Railway tunnel multi-department cooperative emergency rescue method based on two-stage robust optimization

Abstract

The invention provides a railway tunnel multi-department cooperative emergency rescue method based on two-stage robust optimization, and relates to the technical field of railway rescue. According to the method, by constructing the two-stage robust optimization model and the main problem-sub-problem iterative solution algorithm, comprehensive minimization of the resource preset cost and the response cost in the worst accident scene is achieved, and high robustness of the rescue scheme in the face of uncertainties such as requirements and passing time is ensured. According to the method, a joint command mechanism based on department weight is established, actions of multiple departments such as fire fighting and medical treatment are effectively and comprehensively planned, and task collaboration and response speed are greatly improved. Meanwhile, by quantifying the cooperative benefit, the remarkable advantage of the cooperative rescue in shortening the rescue time compared with the independent action is scientifically evaluated, reliable data support is provided for rescue decision making, and the efficiency, reliability and adaptability of railway tunnel emergency rescue are improved.

Description

Technical Field

[0001] This invention relates to the field of railway rescue technology, specifically to a multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization. Background Technology

[0002] Railway tunnels, especially extra-long ones, present significant challenges for emergency rescue efforts in the event of fires, derailments, or other accidents due to their enclosed spaces, complex environments, and limited communication. Currently, emergency rescue operations in railway tunnels largely rely on pre-established static plans and experience-based decisions by rescue personnel, lacking scientific and quantifiable optimization methods.

[0003] Existing technologies suffer from the following shortcomings. First, resource allocation and scheduling schemes are often static and isolated, failing to effectively address the uncertainties in key parameters such as resource demand and travel time in accident scenarios (e.g., sudden changes in CO concentration, unclear casualty distribution, and dynamic changes in traffic conditions), leading to the plan's vulnerability to failure under extreme conditions. Second, there is a lack of quantitative integration and optimization of multi-departmental collaboration mechanisms involving fire, medical, and traffic police, resulting in unclear responsibilities, information barriers, and inconsistent command, leading to dispersed rescue forces, delayed responses, and resource waste. Finally, existing methods struggle to achieve a robust balance between pre-emptive resource costs and the effectiveness of dynamic scheduling during incidents, and lack the means to scientifically evaluate the comprehensive benefits of multi-departmental collaboration, thus failing to provide data support for optimizing the collaborative rescue system.

[0004] Therefore, there is an urgent need in this field for a new emergency rescue method that can coordinate multiple departments, address uncertainties, and quantitatively assess effectiveness, in order to overcome the shortcomings of existing technologies and improve the overall efficiency and reliability of railway tunnel emergency rescue. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization. This method solves the problems of low efficiency in multi-department collaboration, suboptimal resource allocation, and weak dynamic decision-making capabilities in existing technologies. It maximizes rescue efficiency and enhances the robustness of resource scheduling, while quantifying collaborative benefits to ensure the adaptability and reliability of rescue plans under uncertain accident scenarios.

[0006] The technical solution adopted in this invention is as follows:

[0007] A two-stage robust optimization-based multi-department collaborative emergency rescue method for railway tunnels includes the following steps:

[0008] Step S1: Obtain basic data of railway tunnels, including tunnel structure information, resource prepositioning point information, departmental responsibility information, and historical accident data;

[0009] Step S2: Based on the aforementioned railway tunnel basic data, construct a two-stage robust optimization model, which includes:

[0010] The first-stage contingency plan decision model aims to minimize the sum of the resource pre-positioning cost and the second-stage response cost under the worst-case scenario, and determines the resource pre-positioning plan accordingly.

[0011] The second-stage response decision model has the objective function of minimizing the sum of rescue time cost and resource shortage penalty cost under a given resource pre-configuration plan and specific accident scenario, and generating a dynamic rescue scheduling plan.

[0012] The worst-case scenario is defined by a parameterized uncertainty set U, constructed based on the historical accident data, which describes the uncertainty of resource demand and travel time.

[0013] Step S3: Based on the two-stage robust optimization model, the main problem-sub-problem iterative algorithm is used to solve the problem. The main problem optimizes the resource pre-setting scheme, and the sub-problems find the worst scenario and calculate its response cost. After iterative convergence, the optimal resource pre-setting scheme and dynamic rescue scheduling scheme are output.

[0014] Step S4: Based on the optimal resource pre-configuration scheme and the dynamic rescue scheduling scheme, execute multi-department collaborative rescue decisions and output rescue instructions.

[0015] Further, in step S1, the tunnel structure information includes a tunnel structure diagram, which includes tunnel length, slope, cross-sectional dimensions, and emergency exit location information; the resource prepositioning point information includes a set of potential rescue bases, a set of rescue resource types, and resource prepositioning costs; the departmental responsibility information includes a set of departments, basic response time of each department, and departmental decision-making weight.

[0016] Furthermore, the construction of the two-stage robust optimization model in step S2 specifically includes:

[0017] Step S21: Construct an uncertainty set U, which is used to describe the uncertainty parameters of the accident scenario, including resource demand and travel time;

[0018] Step S22: Construct the first-stage contingency plan decision model. The objective function of the first-stage contingency plan decision model is to minimize the pre-set resource cost and the worst-case response cost. Its mathematical expression is:

[0019] ,

[0020] In the formula, Indicates the pre-set cost of resources. This represents the cost of pre-setting one unit of resource r at rescue base j; This represents the quantity of pre-positioned resources r at rescue base j; y and q are... , , ;

[0021] This represents the response cost under the worst-case scenario; Given a pre-defined scheme q and a specific scenario At that time, the maximum cost of the second-stage response decision;

[0022] Step S23: Construct the second-stage response decision model. The objective function of the second-stage response decision model is to minimize the rescue time cost and the resource shortage penalty cost. Its mathematical expression is:

[0023] ,

[0024] In the formula, For the time cost of rescue; For travel time; The number of resources dispatched; The cost of penalizing resource shortages; This is the penalty weighting coefficient; Resource demand; This refers to the actual amount of resources used. This is the penalty function.

