaluation results and, consequently, the accuracy and reliability of optimization schemes.

[0051] A game-theoretic combination weighting optimization analysis is performed on the first weight vector and the second weight vector to obtain a optimal solution for the combination coefficients. The optimal solution for the combination coefficients is then used to score the transfer structure information to obtain a scoring result.

[0052] Furthermore, a game-theoretic combination weighting optimization analysis is performed on the first weight vector and the second weight vector to obtain the optimal solution for the combination coefficients. The method includes: defining a Nash equilibrium objective, which is to maximize the product of the utility gain of the first weight vector and the utility gain of the second weight vector, wherein the utility gain of the first weight vector and the utility gain of the second weight vector are processed using the negative logarithmic distance; defining a regularization constraint, which is a L2 penalty term for prior weight deviation; and performing a game-theoretic combination weighting optimization analysis on the first weight vector and the second weight vector based on the regularization constraint and the Nash equilibrium objective to obtain the optimal solution for the combination coefficients.

[0053] Specifically, when performing game-theoretic combination weighting optimization analysis on the first and second weight vectors, we first define the Nash equilibrium objective. Nash equilibrium is a game theory concept used to describe the stable state of a non-cooperative game. Its core logic is that, given the strategies of other participants, each participant has no incentive to unilaterally change their strategy. Specifically, it is defined as follows: In the game, if each participant's strategy set is Si, and the participant's payoff function is u... i (s1, s2……s n) Strategy combination For a Nash equilibrium to exist, it is true if and only if: , For player i, the optimal strategy is... This represents the equilibrium strategy for all players except player i. The Nash equilibrium objective is to maximize the product of the utility gains of the first and second weight vectors. Utility gain refers to the additional benefit obtained through optimizing weight allocation, quantified using negative logarithmic distance. Specifically, for the first and second weight vectors, the negative Euclidean distance to the ideal weights (such as unit vectors or preset benchmark weights) is calculated, and a logarithmic transformation is applied to smooth out extreme value effects, ensuring that the gain contributions of the two weight vectors maintain proportional coordination when combined, and preventing a single weight from dominating the result due to an excessively large numerical range. Then, a regularization constraint is defined, using a L2 penalty term for deviations from prior weights, such as simple average weights or historical experience weights, as the optimization constraint. The L2 penalty term is a commonly used regularization method that limits the size of the weight vectors to prevent excessively extreme or unreasonable weight allocation, thereby improving the stability of the combined weights. Finally, based on the regularization constraints and the Nash equilibrium objective, a game-theoretic combination weighting optimization analysis is performed on the first weight vector and the second weight vector. Specifically, an optimization model is constructed based on the Nash equilibrium objective and the regularization constraints. The optimization model uses the Nash equilibrium objective as the objective function and the regularization constraints as the constraint conditions. Game theory methods for solving Nash equilibrium, such as alternating optimization, gradient descent, or the Lagrange multiplier method, are used to dynamically adjust the combination coefficients in the relationship between the two weight vectors until an equilibrium state is reached that maximizes the product of utility gains and minimizes the deviation penalty. The optimal solution of the combination coefficients is then output. This optimal solution is used to score the transfer structure information, obtaining a score result reflecting the overall performance of the transfer structure.

[0054] By employing game-theoretic combination weighting optimization analysis, the weights of fuzzy and non-fuzzy indicators are comprehensively considered, avoiding the one-sidedness of single-weighting methods. This effectively balances the contributions of different types of indicators to the optimization objective, ensuring that the scoring results possess both the inclusiveness of fuzzy evaluation to uncertainty and the logical rigor of hierarchical analysis, thereby improving the accuracy and reliability of the entire optimization scheme. Furthermore, the scoring results provide a direct assessment of the performance of the integrated passenger transport transfer system, offering accurate and reliable decision-making basis for system optimization.

[0055] Furthermore, the method of scoring the transfer structure information using the optimal solution of the combination coefficients and obtaining the scoring result includes: connecting the data input module corresponding to the transfer structure information to obtain the hierarchical data model of the hierarchical structure model; and using the optimal solution of the combination coefficients to score based on the hierarchical data model and obtain the scoring result.

