An urban multi-modal public transport network emergency rescue material layout optimization method

Abstract

The application discloses a kind of urban multimodal public transport network emergency rescue material layout optimization method, belong to urban rail transit emergency management technical field, comprising: obtaining the total resource demand point of target city multimodal public transport network;Based on total resource demand point, utilize the rescue demand under the occurrence of sudden event to carry out measurement using triangular fuzzy number to defuzzification method, obtain the emergency resource demand of each resource demand point;Build multimodal emergency rescue material layout optimization model;ε constraint method based multi-objective genetic algorithm is used to solve the multimodal emergency rescue material layout optimization model, generate Pareto non-inferior solution set;Select optimal solution from Pareto non-inferior solution set as emergency rescue material layout scheme, output reserve station location result, resource quota configuration scheme of each reserve station and distribution link scheme.The method provides scientific basis and decision support for super large city emergency resource preposition and traffic system resilience improvement.

Description

Technical Field

[0001] This application relates to the field of urban rail transit emergency management technology, and in particular to a method for optimizing the layout of emergency rescue materials in urban multimodal public transport networks. Background Technology

[0002] With the acceleration of urbanization, megacities face severe challenges from multiple emergencies, including natural disasters and public health emergencies, due to their high population density and complex infrastructure. In emergency management systems, the optimized allocation of pre-disaster emergency resources is a crucial prerequisite for improving rescue efficiency and urban resilience; its scientific nature directly determines the success or failure of the rescue response. The efficient allocation of emergency resources relies on a reliable transportation network. As the core infrastructure for maintaining daily urban operations and emergency evacuation, the multimodal public transportation network, consisting of rail transit and surface buses, often exhibits significant vulnerability in the face of emergencies.

[0003] Existing research has achieved certain results in the field of emergency resource allocation, but the following shortcomings still exist: First, most existing models treat public transportation networks as homogeneous systems, and few studies distinguish the heterogeneity and shared nature of different modes of transportation, such as subways and regular buses, in terms of rescue needs; Second, emergency rescue has a significant "golden time" effect, and most studies use the linear transportation time assumption when calculating rescue costs, ignoring the objectively existing utility decay characteristics of emergency resources during delivery delays; Third, existing objective functions mostly focus on traditional economic costs or coverage efficiency, and rarely consider the core objective of "reducing the residual severity of the system," which reflects the essence of resilience; Fourth, existing research constructs single-dimensional fuzzy or stochastic models based on the uncertainty of demand and the spatiotemporal characteristics of disasters, and rarely considers the multidimensional coupled uncertainty of demand scale, demand type, and response time constraints simultaneously. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this application provides an optimization method for the layout of emergency rescue materials in urban multimodal public transport networks. This method solves the problems of existing technologies such as ignoring the heterogeneity and sharing of multimodal transportation, neglecting the "golden time" effect of rescue, the objective function deviating from the nature of resilience, and not considering the uncertainty of multidimensional coupling.

[0005] To achieve the aforementioned objectives, the technical solution adopted in this application is as follows: This application provides a method for optimizing the layout of emergency rescue supplies in urban multimodal public transport networks, including: S1: Obtain the total resource demand points of the multi-modal public transport network of the target city. The resource demand points include the spatial location information of subway stations, ground bus stops, candidate emergency material reserve stations, as well as the road network distance and transportation speed between each station. S2: Based on the total resource demand points, the rescue demand under the event of an emergency is calculated using the triangular fuzzy number defuzzification method to obtain the emergency resource demand of each resource demand point; S3: Construct a multi-mode emergency rescue material layout optimization model. The multi-mode emergency rescue material layout optimization model takes minimizing the overall system cost and minimizing the residual severity of each disaster point after rescue as the dual objective function. The overall system cost includes the fixed construction cost of the storage station, the resource reserve cost, the dynamic transportation cost, and the fixed transportation cost. S4: The multi-objective genetic algorithm based on the ε-constraint method is used to solve the multi-mode emergency rescue material layout optimization model, generate a Pareto non-dominated solution set, and select the optimal solution from the Pareto non-dominated solution set as the emergency rescue material layout scheme.

[0006] Further, S2 includes: S201: Assume that the fuzzy probability of a sudden event occurring at each resource demand point during the planning period is a triangular intuitionistic fuzzy number, calculated using the following formula:

[0007] in, For resource demand points The fuzzy probability of the occurrence of a sudden event. The triangular membership degree, representing the probability of an emergency occurring, corresponds to the resource demand points. Optimistic, most likely, and pessimistic estimates The triangular non-membership degree represents the probability that a sudden event will not occur, corresponding to the resource demand points. Optimistic, most likely, and pessimistic estimates of the probability that a sudden event will not occur; S202: The triangular intuitionistic fuzzy number is defuzzified using an improved scoring function combined with the centroid method to obtain the expected disaster intensity. The calculation formula is as follows:

[0008] in, For resource demand points The intensity of expected disaster impact; S203: Based on the expected intensity of the disaster, estimate the emergency resource demand for each resource demand point. The calculation formula is as follows:

[0009] in, For resource demand points Emergency resources The demand for emergency resources, For the collection of emergency resources, For a collection of shared resources, A collection of resources specifically for subway use. A collection of dedicated public transportation resources. and To share resources, and Dedicated resources for subway use. Dedicated to public transportation resources For resource applicability coefficient, The comprehensive risk impact coefficient is based on passenger flow. For emergency resources At emergency resource demand points Unit conversion factor.

[0010] Furthermore, the multi-mode emergency rescue material layout optimization model is as follows:

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[0025] in, For the overall system cost, Candidate emergency supplies reserve station Fixed construction costs, To determine whether to select candidate emergency supplies reserve stations The 0-1 variables for building a reserve station Candidate emergency supplies reserve station Configure emergency resources Storage costs, Candidate emergency supplies reserve station The number of emergency resources configured, For emergency resources The unit time transportation rate, For emergency resources From candidate emergency supplies storage stations To the resource demand point The rescue time Candidate emergency supplies reserve station To the resource demand point Road network distance, For emergency resources Delivery speed, For emergency resources Fixed processing time, Candidate emergency supplies reserve station Actual delivery to resource demand points emergency resources The supply, Candidate emergency supplies reserve station Towards resource demand points Fixed delivery costs for transporting resources To determine candidate emergency material reserve stations Resource demand points Does the delivery link contain 0-1 variables? Gathering for candidate emergency supplies storage stations. For total resource demand point, To determine the severity of the remaining damage at each disaster site after the rescue efforts, For resource demand points The residual severity after receiving emergency resources To determine candidate emergency material reserve stations Should we direct resources to the demand point? Provide emergency resources 0-1 variables, This represents the maximum number of candidate emergency material reserve stations that can be built. For candidate emergency supplies storage stations Deployable emergency resources The upper limit, For emergency resources The total system budget For resource demand points Emergency resources The upper limit of a single delivery capacity, For resource demand points The initial severity after encountering a sudden event. For emergency resources The marginal mitigation effect coefficient, For emergency resources To alleviate resource demand points The weighting coefficient of the disaster situation satisfies , It is a time decay function. For resources at the resource demand point Failure threshold For resources at the resource demand point The effective time threshold, For emergency resources Maximum allowed response time It is a constant.