[0025] Furthermore, the construction of the uncertain set U in step S21 specifically includes:

[0026] Step S211: Using the partitioned budget uncertainty set form, determine the nominal value and deviation range of the uncertainty parameter based on the historical accident data;

[0027] Step S212: Determine the zoning uncertainty budget parameters based on the historical accident data, including the uncertainty budget of fire resource demand, the uncertainty budget of medical resource demand, the uncertainty budget of travel time in the core area, and the uncertainty budget of travel time in the outer area, and control the conservatism of the uncertainty set U;

[0028] Step S213: Based on the nominal value, the deviation range, and the partition uncertainty budget parameter, generate the polyhedral representation of the uncertainty set U, the mathematical expression of which is: ,

[0029] In the formula, For resource demand, For resource demand The nominal value, ; This represents the maximum deviation in resource demand. This is the lower bound of resource demand. ;

[0030] For travel time, This is the nominal value of the travel time. This represents the maximum deviation in travel time. This is the lower bound of the passage time. , This is the upper bound of the travel time. ;

[0031] A collection of dedicated firefighting resources; A collection of medical-specific resources; This is a collection of accident points in the core area of ​​the tunnel. This is a collection of accident sites in the area surrounding the tunnel. Budgeting for uncertainties in fire protection resource needs; Budgeting for the uncertainty of healthcare resource needs; Budgeting for uncertain travel times in the core area; Budgeting for the uncertainty of travel time in the outer areas.

[0032] Furthermore, step S3 employs a main problem-subproblem iterative algorithm for solving the problem, specifically including:

[0033] Step S31: Initialize the main problem, and set the initial worst-case scenario set. Set to an empty set and initialize the upper bound of the algorithm. and the lower bound of the algorithm ;

[0034] Step S32: Solve the main problem to obtain the current resource pre-configuration scheme. and current target value And update the lower bound of the algorithm. ;

[0035] Step S33: Based on the current resource provisioning scheme, solve the sub-problem to find the worst-case scenario under the current provisioning scheme. and the corresponding second-phase response cost And update the upper bound of the algorithm. In the formula, The upper bound before the update. The pre-allocated resource quantity obtained from solving the current round master problem;

[0036] Step S34: Determine the convergence condition, if If the conditions are met, then the optimal resource pre-configuration scheme and the dynamic rescue scheduling scheme will be output; otherwise, the worst-case scenario will be output. Add to the worst-case scenario set and return to step S32; where, This is the preset convergence tolerance.

[0037] Furthermore, solving the subproblem in step S33 specifically includes:

[0038] Step S331: Based on the current resource provisioning scheme, construct a sub-problem model. The sub-problem model is a minimax problem, the objective of which is to determine the worst-case scenario that maximizes the response cost of the second stage. Its mathematical expression is:

[0039] ,

[0040] In the formula, The output of the subproblem; This refers to the time cost of resource scheduling. Penalty cost items for resource shortages Weighting for resource shortage penalties; For the scene The amount of resource shortage at the next accident point k relative to resource r;

[0041] For the scene Below, the resource requirement of incident point k for resource r; For the scene Below is the unit resource travel time cost from rescue base j to accident site k; For the inner minimization operator, For resource dispatch quantity variable; For resource usage variables;

[0042] Step S332: Perform dual transformation on the subproblem model, and use strong duality theory to transform the inner minimization problem into a maximization problem, thereby transforming the two-layer problem into a single-layer mixed integer linear programming problem;

[0043] Step S333: Solve the single-layer problem after dual transformation to obtain the worst-case scenario. Second-stage optimal response cost .

[0044] Furthermore, the multi-department collaborative rescue decision-making process in step S4 specifically includes:

[0045] Step S41: Based on the dynamic rescue dispatch scheme, allocate rescue tasks to multiple departments, including fire departments, medical departments, traffic police departments, railway operation departments, and emergency management departments;

[0046] Step S42: Based on the departmental decision-making weights, construct a joint command and decision-making mechanism to coordinate the rescue operations of the multiple departments;

[0047] Step S43: Monitor and dynamically adjust rescue efficiency in real time, wherein the rescue efficiency The calculation formula is:

[0048] ,

[0049] In the formula, To improve the efficiency of collaboration; This represents the environmental complexity impact coefficient. The coefficient representing the influence of carbon monoxide concentration; This represents the influence coefficient of resource sufficiency. This represents the impact coefficient on communication efficiency.

[0050] Furthermore, it also includes: Step S5: Quantifying the benefits of multi-departmental collaboration, Step S5 includes:

[0051] Step S51: Calculate the time without a cooperating reference The calculation formula is:

[0052] ,

[0053] In the formula, This represents the total response time in the non-cooperative mode, where... This represents the number of departments in the department set. This serves as the base response time for each department; The total casualty rescue time in the non-cooperative mode, where m refers to the number of casualty types. This refers to the specific number of wounded in category j; This is the basic rescue time for Category j injured persons; This represents the number of effective rescue teams in a non-cooperative mode.

[0054] Step S52: Calculate collaborative operation time The calculation formula is:

[0055] ,

[0056] In the formula, For coordinated response time, For coordinated rescue time; among them,

[0057] ,

[0058] In the formula, To the degree of coordination; Let be the departmental decision weight for the i-th department;

[0059] ,

[0060] Number of available rescue teams;

[0061] Step S53: Based on the aforementioned non-cooperative reference time and the aforementioned collaborative operation time Calculate the synergistic benefits, which include absolute synergistic benefits and relative synergistic benefits.

[0062] The mathematical expression for absolute synergistic benefits is:

[0063] ;

[0064] The mathematical expression for relative synergistic benefits is:

[0065] .

[0066] The beneficial effects of this invention are:

[0067] This invention presents a two-stage robust optimization-based multi-department collaborative emergency rescue method for railway tunnels. By constructing a two-stage robust optimization model and an iterative algorithm for solving the main problem and sub-problems, it achieves the comprehensive minimization of resource pre-configuration costs and response costs under worst-case scenarios, ensuring the strong robustness of the rescue plan in the face of uncertainties such as demand and travel time. This method establishes a joint command mechanism based on departmental weights, effectively coordinating the actions of multiple departments such as fire fighting and medical services, significantly improving task coordination and response speed. Simultaneously, by quantifying the benefits of collaboration, it scientifically evaluates the significant advantage of collaborative rescue over independent action in shortening rescue time, providing reliable data support for rescue decision-making and improving the efficiency, reliability, and adaptability of railway tunnel emergency rescue. Attached Figure Description

[0068] Figure 1 This is a flowchart of a multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization, according to an embodiment of the present invention.

[0069] Figure 2 This is a flowchart illustrating the construction of a two-stage robust optimization model according to an embodiment of the present invention.