[0056] Specifically, the system interface connects to the data entry module corresponding to the transfer structure information. This data entry module is part of the integrated passenger transfer system used to collect and organize transfer structure information, providing detailed data about the transfer system. By connecting to the data entry module, the hierarchical data model of the hierarchical structure model is obtained. This hierarchical data model contains the actual values ​​of all indicators. The optimal solution for the combination coefficients is obtained through game-theoretic combination weighting optimization analysis, reflecting the relative importance of each indicator in the comprehensive evaluation. The optimal solution for the combination coefficients is used to recursively weight and score the hierarchical data model. Starting from the bottom-level indicators, the actual data is standardized, such as by using range transformation to eliminate the influence of dimensions, and then multiplied by the corresponding level's combination weight. This process is then aggregated layer by layer to the top-level indicator. The weighted values ​​of all indicators are summed to finally generate a score reflecting the overall performance of the transfer structure.

[0057] By connecting the data entry module corresponding to the transfer structure information, a hierarchical data model of the hierarchical structure model is obtained, realizing the integration of multi-source data in the transfer system and clarifying the hierarchical correlation and logical relationship between various indicators. The optimal solution of the combination coefficients is used to evaluate the hierarchical data model, improving the accuracy and reliability of the transfer system performance evaluation, while providing data support for the dynamic optimization of the transfer system, realizing efficient resource allocation, service synergy improvement, and overall efficiency maximization of the urban agglomeration passenger transfer system.

[0058] Furthermore, the method for constructing a hierarchical structure model also includes: connecting the transfer structure information of the integrated passenger transport transfer system; performing flow clustering analysis on the transfer structure information to obtain multiple transfer substructures; constructing multiple hierarchical structure models based on the multiple transfer substructures respectively, and obtaining multiple optimal solutions with combination coefficients using the multiple hierarchical structure models; scoring the transfer structure information with the multiple optimal solutions with combination coefficients to obtain transfer substructures to be optimized, wherein the transfer substructures to be optimized are transfer substructures with scores less than a first scoring threshold.

[0059] Specifically, the system connects the transfer structure information of the integrated passenger transport system and performs flow clustering analysis on this information. Using passenger density, transfer frequency, and time distribution as feature dimensions, the system divides each transfer point and route in the transfer structure into multiple substructures based on flow characteristics. For example, the distance from each data point to the cluster center is calculated using the K-means algorithm, and the data points are assigned to the nearest cluster center, thus forming multiple transfer substructures. Each substructure contains a group of transfer points and routes with similar flow characteristics. Then, multiple hierarchical models are constructed based on these substructures. Each hierarchical model includes a first-level objective layer, a second-level objective layer, and an indicator layer. Similarly, weight calculations and optimization analyses are performed on each hierarchical model to obtain multiple optimal solutions for combined coefficients. These optimal solutions are obtained through game-theoretic combination weighting optimization analysis, reflecting the relative importance of each indicator in the comprehensive evaluation. Through optimization analysis, the most suitable weight allocation scheme for each transfer substructure can be found. Finally, multiple optimal solutions for combined coefficients are used to score the transfer structure information. These optimal solutions are then applied to the hierarchical data model, and a comprehensive score for each transfer substructure is calculated using a weighted summation method. Based on the scoring results, transfer substructures with scores below a first scoring threshold are identified as those requiring optimization.

[0060] By dividing the transfer system into multiple substructures through traffic clustering analysis and identifying the substructures to be optimized through scoring, the focus of optimization can be clarified, providing a clear direction for the optimization measures of the metropolitan area's integrated passenger transfer system. This ensures the rational allocation of resources and the efficient implementation of optimization work, improves the pertinence and effectiveness of optimization, and promotes the high-quality development of the metropolitan area.

[0061] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. 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 this application. Therefore, this application 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.