[0026] Furthermore, the multi-objective genetic algorithm based on the ε-constraint method includes: A two-layer loop architecture is adopted, with the outer loop adjusting the budget constraint by stepping, and the inner loop using an improved genetic algorithm to search for the optimal solution.

[0027] Further, S4 includes: S401: Based on the multi-mode emergency rescue material layout optimization model, key basic data are obtained, key parameters are set, and a budget constraint set is defined. The key parameters include population size, maximum number of iterations, crossover probability, mutation probability, and penalty factor. S402: Based on key basic data and key parameters, form an initial Pareto non-dominated solution set and set initial budget constraints; S403: Obtain the emergency rescue material layout optimization scheme as a chromosome from the initial Pareto non-dominated solution set, use a binary and real number mixed encoding method to segment the chromosome, and generate an initial population based on the gene position of each chromosome gene segment using a random generation method. The chromosome gene segment includes candidate facility status, service link decision and resource allocation amount. S404: Based on the initial population, initial budget constraints, and key parameters, the inner loop is called to search for the optimal solution under the current constraints using an improved genetic algorithm. The outer loop is used to determine whether the budget constraint set has been traversed. If so, a Pareto non-dominated solution set is constructed by using the optimal solutions under each budget constraint. Otherwise, the current budget constraint is updated, and the genetic algorithm is called again to perform inner loop optimization. S405: Select the optimal solution from the Pareto non-dominated solution set as the emergency relief material layout scheme.

[0028] Furthermore, the key basic data obtained based on the multi-mode emergency rescue material layout optimization model includes: The spatial coordinates of candidate emergency material storage stations and resource demand points are read using the readtable operator, along with the emergency resource demand of each resource demand point for various types of emergency materials. The road network distance between candidate emergency material storage stations and resource demand points is calculated based on the Haversine formula, and the time decay function value is calculated by combining the material transportation speed and fixed processing time. The allocation weight coefficient is determined based on the resource applicability coefficient.

[0029] Furthermore, the method of using an improved genetic algorithm to search for the optimal solution under a given budget includes: A1: Using the tournament selection method, a number of individuals are randomly selected from the initial population to compete, and the individual with the highest fitness is selected to enter the next generation. This process is repeated until the mating pool is full. A2: Based on the mating pool, the multi-point crossover method is used to randomly select two paternal chromosomes, generate two random crossover points, exchange the corresponding gene segments of the two paternal chromosomes, and produce two offspring individuals; A3: Based on offspring individuals, a single-point random mutation method is used to generate random natural numbers to represent mutated gene loci; A4: For illegal solutions generated after mutation, perform a two-stage repair including logical repair and greedy budget repair; A5: Based on the repaired illegal solutions, calculate the fitness value of each individual using the fitness function, compare the fitness values ​​of individuals in the current population, and update the globally optimal individual and its corresponding optimal value. The calculation formula is as follows:

[0030] in, For the fitness function, As a penalty factor, Due to budget constraints, Additional penalty value for an individual who violates the constraint; A6: When the maximum number of iterations is reached, the inner loop stops and outputs the optimal solution under the current budget constraint; otherwise, it continues to iterate in A1.

[0031] Furthermore, the logic repair includes: determining whether to select a candidate emergency supplies reserve station. 0-1 variables in the construction of reserve stations If the value is 0, then the amount of a certain emergency resource stored in the relevant emergency material reserve station, the 0-1 variable that determines whether the distribution link is opened, and the amount of a certain resource delivered by the emergency material reserve station to the resource demand point are set to zero, and the timeout service link is shut down according to the failure threshold. The greedy budget repair includes: if the overall system cost exceeds the current budget limit, calculating the overall system cost savings after shutting down each facility, prioritizing the shutdown of the facility with the highest cost contribution, until the overall system cost does not exceed the current budget limit.

[0032] Furthermore, the construction of a Pareto nondominated solution set by combining the optimal solutions under various budget constraints includes: The Pareto non-dominated solution set is obtained by extracting the overall system cost and the residual severity of each disaster site after rescue from the optimal solution under each budget constraint.

[0033] The beneficial effects of this application are: This application provides a method for optimizing the layout of emergency relief supplies in urban multimodal public transport networks. Based on the need to enhance the resilience of urban multimodal public transport networks, and addressing the problem of optimizing the layout of emergency relief supplies before disasters, it proposes an optimization model with dual objectives of minimizing total system cost and residual disaster severity. This model distinguishes between the heterogeneity and shared nature of rescue efforts between subways and buses, introduces triangular fuzzy numbers to estimate the rescue needs of each disaster-stricken point, and integrates a time-effect decay function to characterize the "golden time" effect of emergency resources, making the rescue plan more realistic. Through an improved multi-objective genetic algorithm based on the ε-constraint method, the Pareto non-dominated solution set between cost and resilience is obtained, providing a scientific basis and decision support for the pre-positioning of emergency resources and the enhancement of transportation system resilience in megacities. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of 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 only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0035] Figure 1 This application provides a schematic diagram of the collaborative layout of emergency resources for a multimodal urban public transport network.

[0036] Figure 2 This is a flowchart illustrating a method for optimizing the layout of emergency rescue supplies in a multimodal urban public transport network, as provided in this application.

[0037] Figure 3 A method provided for this application Algorithm flowchart.

[0038] Figure 4 This is a schematic diagram of the spatial distribution of candidate stations and demand points provided for this application.

[0039] Figure 5 This application provides a heat map of the spatial distribution of emergency public transportation demand in Chengdu.

[0040] Figure 6 A method provided for this application A schematic diagram of the Pareto front distribution of the algorithm.

[0041] Figure 7 This is a schematic diagram illustrating the performance comparison of an algorithm provided in this application.

[0042] Figure 8 A convergence iteration graph is provided for this application.

[0043] Figure 9 This is a schematic diagram of the spatial distribution of site selection results provided in this application.

[0044] Figure 10 This is a schematic diagram of the spatial distribution of site selection results and demand points provided for this application.

[0045] Figure 11 This is a schematic diagram of a site selection and resource allocation scheme provided for this application.

[0046] Figure 12 This application provides a different scenario Trend chart. Detailed Implementation

[0047] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.

[0048] Sudden incidents can easily lead to large-scale paralysis of multimodal public transport networks. To restore the normal resilience of the transportation system, rescue measures such as track reinforcement, line clearing, and emergency communication support are typically required. These rescue operations require the use of specialized emergency supplies and equipment, including general resources (such as first aid kits and fire extinguishers), subway-specific resources (such as track repair parts), and bus-specific resources (such as road clearing equipment). To improve emergency response efficiency, management departments need to pre-deploy emergency rescue reserve stations in the transportation network, each with a certain service area (coverage radius). Assuming that various emergency supplies are initially stored in the reserve stations, appropriate types of supplies and equipment are dispatched to carry out targeted rescue operations based on the type of disaster site (subway station or surface bus stop). The timeliness of rescue activities is determined by the response time from each disaster site to the reserve station, and the effectiveness of rescue evolves over time through a process of "full effectiveness - decay - failure." Given limited resource costs, it is urgent to optimize the spatial layout of reserve stations, rationally allocate the reserve quotas for the three types of resources, and establish optimal distribution links to minimize the residual severity of the system and improve the overall resilience of the road network.