[0070] Figure 3 This is a flowchart illustrating the iterative solution process of the main problem and subproblems according to an embodiment of the present invention. Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] like Figures 1-3 As shown in the figure, the multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization according to an embodiment of the present invention includes the following steps:

[0073] Step S1: Obtain basic data of railway tunnels, including tunnel structure information, resource prepositioning point information, departmental responsibility information, and historical accident data.

[0074] The tunnel structure information includes a tunnel structure diagram, which includes tunnel length, gradient, cross-sectional dimensions, and emergency exit locations. This tunnel structure information is used to delineate accident zones. With calculation of travel time parameters Specifically, based on tunnel length, gradient, and emergency exit locations, tunnels can be divided into several accident-prone sections, such as the core section. For sections with a slope greater than 20‰, the outer section For the 1-kilometer section near the entrance, ensure that the environmental characteristics (such as slope) of each section are relatively uniform to facilitate the calculation of travel time; the slope directly affects the speed of rescue vehicles / personnel, such as reducing speed by 20%-30% when going uphill, and the cross-sectional dimensions determine whether rescue equipment, such as large demolition vehicles, can pass through. The location of the emergency exit provides alternative rescue routes, all of which need to be taken into account. The calculation logic, such as the route from rescue base j to accident point k, allows for the selection of either the main tunnel or a horizontal guide via an emergency cross passage; both routes are valid. different.

[0075] Resource prepositioning information includes a set of potential rescue bases. Collection of rescue resource types and resource pre-positioning costs . Specifically, j is the index (integer) of the rescue base. The physical location (mileage coordinates) and resource capacity of each rescue base must be specified, such as... It serves as a rescue station at the tunnel entrance, capable of accommodating 10 ambulances and 5 fire brigades; It serves as the intermediate vertical shaft rescue station, capable of accommodating 3 rescue teams and 20 respirators. 'r' is an index (integer) of the resource type, categorized by departmental and general use. The functional attributes and units of measurement for each resource must be clearly defined, such as: Firefighting: Demolition equipment (units), Respirators (sets), Fire trucks (vehicles); Medical: Ambulances (vehicles), First aid kits (units), ECG monitors (units); General: Lighting equipment (sets), Communication equipment (units). Resource pre-installation cost. is a non-negative real number parameter (unit: yuan / unit resource), representing the total cost of pre-setting 1 unit resource r at rescue base j. This cost must include purchase, storage, and maintenance costs, such as: (One demolition device pre-installed at the entrance base) = Equipment purchase of 200,000 yuan + annual rent of storage garage of 10,000 yuan + annual maintenance of 5,000 yuan = 215,000 yuan.

[0076] Departmental responsibility information includes a collection of departments. , Where i is the index (integer) of the department. Considering the actual needs of railway tunnel rescue scenarios, the standard department set specifically includes fire departments, medical departments, traffic police departments, railway operations departments, and emergency management departments. This set defines the scope of entities participating in coordinated rescue efforts, ensuring that all key rescue forces are included in the decision-making system. Basic response time for each department. This parameter is a non-negative real number (unit: minutes), representing the average preparation time for the i-th department from receiving the alarm to the arrival of the first batch of rescue forces at the tunnel entrance. Its value must be derived based on historical dispatch data for the department (excluding outliers such as extreme weather and traffic congestion). For example, the basic response time for a fire department is typically 15 minutes (receiving the alarm → assembling → departing → arriving at the entrance), for a medical department it is 20 minutes, and for a railway operations department, due to the need to coordinate internal dispatch, the basic response time is slightly longer, approximately 25 minutes. This parameter directly determines the rescue time benchmark in the non-coordinated mode and the optimization space in the coordinated mode. Departmental Decision Weight The parameter is a non-negative real number and satisfies The values ​​are determined based on the statutory responsibilities and criticality of each department in the rescue effort. The weight directly reflects the department's voice in joint decision-making. For example, the fire department, responsible for handling deadly threats (such as fires and hazardous chemical control), has a weight of 0.30 and is the core professional department in joint decision-making. The medical department, with saving lives as its core objective, has a weight of 0.25, second only to the fire department. Together, these three constitute the basis of the collaborative rules for multi-departmental joint rescue, providing a quantitative basis for subsequent joint command, task allocation, and response time optimization.

[0077] Historical accident data is used to construct uncertainty models (uncertainty sets) of accident scenarios. The only source of data for this purpose is to provide quantitative benchmarks for uncertain parameters such as resource demand and travel time by collecting and processing structured data on domestic railway tunnel accidents over the past 5-10 years. The data mainly includes four core categories: accident scenario information, resource demand data, travel time data, and rescue result data, as well as corresponding processing objectives.

[0078] Step S2: Based on the basic data of railway tunnels, construct a two-stage robust optimization model, which includes a first-stage contingency plan decision model and a second-stage response decision model. The objective function of the first-stage contingency plan decision model is to minimize the sum of the resource pre-positioning cost and the second-stage response cost under the worst-case accident scenario, thereby determining the resource pre-positioning scheme. The objective function of the second-stage response decision model is to minimize the sum of the rescue time cost and the resource shortage penalty cost under the given resource pre-positioning scheme and specific accident scenario, thereby generating a dynamic rescue scheduling scheme. The worst-case accident scenario is defined by a parameterized uncertainty set U, constructed based on historical accident data, used to describe the uncertainty of resource demand and travel time.

[0079] In this invention, the two-stage model is specifically a closed loop of pre-event planning and in-event response. The first stage (planning decision) solves how to pre-position resources before an accident, and the second stage (response decision) solves how to schedule resources after an accident. The uncertainty set provides a risk boundary for the connection between the two stages, ensuring that the model can still operate effectively in extreme scenarios.

[0080] In one embodiment of the present invention, the construction of the two-stage robust optimization model in step S2 specifically includes:

[0081] Step S21: Construct an uncertain set Uncertain set Uncertainty parameters used to describe accident scenarios include resource requirements. (Accident point Resources (demand) and travel time (Travel time from rescue base j to accident site k). This step structures the fluctuation range of these two types of uncertainty parameters through a partitioned budget uncertainty set, covering both major risks and controlling model complexity.