[0062] Obviously, those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration, characterized in that, The method includes: Transfer structure information connecting the integrated passenger transport system; A hierarchical structure model is constructed, which includes a first-level target layer, a second-level target layer, and an indicator layer. The second-level target layer consists of sub-targets of the first-level target layer, and the indicator layer consists of sub-targets of the second-level target layer. The hierarchical model is analyzed to obtain a fuzzy hierarchical sub-model and a non-fuzzy hierarchical sub-model; The fuzzy hierarchical sub-model is defuzzified using the fuzzy hierarchical analysis method to obtain the first weight vector corresponding to the defuzzy hierarchical sub-model. The second weight vector is obtained by calculating the non-fuzzy hierarchical sub-model using the analytic hierarchy process (AHP). A game-theoretic combination weighting optimization analysis is performed on the first weight vector and the second weight vector to obtain a optimal solution for the combination coefficients. The optimal solution for the combination coefficients is then used to score the transfer structure information to obtain a scoring result. The process of defuzzifying the fuzzy hierarchical sub-model using fuzzy hierarchical analysis includes: The triangular fuzzy number is obtained based on the preset comparison scale mapping; Based on the triangular fuzzy number, pairwise comparisons are performed on the indicators in the fuzzy hierarchical sub-model to obtain P fuzzy judgment matrices. The P fuzzy judgment matrices are fused by fuzzy averaging to obtain a fused fuzzy judgment matrix. Based on the fused fuzzy judgment matrix, defuzzification is performed to output the first weight vector. The defuzzification process based on the fused fuzzy judgment matrix includes: The fuzzy geometric mean of each row in the fused fuzzy judgment matrix is ​​calculated and normalized to obtain the fuzzy weight vector; The fuzzy weight vector is processed to obtain a scalar weight vector; According to the hierarchical structure of the fuzzy hierarchical sub-model, the scalar weight vector of each indicator is hierarchically synthesized, and the first weight vector corresponding to the fuzzy hierarchical sub-model is output. The step of performing game-theoretic combination weighting optimization analysis on the first weight vector and the second weight vector to obtain the optimal solution of the combination coefficients includes: Define a Nash equilibrium objective, which is to maximize the product of the utility gain of the first weight vector and the utility gain of the second weight vector, wherein the utility gain of the first weight vector and the utility gain of the second weight vector are processed using the negative logarithmic distance. Define a regularization constraint, which is a L2 penalty term for deviation of prior weights; Based on the regularization constraints and the Nash equilibrium objective, a game-theoretic combination weighting optimization analysis is performed on the first weight vector and the second weight vector to obtain the optimal solution of the combination coefficients.

2. The multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration as described in claim 1, characterized in that, The method for parsing the hierarchical model to obtain fuzzy hierarchical sub-models and non-fuzzy hierarchical sub-models includes: Analyze the indicator source method, indicator source object, and indicator evaluation field of all indicators in the hierarchical structure model; Based on the indicator source method, indicator source object, and indicator evaluation field, the indicator quantification confidence analysis is performed. Indicators less than or equal to the preset confidence threshold are classified into fuzzy hierarchical sub-models, and indicators greater than the preset confidence threshold are classified into non-fuzzy hierarchical sub-models.

3. The multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration as described in claim 1, characterized in that, After obtaining the fused fuzzy judgment matrix, a consistency check is performed on the fused fuzzy judgment matrix to obtain the consistency check result; The consistency check step includes splitting the fused fuzzy judgment matrix into a first corner matrix, a second corner matrix, and a third corner matrix, calculating the AHP consistency ratio for each of the first corner matrix, the second corner matrix, and the third corner matrix, and outputting a consistency check result of failing if the AHP consistency ratio of any corner matrix is ​​greater than a set threshold. The fusion fuzzy judgment matrix is ​​then corrected using the average of neighboring experts until the consistency test result passes.

4. The multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration as described in claim 1, characterized in that, The second weight vector is obtained by calculating the non-fuzzy hierarchical sub-model using the analytic hierarchy process (AHP). The method includes: The indices of the non-fuzzy hierarchical sub-model are compared pairwise to obtain Q judgment matrices; Each of the Q judgment matrices is obtained and vector calculation is performed to output Q weight vectors. The Q weight vectors are then fused to obtain a second weight vector.

5. The multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration as described in claim 1, characterized in that, Based on the regularization constraints and the Nash equilibrium objective, a game-theoretic combination weighting optimization analysis is performed on the first weight vector and the second weight vector, including the following methods: Obtain the partial derivatives of the first and second weight vectors under the Nash equilibrium objective; Construct a linear matrix equation based on the partial derivatives of the first and second weight vectors, solve the linear matrix equation, and obtain the optimal solution for the combination coefficients.

6. The multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration as described in claim 1, characterized in that, Methods for constructing hierarchical models also include: Transfer structure information connecting the integrated passenger transport system; Perform traffic clustering analysis on the transfer structure information to obtain multiple transfer substructures; Multiple hierarchical models are constructed based on the multiple transfer substructures, and multiple optimal solutions with combined coefficients are obtained using the multiple hierarchical models; The transfer structure information is scored using the multiple optimal solutions of the combination coefficients to obtain the transfer substructure to be optimized. The transfer substructure to be optimized is the transfer substructure with a score less than the first score threshold.

7. The multi-objective optimization method for an integrated passenger transport transfer system in an urban agglomeration as described in claim 1, characterized in that, The method for scoring the transfer structure information using the optimal solution of the combination coefficients and obtaining the scoring result includes: Connect the data entry module corresponding to the transfer structure information to obtain the hierarchical data model of the hierarchical structure model; The optimal solution of the combined coefficients is used to score based on the hierarchical data model to obtain the scoring result.

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