[0049] How to scientifically allocate emergency relief supplies based on potential risk scenarios before a disaster, thereby enhancing the resilience of urban multimodal public transport networks, has become an important topic that urgently needs in-depth research in the fields of emergency management and urban transportation.

[0050] Urban transportation network resilience is generally defined as the system's ability to absorb shocks, adapt to changes, maintain basic functions, and gradually restore normal operation when subjected to external disturbances. In terms of resilience evaluation, related research mainly focuses on attribute indicators, topological indicators, and performance process indicators. Bi et al. assessed the system's full-cycle disaster resistance capability based on the "4R" attributes: robustness, redundancy, resource abundance, and recovery speed. Charis et al. constructed a topological measurement index system for the resilience of transportation networks, using the Athens urban road network as an example. Lü Biao et al. proposed a cumulative resilience evaluation index based on network efficiency, addressing the entire process of road network performance degradation and recovery. Regarding disaster scenario simulation and network evolution research, Chen et al. constructed a resilience assessment model considering rainfall intensity and spatiotemporal distribution characteristics for a combined road-rail network under rainstorm disasters, verifying that the combined network has higher disaster resistance resilience than a single network. Fang et al. introduced the Spatial Local Failure (SLF) model and Monte Carlo simulation to characterize the performance evolution process of high-speed rail and civil aviation networks under typhoon disasters.

[0051] In the disaster preparedness phase, scientific site selection and allocation of emergency resources are core means to prevent the cascading effects of disasters and improve the resilience of transportation systems. In this regard, some researchers focus on multi-objective collaboration and network characteristic optimization under deterministic scenarios, emphasizing the pursuit of an optimal balance among conflicting objectives such as economic cost, rescue efficiency, and system resilience. Wang Xiaorong et al. used a multi-objective bi-level programming model to reveal the diminishing marginal returns between road network investment costs and resilience improvement. Wu Ying et al. constructed a rescue time matrix under zoned speed limits based on the characteristics of urban road ring roads, obtaining a site selection scheme that balances economy and coverage efficiency. Zhu Li et al. characterized the vulnerability heterogeneity of emergency reserve depots and transportation routes based on complex network theory. For transportation networks, Li Linchao et al. and Tao Chanjuan incorporated station priority and passenger flow weighted efficiency based on collective influence into their models. Guo Qiang introduced graph neural networks to encode high-dimensional features of urban rail transit stations, realizing intelligent sorting and optimization of emergency logistics facility layout. Yan et al., Wang Fuyu et al., and Du Yikang et al. respectively designed a multi-objective swarm intelligence optimization (MSIO) algorithm and an improved NSGA algorithm. The II algorithm and the quantum non-dominated sorting genetic algorithm have achieved efficient coordination of multiple objectives such as material classification, disaster victim psychological perception and risk management.

[0052] Other researchers have addressed the extreme uncertainty brought about by sudden disasters by constructing robust and stochastic site selection models to improve the reliability of rescue plans in complex and fluctuating environments. Guo et al. and Wang Qingrong respectively introduced hesitant intuitionistic fuzzy sets, the TOPSIS multi-attribute decision-making method, and triangular fuzzy numbers to characterize the fuzziness of post-disaster rescue needs, and combined them with hyperheuristic algorithms to achieve simultaneous planning of site selection and routes. Yang Shuang et al., from the perspective of the synergy between pre-disaster planning and post-disaster scheduling, constructed a two-stage stochastic programming model that considers uncertainties such as the degree of road damage and the repair period. Li et al., considering the chain reaction of disasters, constructed a "reinforcement-chain uncertainty-recovery" resilience enhancement framework, and used a two-stage robust optimization model to characterize the endogenous relationship between facility interruption and demand fluctuations. Addressing the dynamic nature of post-disaster repair time and uncertain scenarios such as earthquakes, Hu Yan et al. and Yu et al., by constructing robust optimization and two-stage robust stochastic models, respectively achieved optimized decision-making for site selection-route planning (LRP) and the quantity of pre-positioned materials.

[0053] like Figure 1 The diagram illustrates a simple example of a multi-modal public transport network's emergency resource coordination. Solid lines represent subway lines, and dashed lines represent bus lines. Red nodes represent subway stations with emergency needs, and blue nodes represent bus stops with needs. Assume that to address potential network risks, an emergency rescue point is set up at the network's center (orange node). This point is equipped with different types of supplies based on the type of need, and can only provide effective services to needs within its coverage radius (dashed circle). Figure 1As shown, subway and bus stops within the dashed circles receive timely assistance; while stops outside the circles (such as the bus demand point in the upper right corner) face the risk of delayed assistance, constituting the residual severity of the system. The efficient use and response of resources are achieved through the rational matching of shared resources (green arrows) and dedicated resources (red and blue arrows).

[0054] Example 1: Based on this, this application provides a method for optimizing the layout of emergency rescue materials in a multimodal urban public transport network. To ensure the solvability and practical applicability of the model in the proposed method, this embodiment is based on the following reasonable assumptions: the coordinates of all candidate stations, subway stations, and bus stations are known, and the road network distance and transport speed between each pair of points are predetermined; the applicability relationship between emergency resources and stations is clear, and unsuitable resources cannot generate rescue utility for the corresponding demand points; resource supply is continuous and subdivisible, that is, a certain resource demand of a demand point is not forced to be met by a single facility point, but can be provided by multiple facility points in a coordinated manner; fixed construction costs and inventory are only incurred when a candidate station is selected to be built as a reserve station; the resource storage capacity of each selected station is constrained by its physical capacity and inventory limit; the mitigation effect of rescue resources changes over time, with the highest utility within the "golden rescue time," and linearly decaying after exceeding the timely threshold; if the failure threshold is exceeded, the rescue plan is determined to be infeasible. This method can be found in [reference needed]. Figure 2 , Figure 2 The diagram shown is a flowchart illustrating a method for optimizing the layout of emergency rescue supplies in an urban multimodal public transport network according to an embodiment of this application, including: S1: Obtain the total resource demand points of the multi-modal public transport network in the target city. The resource demand points include the spatial location information of subway stations, ground bus stops, candidate emergency material reserve stations, as well as the road network distance and transportation speed between each station.

[0055] S2: Based on the total resource demand points, the rescue demand under the event of an emergency is calculated using the triangular fuzzy number defuzzification method, and the emergency resource demand of each resource demand point is obtained.

[0056] In one embodiment of this application, due to the randomness of disaster occurrence and the incompleteness of information, the resource demand of disaster-stricken sites often exhibits a high degree of uncertainty. To scientifically quantify this parameter, this step introduces the theory of Intuitive Fuzzy Sets (IFS), using Triangular Intuitive Fuzzy Numbers (TIFS) to characterize the disaster intensity of the demand points. Specifically, this includes the following: set up X If a set is a non-empty set, then the set X Intuitive Fuzzy Set Defined as: (1) In the formula, Representing elements respectively belong The membership function and non-membership function both take values ​​between [0,1] and satisfy the following conditions: .