[0082] Specifically, in step S21, an uncertainty set is constructed. Specifically, it includes:

[0083] Step S211: Using the partitioned budget uncertainty set form, determine the nominal value and deviation range of the uncertainty parameter based on historical accident data;

[0084] Step S212: Determine the uncertain budget parameters for each zone based on historical accident data, including the uncertain budget for fire resource requirements. Uncertainty in the budget for medical resource needs Uncertainty in travel time within the core area (budget) Uncertainty in travel time in the outer areas (budget) To control uncertain sets The degree of conservatism;

[0085] Step S213: Based on the nominal value, deviation range, and partition uncertainty budget parameters, generate the polyhedral representation of the uncertainty set U, whose mathematical expression is:

[0086] ,

[0087] This expression limits the resource requirement. With travel time The absolute fluctuation range is defined to avoid parameters deviating from actual conditions without limit. In the formula, For resource demand The nominal value, i.e., the average demand for resource r at accident point k in similar accidents, can be statistically analyzed in the past 5-10 years for similar accidents (such as CO leaks). The arithmetic mean of all historical values ​​is calculated (excluding extreme outliers). ; The maximum deviation in resource demand: among similar accidents Compared with nominal value The maximum difference (only positive values ​​are considered); This is the lower bound of resource demand, i.e. The minimum possible value is used to ensure that the demand is not excessively lower than the actual demand (to avoid wasting resources). .

[0088] This is the nominal value of travel time, i.e., the average travel time from rescue base j to accident point k in the same section / scenario; This represents the maximum deviation in travel time, i.e., within the same section / same scenario. Compared with nominal value The maximum difference; This is the lower bound of the travel time, i.e. The minimum possible value (fastest travel time); This is the lower bound of the travel time, i.e. The minimum possible value (fastest travel time). ; The upper bound of the travel time, i.e. The maximum possible value (slowest travel time). ;

[0089] This is a collection of resources specifically for firefighting, meaning resources used solely by the fire department to handle disasters. It is a prerequisite for safe rescue operations and includes equipment such as demolition equipment. ), positive pressure respirator ( ), fire truck ( ), fire extinguishing bombs ( )wait;

[0090] This refers to a collection of resources specifically for medical use, meaning resources used solely by medical departments to treat the injured, such as ambulances. ), first aid kit ( ), ECG monitor ( ),stretcher( )wait.

[0091] This refers to the set of accident points in the core area of ​​the tunnel, namely accident sections with complex environments and high rescue difficulty (such as steep slopes and middle sections). Based on tunnel structural information, these are divided into sections such as K23+100-K25+400 (maximum slope 23.5‰) and the middle section of the tunnel, K24+500-K26+000.

[0092] This refers to the set of accident points in the outer area of ​​the tunnel, that is, accident sections that are close to the outside and have low rescue difficulty (such as near the entrance and emergency exit). It is divided based on tunnel structure information, such as the tunnel entrance section K22+000-K23+000 and the emergency exit section K27+000-K27+500.

[0093] Budgeting for uncertainties in fire protection resource needs, i.e., dedicated fire protection resources The upper limit of the total relative deviation; Budgeting for uncertain healthcare resource needs, i.e., dedicated healthcare resources The total relative deviation upper limit, formula (4) limits the overall fluctuation of medical resources, and avoids excessive pre-positioning of medical resources leading to cost waste; Budgeting for uncertain travel times in the core area, i.e., the core area The total relative deviation of travel time is limited by formula (5), which limits the overall fluctuation of travel time in the core area and ensures that the model takes into account the time risk of rescue in the core area. Budgeting for the uncertainty of travel time in the outer area, i.e., the outer area The upper limit of the total relative deviation of travel time, formula (6) limits the overall fluctuation of travel time in the outer area, and avoids excessive increase in the model’s conservatism due to the low risk in the outer area.

[0094] Step S22: Construct the first-stage contingency plan decision-making model. The first stage is the contingency plan decision-making stage before the accident occurs, used to determine the resource pre-positioning plan, including whether to pre-position resources r (0-1 variables) at the rescue base j. And the specific quantity of resources r pre-positioned at rescue base j (a non-negative integer variable). The objective function of the first-stage contingency plan decision model is to minimize the pre-set resource cost and the worst-case response cost. The mathematical expression of the objective function is:

[0095] ,

[0096] In the formula, This refers to the pre-positioning cost of resources, i.e., the total cost of pre-positioning resources at all rescue bases. This represents the cost of pre-positioning 1 unit of resource r at rescue base j, such as the cost of pre-positioning 1 ambulance at the entrance base being 200,000 yuan; This represents the quantity of pre-set resources r at rescue base j (a decision variable). These are the decision variables for the first-stage contingency plan decision-making model; , ;

[0097] This represents the worst-case response cost (after the fact), which is the maximum cost of the second-stage response decision among all scenarios within the uncertainty set U. For a given preset scheme and specific scenarios At that time, the optimal response cost in the second stage; This means iterating through all possible scenarios to find the worst-case scenario that results in the highest response cost.

[0098] It should be further clarified that the decision-making in the first stage must meet budget constraints, logical constraints, and variable domain constraints; specifically, That is, the total cost of pre-positioned resources cannot exceed the preset budget B, such as the railway operator's annual emergency resource budget of 10 million yuan; That is, if resources are not pre-positioned at the rescue base (j), ), then the preset quantity ( If you choose the preset ( ),but , Use a sufficiently large constant, such as 1000, to avoid an unlimited number; , ; It is a 0-1 discrete variable (only two choices). It must be a non-negative integer, and the quantity of resources cannot be negative or a decimal. For example, if 3 ambulances are to be pre-installed, it cannot be 2.5.

[0099] Step S23: Construct the second-stage response decision model. The second stage is the response decision stage after the accident occurs, based on the known pre-set solutions from the first stage. and actual accident scenarios (such as accident point k, resource requirements) Travel time In this case, to determine the resource scheduling plan, the objective function of the second-stage response decision model is to minimize the rescue time cost and the resource shortage penalty cost. The mathematical expression of the objective function is:

[0100] ,

[0101] In the formula, The rescue time cost is the total time consumed for all resources to travel from the rescue base to the accident site. The passage time is the time during which passage is permitted, i.e., during the accident scene. (Considering traffic conditions and tunnel environment in this scenario), the travel time from rescue base j to accident point k is an uncertain parameter, and its value depends on the specific scenario. ; The number of resources dispatched, i.e., in the scenario. Below, the number of resources r dispatched from rescue base j to accident site k (a core decision variable for the second stage, a non-negative integer). Among them, This is an index for the rescue base, belonging to the set of rescue bases. , This is the index of the accident point, belonging to the set of accident sections. ; An index for a resource type, belonging to the resource type set. .

[0102] The cost of resource shortage penalties refers to the losses or risks incurred due to the failure of rescue resources to fully meet on-site needs. The penalty weighting coefficient is used to balance the importance of rescue time and resource scarcity in the objective function, such as... This means that the penalty for a shortage of 1 unit of resource is equivalent to a time cost of 10 minutes; The actual amount of resources used, i.e., in the scenario. Down, accident point resources actually put into use quantity, For the second stage decision variables (integers). The decision is the sum of the deployments from all rescue bases; This refers to the resource demand, i.e., in the accident scenario. Down, accident point Resources The actual number of (such as ambulances, ventilators, and fire brigades) required.

[0103] For the penalty function, The penalty function calculates the shortage amount, when the actual usage amount... Greater than or equal to demand When the shortage is zero, there is no penalty; when At that time, the penalty value is the amount of shortage. For example, if the accident point k requires an ambulance r... Vehicles, actually dispatched If the number of vehicles is 5, then the shortage quantity = 5 - 3 = 2, and the penalty cost = ×2, if α=10, then the penalty cost =20.

[0104] It should be further explained that the second-stage decision-making process must satisfy four types of constraints: resource availability constraints, resource balance constraints, demand ceiling constraints, and variable domain constraints, to ensure that the scheduling plan conforms to resource constraints and rescue logic. Specifically, That is, the total amount of resources r dispatched from rescue base j cannot exceed the amount pre-positioned at that rescue base in the first phase. If rescue base J1 has 3 ambulances pre-positioned, then the total number of ambulances dispatched to all accident sites will be ≤3, thus establishing a connection between the first and second phases and ensuring that the dispatch plan is based on the actual pre-positioned resources. That is, the actual amount of resources r used at accident point k is equal to the sum of the amount of resources r dispatched by all rescue bases to that accident point, thereby ensuring that the dispatch amount is consistent with the usage amount and avoiding data contradictions. For example, if 3 ambulances are dispatched, but 4 are actually used. That is, the amount of resource r actually used at the accident point k cannot exceed the demand in that scenario. This avoids wasting resources, such as dispatching 8 ambulances when 5 are needed, leaving 3 extra ambulances unused and increasing time costs. This means that both the number of resources dispatched and the number of resources used are non-negative integers. For example, if 2 ambulances are dispatched, it cannot be 1.5 ambulances, which conforms to the resource counting logic in actual rescue operations.

[0105] Step S3: Based on the two-stage robust optimization model, the main problem-subproblem iterative algorithm is used to solve the problem and obtain the optimal resource pre-configuration scheme (first-stage decision variables). , ) and dynamic rescue dispatch scheme (second stage decision variables) , ).

[0106] It should be noted that the two-stage robust optimization model is essentially a two-level optimization problem, and its direct solution has extremely high complexity. This invention employs a main problem-subproblem iterative algorithm, which decomposes the two-level problem into two efficiently solvable single-level problems (mixed integer linear programming, MILP) through problem decomposition and iterative feedback. This ensures both solution efficiency and robustness of the results, covering all scenarios within the uncertainty set U.

[0107] Specifically, step S3 employs a main problem-subproblem iterative algorithm for solving the problem, which includes:

[0108] Step S31: Initialize the main problem, and set the initial worst-case scenario set. Set to an empty set and initialize the upper bound of the algorithm. and the lower bound of the algorithm .

[0109] Step S32: Solve the main problem to obtain the current resource provisioning scheme. and current target value And update the lower bound of the algorithm. The main problem is a mixed-integer linear programming problem (MILP) to find the resource provisioning scheme for the first stage under the constraints of the known worst-case scenario set L. And calculate the lower bound (LB) of the algorithm, which is the minimum possible total cost of the current optimal solution.

[0110] The decision variables for the main problem fall into three categories, each corresponding to a different decision dimension. The core variables for the first stage include... and ,in It is a 0-1 type variable used to determine whether to pre-set resources r at rescue base j. A non-negative integer variable, specifying the exact quantity of the resource pre-positioned at the rescue base; auxiliary variable. These are non-negative continuous variables, serving to replace the maximum response cost in the worst-case scenario of the original two-stage model, transforming the complex mini-maximum nested structure into a directly constrained linear term, making the main problem a standard MILP; the scenario-specific variables are for each scenario p in the scenario set L, including (Resource dispatch volume in this scenario) and (Resource usage in this scenario) is used to accurately match the rescue needs of the identified scenarios and ensure that the pre-set solutions can cope with these risk scenarios.

[0111] The mathematical expression for the objective function of the main problem is:

[0112] ,

[0113] In the formula, The actual resource pre-positioning cost corresponding to the first phase is the cost of pre-positioning a unit resource r by rescue base j. With preset quantity The product is obtained by summing the products; auxiliary variables This serves as the upper limit for response costs across all identified scenarios, ensuring that the objective function covers the worst-case scenarios and preventing the solution from failing due to ignoring known risks.

[0114] The constraints of the main problem are divided into two categories. The basic constraints in the first stage follow the core rules of step S22, including budget constraints. Ensure that the total pre-set cost does not exceed the preset budget B; logical constraints. To avoid logical contradictions where resources are not pre-set but have a certain quantity; variable domain constraints are clearly defined. 0-1 properties and The non-negative integer attribute. The scenario-based optimality cutting constraint is applied to each discovered scenario. These include resource availability constraints (dispatch volume does not exceed the preset volume), resource balancing constraints (actual usage equals total dispatch volume), demand ceiling constraints (usage volume does not exceed scenario demand), and the crucial upper bound constraint on response cost. This constraint is mandatory The response cost should not be less than that under scenario p, ensuring that the optimization results of the main problem fully consider the risks of the known worst-case scenario.

[0115] This invention can solve the main problem using mature MILP solvers such as Gurobi and CPLEX, yielding corresponding output results, including the current optimal resource provisioning scheme. That is, each rescue base's decision on whether to pre-position each type of resource. and specific preset quantity ; and including the objective value of the main problem. This equals the total pre-installation cost of the pre-installed solution plus auxiliary variables. The sum of the optimal values. Because It is the upper bound of response cost. The lower bound of the algorithm must be less than or equal to the actual total cost; therefore, the lower bound of the algorithm is updated to... This lower bound will continuously improve as the scenario set L expands during the iteration process, gradually approaching the true robust optimal total cost.