[0057] definition For elements belong The degree of hesitation. The larger the value, the less sufficient the information about the demand at that point is.

[0058] If the membership degree of an intuitionistic fuzzy set is represented by a triangular fuzzy number, it is called a triangular intuitionistic fuzzy number. Let resource demand points... The fuzzy probability of an emergency occurring during the planning period is: Its expression is as follows: (2) in, The triangular membership degree, representing the probability of an emergency occurring, corresponds to the resource demand points. Optimistic, most likely, and pessimistic estimates The triangular non-membership degree represents the probability that a sudden event will not occur, corresponding to the resource demand points. Optimistic, most likely, and pessimistic estimates of the probability that a sudden event will not occur.

[0059] To perform computations within a deterministic model, triangular intuitionistic fuzzy numbers need to be transformed into deterministic score values. An improved score function is introduced, combined with the centroid method, to... Perform deblurring. Define resource requirement points. Disaster expectation intensity for: (3) Then estimate the site Resources The demand is: (4) in, For resource demand points Emergency resources The demand for emergency resources, For the collection of emergency resources, For a collection of shared resources, A collection of resources specifically for subway use. A collection of dedicated public transportation resources. and To share resources, and Dedicated resources for subway use. Dedicated to public transportation resources This is the resource applicability coefficient, if emergency resources At the point of resource demand If applicable, it is 1; otherwise, it is 0 (shared resources are all 1; subway-specific resources are 1 at subway stations and 0 at bus stops; bus-specific resources are the opposite). At that time, demand ; The comprehensive risk impact coefficient is based on passenger flow, according to resource demand points. Calculations based on passenger flow show that the denser the passenger flow at a station, the greater the evacuation pressure and the greater the support gap during emergencies. The larger; For emergency resources At emergency resource demand points Unit conversion factor.

[0060] S3: Construct a multi-mode emergency rescue material layout optimization model. The multi-mode emergency rescue material layout optimization model takes minimizing the overall system cost and minimizing the residual severity of each disaster point after rescue as the dual objective function. The overall system cost includes the fixed construction cost of the storage station, the resource reserve cost, the dynamic transportation cost, and the fixed transportation cost.

[0061] In one embodiment of this application, this step constructs a multi-modal emergency relief material layout optimization model. The model comprehensively considers the heterogeneity of the subway and bus systems, and seeks the optimal balance between rescue costs and disaster relief effectiveness under limited budget and response time constraints by optimizing the location of reserve stations, resource quota allocation, and multi-modal distribution schemes. The model is as follows: (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) In the formula, For the overall system cost, To determine the severity of the remaining damage at each disaster site after the rescue efforts, Candidate emergency supplies reserve station Fixed construction costs, To determine whether to select candidate emergency supplies reserve stations The 0-1 variables for constructing reserve stations, if candidate stations are selected. The value is 1 if a storage station is to be built, otherwise it is 0. Candidate emergency supplies reserve station Configure emergency resources Storage costs, Candidate emergency supplies reserve station The number of emergency resources configured, For emergency resources The unit time transportation rate, For emergency resources From candidate emergency supplies storage stations To the resource demand point The rescue time Candidate emergency supplies reserve station To the resource demand point Road network distance, For emergency resources Delivery speed, For emergency resources Fixed processing time, Candidate emergency supplies reserve station Actual delivery to resource demand points emergency resources The supply, Candidate emergency supplies reserve station Towards resource demand points Fixed delivery costs for transporting resources To determine candidate emergency material reserve stations Resource demand points Does the delivery link between the candidate stations have a 0-1 variable? With demand points If a delivery link exists, the value is 1; otherwise, it is 0. Gathering for candidate emergency supplies storage stations. For total resource demand point, For resource demand points The residual severity after receiving emergency resources To determine candidate emergency material reserve stations Should we direct resources to the demand point? Provide emergency resources The 0-1 variables, if candidate station o is directed towards the demand point Provide resources The value is 1 if it is 1, otherwise it is 0. This represents the maximum number of candidate emergency material reserve stations that can be built. For candidate emergency supplies storage stations Deployable emergency resources The upper limit, For emergency resources The total system budget For resource demand points Emergency resources The upper limit of a single delivery capacity, For resource demand points The initial severity after encountering a sudden event. For emergency resources The marginal mitigation effect coefficient, For emergency resources To alleviate resource demand points The weighting coefficient of the disaster situation satisfies , It is a time decay function. For resources at the resource demand point The failure threshold is the time taken to resolve a problem when the response time exceeds a certain threshold. The rescue efforts were largely ineffective in alleviating the situation, so the attenuation coefficient was set to 0. For resources at the resource demand point The effective time threshold is within a response time of no more than Under these circumstances, the rescue can achieve the expected results, and the attenuation coefficient is set to 1; For emergency resources Maximum allowed response time It is a sufficiently large constant.

[0062] Equations (5) and (6) are the objective functions of the model. Equation (5) minimizes the overall system cost, which mainly consists of fixed construction costs of stations, resource reserve costs, dynamic transportation costs, and fixed costs for initiating transportation. Equation (6) optimizes the rescue effect, which is manifested in minimizing the sum of the residual severity of the disaster at each disaster-stricken point after disaster relief intervention. Equation (7) ensures that resource distribution tasks can only be carried out in the selected reserve stations. Equation (8) ensures that once a resource distribution action occurs, it is included in the fixed costs for initiating transportation. Equation (9) specifies the maximum number of reserve stations that can be activated within the entire system. Equation (10) limits the upper limit of the reserves of various emergency resources in a single reserve station. Equation (11) is the global resource budget constraint. Equation (12) ensures that resources from each reserve station... The total amount of a certain resource transported shall not exceed the actual reserve in the station; Equation (13) ensures that the total amount of resources received by each disaster point does not exceed its demand; Equation (14) stipulates that the delivery must be based on the established link and shall not exceed the upper limit of the single transport of materials; Equation (15) stipulates the relationship between the initial disaster severity, the amount of resources invested, the time decay effect and the residual disaster; Equation (16) ensures that the residual severity after the rescue intervention has practical significance at the physical level; Equation (17) stipulates that the delivery task must be completed within the maximum response time; Equation (18) indicates that if the arrival time of the resources exceeds the failure limit boundary of the disaster point, the rescue action is invalid, and the corresponding link variable and delivery amount are both set to 0; Equation (19) limits the value of the variable.

[0063] S4: The multi-objective genetic algorithm based on the ε-constraint method is used to solve the multi-mode emergency rescue material layout optimization model to generate a Pareto non-dominated solution set.

[0064] S5: Select the optimal solution from the Pareto non-dominated solution set as the emergency relief material layout scheme, and output the storage station site selection results, the resource quota allocation scheme of each storage station, and the distribution link scheme.