[0116] Step S33: Based on the current resource provisioning scheme, solve the sub-problems to find the worst-case scenario under the current provisioning scheme. and the corresponding second-phase response cost And update the upper bound of the algorithm. In the formula, The upper bound before the update. The total provisioning cost of the current resource provisioning scheme. The number of resources pre-set for the current main problem.

[0117] Specifically, solving the subproblem in step S33 includes:

[0118] Step S331: Based on the current resource provisioning scheme, construct a sub-problem model. The sub-problem model is a minimax problem, and its goal is to determine the worst-case scenario that maximizes the response cost in the second stage. Specifically, for the current resource provisioning scheme output by the main problem... Among all possible accident scenarios covered by the uncertainty set U, accurately locate the worst-case scenario that maximizes the cost of the second-stage response. And calculate the optimal response cost in this scenario. Through this process, the algorithm can identify the risks and shortcomings of the current pre-defined scheme, providing crucial feedback for subsequent iterative optimization, while also updating the upper bound UB of the algorithm, driving the upper and lower bounds to gradually converge.

[0119] The original mathematical form of the subproblem presents a double-nested structure, with the outer layer being a maximization operation and the inner layer a minimization operation. Its mathematical expression is:

[0120] ,

[0121] In the formula, The output of the subproblem is the current resource provisioning scheme. The minimum response cost in the worst-case scenario; This is the time cost item for resource scheduling, which is the total travel time cost of dispatching resources from all bases to each accident site; Penalty cost items for resource shortages The resource shortage penalty weight represents the penalty cost for each unit of resource shortage r, reflecting the degree of impact of resource shortage on rescue efforts. For the scene The amount of resource shortage at the next accident point k relative to resource r; For the scene Below, the resource requirement of incident point k for resource r; For the scene Below is the unit resource travel time cost from rescue base j to accident site k; The inner minimization operator optimizes the resource scheduling variables in the second stage. and ; The resource dispatch quantity variable (a non-negative integer) represents the scenario. The following refers to the amount of resources r dispatched from rescue base j to accident site k; The resource usage variable (a non-negative integer) represents the scenario. Below, the amount of resource r actually used at accident point k.

[0122] The core of the outer maximization operation is to traverse all scenarios in the uncertain set U. The first step is to find the combination that is most unfavorable to the current preset solution; the second step is to minimize the operation within a given scenario. and pre-set solutions Given the given conditions, find the optimal resource scheduling scheme, i.e., the decision variables. and The goal is to minimize the sum of rescue time cost and resource shortage penalty cost in this scenario. Simultaneously, the inner optimization must satisfy resource constraints, resource balance constraints, and variable domain constraints. Ensure that the number of resources dispatched from each rescue base does not exceed the pre-positioned amount. Resource balance constraints To ensure that the actual amount of resources used at the accident site equals the total number of resources dispatched from all rescue bases, variable domain constraints are applied. This restricts the scheduling variable to a non-negative integer, which aligns with the resource counting logic in actual rescue operations.

[0123] Step S332: Perform dual transformation on the subproblem model, and use strong duality theory to transform the inner minimization problem into a maximization problem, thereby transforming the two-layer problem into a single-layer mixed integer linear programming problem.

[0124] Since the nested structure of the original subproblems cannot be directly solved using conventional solvers, it must be transformed using strong duality theory. Specifically, the inner minimization linear programming problem is transformed into an equivalent maximization dual problem, thus decomposing the entire bi-level optimization problem into a single-level mixed integer linear programming (MILP) problem. During this transformation, dual variables need to be introduced. (Corresponding resource constraints) (Corresponding resource balance constraints) and (Corresponding to the requirement constraints), and through dual transformation, a new objective function and constraints are derived. The objective function of the transformed subproblem (single-level MILP) is:

[0125] ,

[0126] The corresponding constraints are as follows:

[0127] ;

[0128] ;

[0129] ;

[0130] If the transformed objective function contains bilinear terms, such as That is, the product of the uncertain parameter and the dual variable needs to be transformed into a linear term through the Big M method or linearization techniques to ensure that the subproblem becomes a standard MILP and can be solved efficiently by solvers such as Gurobi and CPLEX.

[0131] Step S333: Solve the single-layer problem after dual transformation to obtain the worst-case scenario. Second-stage optimal response cost .

[0132] Among them, the worst scenario That is, resource demand With travel time A specific combination that allows the current pre-configured solution to reach its peak response cost; maximum response cost. That is, the upper limit of the optimal cost of the second-stage scheduling scheme.

[0133] Based on these two results, calculate the total cost of the current pre-defined solution: (Resource pre-positioning costs and) (sum of), and update the upper bound of the algorithm to This preserves the minimum total cost in the worst-case scenario of historical iterations, ensuring that the upper bound continues to decrease monotonically, gradually approaching the true robust optimum. Simultaneously, the newly discovered worst-case scenario... This will serve as an important constraint for subsequent iterations of the main problem, helping to optimize the pre-defined solutions in a targeted manner and make up for current risk shortcomings.

[0134] Step S34: Determine the convergence condition, if If the conditions are met, the optimal resource pre-configuration scheme and dynamic rescue scheduling scheme will be output; otherwise, the worst-case scenario will be output. Add to worst-case scenario set and return to step S32; where, This is the preset convergence tolerance.

[0135] This step determines whether the currently obtained resource provisioning scheme has reached a robust optimal level by checking the difference between the upper bound (UB) and the lower bound (LB) of the algorithm. When the algorithm converges, it is considered to have converged, meaning that the total cost (UB) in the worst-case scenario is sufficiently close to the minimum possible total cost (LB) of the current optimal solution, and further iterations cannot significantly improve the quality of the solution. This solution can then be considered a robust optimal solution, guaranteeing optimal total cost while also mitigating the risks of the worst-case scenario. It is a pre-defined small positive number, such as or Its value needs to balance the accuracy and efficiency of the solution.

[0136] In this embodiment of the invention, if the convergence condition is met, the algorithm will stop iterating and output the final result. The output includes a robust optimal resource pre-configuration scheme and a dynamic rescue scheduling scheme. Clarify whether each rescue base has a pre-positioned decision-making process for each type of resource. ) and specific preset quantity ( The dynamic rescue dispatch scheme covers the resource dispatch volume in key scenarios within an uncertain set (); ) and actual usage ( This includes, in particular, all worst-case scenarios identified during the iteration process. These solutions can be directly applied to actual rescue decisions, providing a clear basis for multi-departmental collaborative actions.

[0137] If the convergence condition is not met, i.e. If this fails, a new round of iterative optimization needs to be initiated. The specific steps are as follows: First, the worst-case scenario newly discovered for the sub-problem is... Add it to the worst-case scenario set L of the main problem, i.e. First, to ensure that this risk and weakness are fully considered in subsequent solutions to the main problem; second, to add optimality cutting constraints corresponding to this scenario to the main problem. These constraints will force the main problem to specifically compensate for the shortcomings of the current solution in the worst-case scenario when optimizing the pre-set solutions, such as increasing the number of pre-set key resources and optimizing the distribution of pre-set bases. After completing the above operations, the algorithm will return to sub-step S32, resolve the main problem, and start a new round of processes.

[0138] In addition, it should be noted that if the number of iterations reaches the preset maximum number of iterations... However, if the convergence condition is still not met, such as at the 50th or 100th iteration, the iteration must be forcibly terminated. In this case, the resource provisioning scheme and scheduling scheme obtained in the current iteration are output as an approximate robust optimal solution, and the convergence tolerance can be increased. Alternatively, the maximum number of iterations can be adjusted to further balance the accuracy of the solution with the efficiency of the solution.

[0139] Step S4: Based on the optimal resource pre-configuration plan and dynamic rescue dispatch plan, execute multi-department collaborative rescue decisions and output rescue instructions.

[0140] Specifically, step S4, which involves making multi-departmental collaborative rescue decisions, includes:

[0141] Step S41: Based on the dynamic rescue dispatch plan, allocate rescue tasks to multiple departments, including fire departments, medical departments, traffic police departments, railway operation departments, and emergency management departments.

[0142] In this invention, this step transforms the dynamic rescue dispatch plan output in step S3 into specific tasks that each department can directly execute, ensuring that each rescue action has a clearly defined responsible party and avoiding task overlap, omissions, or resource conflicts. Key parameters in the dynamic rescue dispatch plan are the direct basis for task allocation, such as the amount of resources dispatched. Resource usage Travel time .

[0143] For fire departments, task allocation is directly linked to the deployment volume of dedicated fire-fighting resources in the dynamic rescue dispatch plan. Corresponding resource type set For example, rescue equipment such as demolition equipment, respirators, and fire trucks are used. Specific tasks include, in response to the actual disaster situation at accident point k (such as fire or toxic gas leak), performing risk control operations such as fire fighting and toxic gas dilution, and opening rescue channels through demolition equipment. For the medical department, task allocation is based on the deployment volume of dedicated medical resources in the dynamic rescue dispatch plan. Based on the distribution of the injured at the scene, the set of resource types corresponding to the volume of medical resources dispatched is determined. Equipment such as ambulances, first-aid kits, and electrocardiogram monitors are provided. Specific tasks include setting up temporary medical points near the accident site and classifying the injured according to their severity (minor / serious / critical). For traffic police departments, task allocation is primarily based on travel time as defined in the dynamic rescue dispatch plan. To ensure unimpeded access from rescue base J to accident site K, and from the accident site to the hospital, the railway operations department allocates tasks based on the location of the accident section K and tunnel structure information in the dynamic rescue dispatch plan. Leveraging its exclusive control over the tunnel's internal environment and equipment systems, tasks include providing the joint command system with detailed tunnel structure diagrams, power supply and ventilation system control permissions, cutting off power to the accident section and activating emergency ventilation as needed to reduce harmful environmental impacts such as CO concentration, and inspecting track safety in the accident section, taking measures such as preventing runaway trains to avoid secondary accidents. For the emergency management department, task allocation is not limited to single resource or scenario parameters, but is based on the overall requirements of the dynamic rescue dispatch plan and feedback from various departments. Specific tasks include establishing a real-time information sharing mechanism to collect progress data from departments such as fire, medical, and traffic police, including disaster control progress, casualty treatment, and resource consumption status, and simultaneously disseminating this information to all relevant parties.

[0144] Step S42: Based on the decision-making weight of each department, establish a joint command and decision-making mechanism to coordinate rescue operations across multiple departments.

[0145] This step is based on the departmental decision-making weights defined in step S1. To establish an integrated command system led by professionals and coordinated in a unified manner, the specific structure of the command system is as follows: The chief commander is the head of the emergency management department, who is mainly responsible for overall planning, cross-departmental coordination, and approval of additional resources, and does not directly interfere with professional and technical decisions. His decision-making weight can be set to 0.10; the professional deputy commanders are jointly held by the heads of the fire department and the medical department, with a combined decision-making weight of 0.55. They respectively lead the professional decisions and task allocation for disaster response and casualty treatment, ensuring the professionalism of core rescue links; the heads of the traffic police department and the railway operation department, as members of the command system, are mainly responsible for providing feedback on the execution of tasks in their respective departments and providing professional and technical support to ensure smooth task coordination.

[0146] The corresponding mechanism can adopt a weighted voting system, where any department can propose a decision based on the actual situation on site. For example, the medical department could propose prioritizing the transfer of seriously injured patients, or the fire department could propose adjusting the disaster response plan. Each department can vote for or against the proposal based on its own responsibilities and on-site judgment, with the voting weight directly corresponding to the department's decision weight. A decision can be passed if the overall weighted support rate reaches 60%. For professional and technical issues such as fire fighting and first aid for the wounded, the weight of the corresponding professional department (fire or medical) will be temporarily doubled to avoid non-professional opinions interfering with key technical decisions and to ensure the professionalism and safety of rescue operations.

[0147] Step S43: Monitor and dynamically adjust rescue efficiency in real time to respond to dynamic changes at the rescue site. By monitoring rescue efficiency in real time and making targeted adjustments to actions, ensure that rescue efforts are always maintained at a high level and avoid a significant drop in efficiency due to sudden environmental changes, resource consumption, or lack of coordination.