[0065] In one embodiment of this application, the Genetic Algorithm (GA) is an optimization method that employs random search, referencing the rules of biological evolution in nature. By simulating natural selection and genetic mechanisms, it performs parallel searches within the solution space, exhibiting high search flexibility, fast convergence speed, and resistance to getting trapped in local optima. For the dual-objective optimization model of resource scheduling and facility location constructed in this application, this step designs a method based on... Constraint-based multi-objective genetic algorithm -GA). The algorithm employs a two-layer loop architecture, with the outer loop adjusting the budget constraint via stepping. This process involves cutting the target space; the inner loop calls an improved genetic algorithm to search for the optimal solution under a given budget, and finally constructs a Pareto Front by collecting the optimal solutions at each budget point. The algorithm flowchart is shown below. Figure 3 As shown, it specifically includes: (1) Parameter initialization and data preprocessing In the algorithm startup phase, the multi-source heterogeneous data is first read in a formatted manner. The readtable operator is used to read in the spatial coordinates and resource requirements of candidate stations and demand points, and the spherical distance matrix between candidate stations and demand points is calculated based on the Haversine formula. The time decay coefficient is calculated by combining the resource transportation speed and the fixed processing time. According to the resource suitability matrix Determine the allocation weights of various resources at the demand points. Then, key parameters such as population size, maximum number of iterations, crossover probability, and mutation probability are set, and a penalty factor is defined to ensure the hard effectiveness of the constraints.

[0066] (2) Individual coding and initial population generation The chromosome is segmented and encoded based on candidate facility status, service link decisions, and resource allocation. To cover the multidimensional decision variables in the model, a hybrid binary and real number encoding method is used, and the encoding structure is shown in Table 1.

[0067] Table 1 Chromosome segmentation coding scheme

[0068] in, The total demand point set is composed of a subset of subway station points. Subset of ground bus stops Composition, that is The index is ; This is a collection of candidate emergency supplies storage stations, indexed as follows: ; For the collection of emergency resources.

[0069] The initial population is generated randomly, with the generation range of each gene locus limited by the facility's capacity limit and actual demand. If the basic constraint logic is met, it is "included in the initial population," and this process is repeated until the preset population size is reached.

[0070] (3) Genetic evolution In each generation of genetic iteration ( In the algorithm, the following genetic operators are executed sequentially.

[0071] 1) Selection. A tournament selection method is used to retain high-fitness individuals for the next generation through a competitive mechanism.

[0072] 2) Crossover. A multi-point crossover method is used, randomly selecting two chromosomes as the parent chromosomes to generate two random numbers. , As a crossover point, corresponding gene segments between the fathers are exchanged to produce offspring chromosomes with characteristics of both parents.

[0073] 3) Mutation. A single-point random mutation method is used to generate a random natural number. Indicates the first Genes at certain loci undergo mutation. Within the corresponding gene value range, random perturbation is used to induce gene mutation, thereby maintaining population diversity.

[0074] 4) Repair. A key two-stage repair operator was designed to address the illegal solutions after mutation.

[0075] The first phase involves logical repair. The "no facility, no allocation" principle is enforced (if...). The amount of a certain resource stored on the relevant site. 0-1 variables that determine whether the allocation link is enabled The amount of a certain resource delivered from the station to the demand point Set to zero), and based on the delivery time threshold Shut down the timed-out service link.

[0076] The second phase involves fixing the greedy budget. If the individual's total cost... Exceeding the current budget The algorithm calculates the overall cost savings from shutting down each facility, prioritizing the closure of the facilities with the highest cost contribution, until... This allows it to return to the feasible region.

[0077] 5) Fitness calculation After repair, the fitness value of each individual is calculated. The fitness function is defined as minimizing the sum of the objective value and the penalty term: (20) in, For the fitness function, As a major punitive factor, Due to budget constraints, This is an additional penalty value for an individual violating constraints. When an individual violates budget constraints or hard logic constraints, its fitness is rapidly reduced to ensure that the evolutionary direction moves towards the feasible solution region. This is achieved by minimizing... The algorithm can continuously approach the solution with the least severity while satisfying the budget constraint.

[0078] 6) Record the best Record and update the best individual in the current population and its corresponding best value in real time.

[0079] (4) Pareto front generation When the preset number of iterations is reached, the inner layer operation stops and the current budget is output. The optimal solution is recorded as a "Pareto point" in a set. The outer loop checks if the entire set has been traversed. If not, iterates through the entire set. Update the current budget threshold The genetic algorithm is called again to perform inner-layer optimization, where... The index value is used when the outer loop iterates through the budget set, indicating the index at the 1st position. Budget level.

[0080] After traversing all budget points, the algorithm summarizes the best individual across all budget levels and extracts its actual cost. Severity We obtain the Pareto nondominated solution set and plot the Pareto front curve.

[0081] Example 2: This embodiment takes the multimodal public transport network in the central urban area of ​​Chengdu as the research object to verify the effectiveness of the method proposed in this invention.

[0082] Data preparation: The study area was selected as the central urban area of ​​Chengdu ( E— E, N— N). The required spatial coordinates and topological data were collected using the Gaode Map API and the Chengdu Transportation Open Dataset. This embodiment identifies public transportation stations within the area as emergency resource demand points, ultimately extracting 156 subway demand points and 1618 bus demand points. Some demand point distribution information is shown in Table 2.

[0083] Table 2: Location Information of Partial Demand Points

[0084] Corresponding to the demand points, this application embodiment selects bus stations and subway depots with a certain site size and vehicle dispatching capacity as candidate sites for emergency rescue reserve stations, resulting in 32 candidate sites. The spatial location information of some candidate sites is shown in Table 3.

[0085] Table 3: Location Information of Some Candidate Stations

[0086] After obtaining the latitude and longitude information of all candidate stations and demand points, they are mapped to a two-dimensional coordinate system for scatter visualization, resulting in the spatial distribution of candidate stations and demand points as shown below. Figure 4 As shown.

[0087] Based on the demand calculation method described in Embodiment 1 of this application, the resource demand of each demand point in the region is calculated. The resource demand of some sites is shown in Table 4.

[0088] Table 4 Resource Requirements for Some Sites

[0089] Based on the site resource demand, a heat map of the spatial distribution of emergency demand is drawn as follows: Figure 5 As shown, in terms of spatial agglomeration characteristics, high-demand areas are mainly located around large transportation hubs in the central urban area and along radial main roads. The overall demand intensity decreases from the core area to the periphery, while secondary demand clusters have formed in some suburban cluster centers.

[0090] Parameter settings and model solution: Based on the actual operating environment and emergency rescue needs of Chengdu's multimodal transportation network, the relevant parameters in the model are set as shown in Table 5.

[0091] Table 5 Model Parameter Settings

[0092] Based on this, in order to balance solution efficiency and global search capability, this embodiment was adjusted through multiple preliminary experiments and set... The relevant parameters of the GA algorithm are shown in Table 6.

[0093] Table 6 -GA algorithm parameter settings

[0094] Based on the actual measurement scale in this example, the constraint limit values ​​of non-primary targets will be... Divided into 7 gradients, ∈{1500,1600,1700,1800,1900,2000,2100}. During the solution process, the algorithm iterates through each... The values ​​are iterated independently to obtain -Pareto front distribution of the GA algorithm, as shown Figure 6 As shown in the figure. The horizontal axis... f 1 represents the actual total cost of emergency resource deployment, vertical axis f 2 represents the residual severity of the system. It can be seen that... f 1 and f 2. The algorithm exhibits a clear negative correlation pattern and generates a uniformly distributed set of candidate solutions.

[0095] Algorithm performance comparison and verification: To further verify To assess the effectiveness and superiority of the GA algorithm in terms of solution quality, the classic Simulated Annealing (SA) algorithm was selected as the benchmark for comparison, and the parameter settings are shown in Table 7.

[0096] Table 7 SA Algorithm Parameter Settings

[0097] Run the SA algorithm independently under the same conditions, and obtain its solution set and... - Comparison with the GA algorithm, the results are as follows Figure 7 As shown in the comparison diagram, it can be seen that in the target space... - The Pareto front curve generated by the GA algorithm is generally located to the lower left of the curve generated by the SA algorithm, indicating that under any identical cost budget, -GA can find high-quality layout solutions with lower system severity. In situations with strict cost constraints (such as...) At values ​​of 1500, 1600, and 1700, the SA algorithm is prone to getting trapped in poor local optima. The GA algorithm, with its powerful global parallel search capability, exhibits stronger robustness and reliability. With budget constraints... With the increase in performance, the solution quality of the SA algorithm has improved, and... The gap in the GA algorithm is gradually narrowing, but - The GA algorithm remains in the lead.

[0098] Based on the above analysis, The GA algorithm is better suited to emergency resource allocation models with complex network topologies and large-scale discrete variables, obtaining a more uniform and comprehensive solution set while ensuring convergence quality. In contrast, the traditional SA single-point neighborhood search mechanism is susceptible to premature convergence in such problems, resulting in relatively insufficient globality and stability of the solution.

[0099] Optimization Result Analysis: Targeting Figure 6 Analyzing the Pareto nondominated solution set shown, it can be seen that: when When ∈[1500,1600], the curve drops almost vertically, indicating that in the initial stage, a very small increase in cost can significantly improve emergency response capabilities, demonstrating extremely high marginal benefits. When ∈ [1600, 1900], the slope of the curve tends to flatten. When the range is [1900, 2000], the curve shows a significant downward trend again, followed by a flattening. To find the optimal balance between cost control and response efficiency, a "Knee Point Search" is used for screening. An inflection point represents the optimal balance between two conflicting objectives; that is, after crossing this point, further optimization of one objective must come at the cost of significantly sacrificing the other. The inflection points marked with an asterisk (★) in the figure correspond to the upper limit of the budget. =2000, Actual Total Cost f 1 = 19,151,100 yuan, total severity f2=678.89) is the optimal solution. At this point, the system achieves an ideal balance between cost control and response efficiency. To the left of this decision point, a small increase in budget can significantly reduce system risk; however, once this point is crossed to the right end ( As the curve extends from 2100, it quickly flattens out, and an additional investment of approximately 1.3 million yuan only results in a less than 1% reduction in severity, demonstrating extremely low marginal benefits. In conclusion, the inflection point solution achieves an ideal balance between resource input and efficiency, avoiding both insufficient emergency response capabilities and the waste of funds caused by redundant construction. Therefore, it is selected as the optimal decision-making scheme for the emergency resource layout of Chengdu's multimodal transportation network.

[0100] In the optimal solution (corresponding constraints) At (=2000), the convergence curve of the algorithm is as follows: Figure 8 As shown, both curves show a rapid decline from generation 0 to 50, followed by a slow improvement phase. When the iterations approach 350 generations, the gap between the optimal fitness and the average fitness significantly narrows and both tend towards a stable plateau, stabilizing at approximately [value missing] in the final stage. Nearby, the differences within the population converge, and the improvement rate tends to saturate.

[0101] The location selection results obtained by analyzing the converged decision vectors of the algorithm are shown in Table 8, and the corresponding spatial distribution is as follows: Figure 9 As shown in the figure, the red nodes represent the selected stations, including 10 bus stations and 4 subway depots, while the blue nodes represent the stations that were not selected.

[0102] Table 8 Site Selection Results

[0103] Projecting the above site selection results and demand points onto a geographic information coordinate system yields the spatial distribution of the site selection results and demand points as shown below. Figure 10As shown in the figure, red dots represent selected stations, yellow dots represent unselected stations, and blue and green dots represent subway and bus demand points, respectively. In terms of demand point distribution, the blue-green dot clusters in the figure form a high-density core area between longitude 104.05° and 104.15° and latitude 30.60° and 30.70°, extending into several discrete corridors in the northwest, northeast, and south directions. Most selected stations are located within the dense blue and green dots, surrounded by both subway and bus demand points, maximizing the coverage efficiency of the core road network; a small number of selected stations are located near the outward-extending corridors to maintain basic demand response in peripheral areas. In contrast, unselected stations are concentrated in discrete areas in the northeast and southeast directions, as well as at the far-end nodes of each radial corridor. Comparing the blue-green dot distribution at these locations, it can be observed that the demand point density is significantly lower in these areas than in the core area and the middle section of the corridors, and the blue-green dot clusters tend to be discontinuous or even disappear spatially. Comparing the density of blue and green dots at these locations reveals that the demand is significantly lower than in the central area. The additional coverage gains from continuing to deploy dots in these locations are insufficient to offset the corresponding construction costs, and therefore they are abandoned by the algorithm.

[0104] After determining the spatial distribution of sites, a site selection-resource allocation scheme is further obtained, such as... Figure 11 As shown in the figure, the color gradient and geometric dimensions of the dots intuitively reflect the resource allocation received by each demand point. Warm-colored areas (red and orange) represent key areas with high resource allocation intensity, while cool-colored areas (dark blue) correspond to peripheral nodes with lower allocation. Spatially, the high-demand allocation clusters exhibit a strong corridor agglomeration effect, mainly radiating outwards along the city's backbone road network and rail transit axes. The 14 selected sites (diamond-shaped) are all located at the path center or transportation hub of these high-demand paths, ensuring the efficiency of emergency supplies flow along the linear framework by shortening the effective path distance between supply and demand. This layout logic reflects the model's optimization tendency in ensuring efficiency: prioritizing the non-equilibrium allocation of limited reserve resources to areas with high demand density and strong road network accessibility, thereby improving the coverage rate of the initial response at the system level. The unselected candidate points (cross-shaped) are mostly located in areas with extremely low demand or far from the core logistics routes. In comparison, it was found that for the dark blue nodes far from the center and with small allocation, the model maintained the allocation threshold to meet basic survival needs through long-distance delivery links. This tiered allocation strategy based on distance decay ensures the allocation targets at each demand point while minimizing the overall system's logistics turnover costs, providing a quantitative spatial decision-making reference for urban emergency dispatch during public emergencies.

[0105] Sensitivity analysis: Introducing a velocity decay coefficient Sensitivity analysis was performed on resource transportation speed. Four gradient test sets were set up in the experiment. .in, This indicates that the system is in normal operating condition. The smaller the value, the more severe the traffic damage. In the mathematical model of this application, resources are classified into subway-dedicated resources, bus-dedicated resources, and shared resources according to their service attributes. Based on this classification logic, three typical scenarios are designed: Scenario A sets the speed of bus-dedicated and shared resources to vary with... Synchronous reduction, dedicated subway resources remain unaffected; Scenario B sets the speed of dedicated and shared subway resources to decrease accordingly. The speed of all three resources is reduced simultaneously, while dedicated public transport resources remain unaffected; in scenario C, the speed of all three resources is set to decrease accordingly. It decreases as a result of the decrease.

[0106] The severity of system residuals was calculated for each scenario. Follow The trends and results are shown in Table 9 and Figure 12 As shown.

[0107] Table 9 Sensitivity Analysis Results

[0108] observe Figure 12 As can be seen from the curve, It exhibits significant nonlinear accelerated damage characteristics in response to fluctuations in different categories of parameters. All three curves show a downward convex growth trend, with... As traffic damage decreases, the slope of the curve continuously increases, indicating that once the traffic loss exceeds a certain threshold, the marginal loss of the system will amplify dramatically, and the system risk will experience explosive growth. Under the same attenuation rate, scenario A (red line)... The line consistently higher than Scenario B (blue line) indicates a higher reliance on dedicated public transport resources. This is because public transport demand points are more widely and densely distributed throughout the urban space, far exceeding the total number of subway demand points. A decrease in public transport speed will simultaneously affect the vast majority of response terminals across the city, resulting in a severe risk amplification through a massive cumulative effect across numerous nodes.

[0109] Further analysis of different attenuation coefficients The following site selection scheme found that: When the coefficient of performance (COP) is 0.8, the model converges to the 14 site selection schemes under normal conditions in all three scenarios, indicating that under slight perturbations, the existing spatial layout has sufficient topological redundancy and there is no need to change the site selection coordinates. When the value dropped to 0.6, the model obtained the same new site selection scheme for 14 stations in both scenario A and scenario B, indicating that the system possesses a set of highly robust solutions to cope with non-global traffic fluctuations when facing the risk of heterogeneous single-mode failure. When traffic pressure further increased to the point of global damage (scenario C), the model triggered a spatial redundancy compensation mechanism, adding emergency stations to compensate for the reduction in the radius of a single station, increasing the number of stations to 15. The newly added stations are located in densely populated and highly dispersed peripheral areas, aiming to shorten the average delivery distance in these highly sensitive areas, thereby mitigating speed attenuation at the global level, reflecting a "space-for-time" disaster prevention strategy. As the severity of the residual damage decreased further to 0.4, the system residual severity in scenario C skyrocketed, plunging the system into a near-undefended state of paralysis. The number of model site selections actually decreased from 15 to 14. This is because even adding more sites at this point would not yield sufficient marginal benefits to offset the nonlinear surge in time delays, so the model abandoned its expansion strategy. This demonstrates that under extreme damage conditions, conventional site selection optimization alone is insufficient to maintain system stability, necessitating intervention through other means such as traffic emergency recovery.

[0110] Based on the above sensitivity analysis, the following suggestions are given for the construction of an emergency rescue system: 1) In areas where traffic damage is relatively minor ( When the disaster risk level is ≥0.8, priority should be given to the optimized baseline scheme consisting of 14 core sites, which should be given the highest level of disaster resistance standards and resource priority in urban planning to ensure basic resilience.

[0111] 2) When traffic damage reaches the moderate threshold ( When the velocity is 0.6, a "secondary resilience solution" with multi-scenario adaptability should be activated, and new emergency points should be deployed for highly sensitive areas with discrete needs, such as the southern edge, to offset the velocity decay across the entire domain using spatial redundancy.

[0112] 3) Facing extreme damage ( In cases where the time delay is ≤0.4, simply increasing the size of the stations is no longer sufficient to offset the nonlinear surge in time delays. The focus of decision-making should shift to the deep synergy of multiple rescue modes to fundamentally break through the bottleneck of system efficiency.

[0113] This application, based on the need to enhance the resilience of urban multimodal public transport networks, proposes an optimization model with dual objectives: minimizing total system cost and the severity of residual disasters, specifically addressing the problem of optimizing the layout of pre-disaster emergency relief supplies. The model distinguishes between the heterogeneity and shared nature of rescue efforts between subways and buses, introduces triangular fuzzy numbers to estimate the rescue needs of each disaster-stricken point, and integrates a time-decrease function to characterize the "golden time" effect of emergency resources, making the rescue plan more realistic. Through improvements... The GA algorithm yielded the Pareto non-dominated solution set balancing cost and resilience. Validation using Chengdu's central urban area as an example demonstrates that this method effectively identifies the optimal balance point, providing a scientific basis and decision support for emergency resource pre-positioning and transportation system resilience enhancement in megacities. Future development could further incorporate dynamic road network impedance and random damage models to promote spatiotemporal collaborative optimization of "pre-disaster pre-positioning—in-disaster scheduling"; combine multi-source big data and machine learning algorithms to improve the accuracy of demand forecasting and parameter calibration to adapt to larger-scale urban networks; and delve into adaptive response mechanisms under complex disaster chain scenarios, thereby comprehensively enhancing the overall resilience of multimodal transportation networks in megacities.

[0114] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping readers understand the principles of this application, and should be understood as not limiting the scope of protection of this application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this application without departing from the essence of this application, and these modifications and combinations are still within the scope of protection of this application.

Claims

1. A method for optimizing the layout of emergency rescue supplies in urban multimodal public transport networks, characterized in that, include: S1: Obtain the total resource demand points of the multi-modal public transport network of the target city. The resource demand points include the spatial location information of subway stations, ground bus stops, candidate emergency material reserve stations, as well as the road network distance and transportation speed between each station. S2: Based on the total resource demand points, the rescue demand under the event of an emergency is calculated using the triangular fuzzy number defuzzification method to obtain the emergency resource demand of each resource demand point; S3: Construct a multi-mode emergency rescue material layout optimization model. The multi-mode emergency rescue material layout optimization model takes minimizing the overall system cost and minimizing the residual severity of each disaster point after rescue as the dual objective function. The overall system cost includes the fixed construction cost of the storage station, the resource reserve cost, the dynamic transportation cost, and the fixed transportation cost. S4: The multi-objective genetic algorithm based on the ε-constraint method is used to solve the multi-mode emergency rescue material layout optimization model, generate a Pareto non-dominated solution set, and select the optimal solution from the Pareto non-dominated solution set as the emergency rescue material layout scheme.

2. The method for optimizing the layout of emergency rescue supplies in urban multi-modal public transport networks according to claim 1, characterized in that, S2 includes: S201: Assume that the fuzzy probability of a sudden event occurring at each resource demand point during the planning period is a triangular intuitionistic fuzzy number, calculated using the following formula: in, For resource demand points The fuzzy probability of the occurrence of a sudden event. The triangular membership degree, representing the probability of an emergency occurring, corresponds to the resource demand points. Optimistic, most likely, and pessimistic estimates The triangular non-membership degree represents the probability that a sudden event will not occur, corresponding to the resource demand points. Optimistic, most likely, and pessimistic estimates of the probability that a sudden event will not occur; S202: The triangular intuitionistic fuzzy number is defuzzified using an improved scoring function combined with the centroid method to obtain the expected disaster intensity. The calculation formula is as follows: in, For resource demand points The intensity of expected disaster impact; S203: Based on the expected intensity of the disaster, estimate the emergency resource demand for each resource demand point. The calculation formula is as follows: in, For resource demand points Emergency resources The demand for emergency resources. For the collection of emergency resources, For a collection of shared resources, A collection of resources specifically for subway use. A collection of dedicated public transportation resources. and To share resources, and Dedicated resources for subway use. Dedicated to public transportation resources For resource applicability coefficient, The comprehensive risk impact coefficient is based on passenger flow. For emergency resources At emergency resource demand points Unit conversion factor.

3. The method for optimizing the layout of emergency rescue supplies in urban multi-modal public transport networks according to claim 2, characterized in that, The proposed multi-mode emergency rescue material layout optimization model is as follows: in, For the overall system cost, Candidate emergency supplies reserve station Fixed construction costs, To determine whether to select candidate emergency supplies reserve stations The 0-1 variables for building a reserve station Candidate emergency supplies reserve station Configure emergency resources Storage costs, Candidate emergency supplies reserve station The number of emergency resources configured, For emergency resources The unit time transportation rate, For emergency resources From candidate emergency supplies storage stations To the resource demand point The rescue time Candidate emergency supplies reserve station To the resource demand point Road network distance, For emergency resources Delivery speed, For emergency resources Fixed processing time, Candidate emergency supplies reserve station Actual delivery to resource demand points emergency resources The supply, Candidate emergency supplies reserve station Towards resource demand points Fixed delivery costs for transporting resources To determine candidate emergency material reserve stations Resource demand points Does the delivery link contain 0-1 variables? Gathering for candidate emergency supplies storage stations. For total resource demand point, To determine the severity of the remaining damage at each disaster site after the rescue efforts, For resource demand points The residual severity after receiving emergency resources To determine candidate emergency material reserve stations Should we direct resources to the demand point? Provide emergency resources 0-1 variables, This represents the maximum number of candidate emergency material reserve stations that can be built. For candidate emergency supplies storage stations Deployable emergency resources The upper limit, For emergency resources The total system budget For resource demand points Emergency resources The upper limit of a single delivery load, For resource demand points The initial severity after encountering a sudden event. For emergency resources The marginal mitigation effect coefficient, For emergency resources To alleviate resource demand points The weighting coefficient of the disaster situation satisfies , It is a time decay function. For resources at the resource demand point Failure threshold For resources at the resource demand point The effective time threshold, For emergency resources Maximum allowed response time It is a constant.

4. The method for optimizing the layout of emergency rescue supplies in urban multimodal public transport networks according to claim 3, characterized in that, The multi-objective genetic algorithm based on the ε-constraint method includes: A two-layer loop architecture is adopted, with the outer loop adjusting the budget constraint by stepping, and the inner loop using an improved genetic algorithm to search for the optimal solution.

5. The method for optimizing the layout of emergency rescue supplies in urban multi-modal public transport networks according to claim 4, characterized in that, The S4 includes: S401: Based on the multi-mode emergency rescue material layout optimization model, key basic data are obtained, key parameters are set, and a budget constraint set is defined. The key parameters include population size, maximum number of iterations, crossover probability, mutation probability, and penalty factor. S402: Based on key basic data and key parameters, form an initial Pareto non-dominated solution set and set initial budget constraints; S403: Obtain the emergency rescue material layout optimization scheme as a chromosome from the initial Pareto non-dominated solution set, use a binary and real number mixed encoding method to segment the chromosome, and generate an initial population based on the gene position of each chromosome gene segment using a random generation method. The chromosome gene segment includes candidate facility status, service link decision and resource allocation amount. S404: Based on the initial population, initial budget constraints, and key parameters, the inner loop is called to search for the optimal solution under the current constraints using an improved genetic algorithm. The outer loop is used to determine whether the budget constraint set has been traversed. If so, a Pareto non-dominated solution set is constructed by using the optimal solutions under each budget constraint. Otherwise, the current budget constraint is updated, and the genetic algorithm is called again to perform inner loop optimization. S405: Select the optimal solution from the Pareto non-dominated solution set as the emergency relief material layout scheme.

6. The method for optimizing the layout of emergency rescue supplies in urban multimodal public transport networks according to claim 4, characterized in that, The key basic data obtained by the multi-mode emergency rescue material layout optimization model includes: The spatial coordinates of candidate emergency material storage stations and resource demand points are read using the readtable operator, along with the emergency resource demand of each resource demand point for various types of emergency materials. The road network distance between candidate emergency material storage stations and resource demand points is calculated based on the Haversine formula, and the time decay function value is calculated by combining the material transportation speed and fixed processing time. The allocation weight coefficient is determined based on the resource applicability coefficient.

7. The method for optimizing the layout of emergency rescue supplies in urban multimodal public transport networks according to claim 5, characterized in that, The method of using an improved genetic algorithm to search for the optimal solution under a given budget includes: A1: Using the tournament selection method, a number of individuals are randomly selected from the initial population to compete, and the individual with the highest fitness is selected to enter the next generation. This process is repeated until the mating pool is full. A2: Based on the mating pool, the multi-point crossover method is used to randomly select two paternal chromosomes, generate two random crossover points, exchange the corresponding gene segments of the two paternal chromosomes, and produce two offspring individuals; A3: Based on offspring individuals, a single-point random mutation method is used to generate random natural numbers to represent mutated gene loci; A4: For illegal solutions generated after mutation, perform a two-stage repair including logical repair and greedy budget repair; A5: Based on the repaired illegal solutions, calculate the fitness value of each individual using the fitness function, compare the fitness values ​​of individuals in the current population, and update the globally optimal individual and its corresponding optimal value. The calculation formula is as follows: in, For the fitness function, As a penalty factor, Due to budget constraints, Additional penalty value for an individual who violates the constraint; A6: When the maximum number of iterations is reached, the inner loop stops and outputs the optimal solution under the current budget constraint; otherwise, it continues to iterate in A1.

8. The method for optimizing the layout of emergency rescue supplies in urban multimodal public transport networks according to claim 7, characterized in that, The logic repair includes: determining whether to select a candidate emergency supplies reserve station. 0-1 variables in the construction of reserve stations If the value is 0, then the amount of a certain emergency resource stored in the relevant emergency material reserve station, the 0-1 variable that determines whether the distribution link is opened, and the amount of a certain resource delivered by the emergency material reserve station to the resource demand point are set to zero, and the timeout service link is shut down according to the failure threshold. The greedy budget repair includes: if the overall system cost exceeds the current budget limit, calculating the overall system cost savings after shutting down each facility, prioritizing the shutdown of the facility with the highest cost contribution, until the overall system cost does not exceed the current budget limit.

9. The method for optimizing the layout of emergency rescue supplies in urban multimodal public transport networks according to claim 5, characterized in that, The construction of a Pareto non-dominated solution set by combining the optimal solutions under various budget constraints includes: The Pareto non-dominated solution set is obtained by extracting the overall system cost and the residual severity of each disaster site after rescue from the optimal solution under each budget constraint.

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