[0148] rescue efficiency The calculation formula is:

[0149] ,

[0150] In the formula, To improve basic efficiency, , The value represents the degree of collaboration among multiple departments and ranges from 0 to 1. This is the environmental complexity impact coefficient, set to 0.8 in high-complexity scenarios, such as tunnel structure damage or multiple types of accidents, and set to 1.0 in low-complexity scenarios. The CO concentration impact factor, for example, drops to 0.85 when the concentration exceeds 500 ppm, and is 1.0 when the concentration is safe, directly related to the safety and efficiency of frontline workers; The resource sufficiency impact coefficient exhibits a linear variation, ranging from 0.5 to 1.2, depending on actual resource usage. Meet or even exceed demand The coefficient approaches 1.2 during periods of severe resource shortage, but drops to 0.5 during periods of severe resource scarcity. The communication efficiency impact coefficient ranges from 0.6 to 0.95. For example, it is 0.95 when messages are delivered promptly and the response delay is ≤1 minute, and drops to 0.6 when the delay is ≥5 minutes or communication is poor.

[0151] In a specific embodiment of the present invention, the calculation can be performed every 15 minutes. This generates an efficiency change curve, facilitating the timely detection of declining trends; in emergency situations such as sudden changes in CO concentration or the addition of critically injured patients, efficiency is calculated and evaluated in real time. Simultaneously, clearly defined efficiency threshold ranges are preset, among which... A state of high efficiency indicates that all processes are smoothly connected and resources are allocated reasonably. This is a normal situation; maintaining the existing action framework is sufficient. The situation is inefficient and adjustment measures need to be initiated immediately to avoid delays in rescue efforts.

[0152] In this invention, the dynamic adjustment strategy takes targeted measures to address the efficiency decline caused by different influence coefficients. For example, if f CO If the CO concentration is too low (increased), efficiency will decrease. Priority should be given to deploying the fire department's backup ventilation equipment to increase the dilution of toxic gases. Simultaneously, the rescue sequence should be adjusted, controlling environmental risks before proceeding with the transfer of the injured. Additional protective resources such as respirators should be provided to frontline personnel to ensure operational safety. If the resources are too low (shortage of resources), the emergency management department will initiate additional dispatch to call up pre-positioned backup resources from nearby rescue bases, while optimizing the allocation of existing resources and concentrating limited resources on core tasks such as emergency treatment of seriously injured people and disaster control. If necessary, external forces will be coordinated to provide reinforcements.

[0153] In one embodiment of the present invention, the multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization further includes: step S5: quantifying the benefits of multi-department collaboration, specifically, step S5 includes:

[0154] Step S51: Calculate the time without a cooperating reference , It is a key reference point for measuring the value of multi-department collaborative rescue. The time without collaboration specifically refers to the total time spent by each rescue department to carry out rescue operations completely independently in the absence of a unified command system, information sharing mechanism and resource coordination rules.

[0155] No Coordinated Reference Time The calculation formula is:

[0156] ,

[0157] In the formula, This refers to the total response time in the non-coordinated mode, which is simply the sum of the basic response times of each department. For example, the 15-minute basic response time of the fire department and the 20-minute basic response time of the medical department would be directly added together. This contrasts with the parallel processing in the non-coordinated mode. This refers to the number of departments in department set I, which is typically five departments: fire protection, medical services, traffic police, railway operations, and emergency management. This serves as the base response time for each department.

[0158] The total casualty rescue time in the non-cooperative mode, where m refers to the number of casualty types, usually classified into three categories according to the severity of the injury: minor injury, serious injury, and critical injury. It is the specific number of the j-th type of injured persons, which comes from the actual rescue data in step S4; This refers to the basic rescue time for Category j injured persons, such as 20 minutes for minor injuries, 40 minutes for serious injuries, and 60 minutes for critical injuries; The coefficient representing the influence of CO concentration is consistent with the monitoring data in step S4. When the CO concentration is >500ppm, it can be taken as 0.85, and when the concentration is safe, it can be taken as 1.0. In addition, 0.3 is the fixed baseline efficiency under the non-synergistic mode. This represents the number of effective rescue teams in the non-coordination mode. By default, a maximum of two rescue teams can be coordinated to avoid conflicts caused by too many teams and lack of coordination. When the number of injured is small, it is counted as one team.

[0159] For example, the total basic response time for the five departments is 15 (fire department) + 20 (medical) + 10 (traffic police) + 25 (railway operations) + 5 (emergency management) = 75 minutes; the injured are distributed as follows: 5 with minor injuries, 15 with serious injuries, and 5 with critical injuries; CO concentration is 700 ppm. ),but:

[0160] Time for first aid for minor injuries: minute,

[0161] Time for rescue of seriously injured: minute,

[0162] Critical rescue time: minute,

[0163] No coordinated reference time: minute.

[0164] Step S52: Calculate collaborative operation time Collaborative operation time This is the actual total time consumed under the multi-department collaborative rescue model, which includes the collaborative response time and collaborative rescue time. Its value is less than the baseline time without collaboration. Collaborative operation time The calculation formula is:

[0165] ,

[0166] in, For coordinated response time, This refers to the time for coordinated rescue efforts; among which, the coordinated response time... The mathematical expression for the optimized sum of response times of all departments in the collaborative mode is:

[0167] ,

[0168] In the formula, For the first Basic response time for each department; To the degree of coordination; Let i be the departmental decision-making weight of the i-th department, such as fire protection 0.30, medical care 0.25, etc. To the degree of coordination; This is the communication efficiency coefficient; This represents the environmental complexity impact coefficient. This indicates that the higher the weight of a department, the more significant the response optimization brought about by collaboration. For example, the fire department has the highest weight and the greatest reduction in response time.

[0169] Coordinated rescue time The total rescue time for all types of injured persons in the collaborative mode is expressed mathematically as follows:

[0170] ,

[0171] This represents the number of available rescue teams in the collaborative mode.

[0172] For example, if (High degree of collaboration) , , Other parameters are the same as in the non-cooperative mode. Therefore, the cooperative response time... :

[0173] Firefighting: minute;

[0174] Medical: minute;

[0175] Traffic police: minute;

[0176] Railway operations: minute;

[0177] Emergency Management: minute;

[0178] sum: minute;

[0179] Coordinated rescue time :

[0180] Minor injury: minute;

[0181] Seriously injured: minute;

[0182] Critical condition: minute;

[0183] sum: minute;

[0184] Collaborative operation time minute.

[0185] Step S53: Based on non-cooperative reference time and collaborative operation time The calculation of synergistic benefits includes both absolute and relative synergistic benefits.

[0186] Specifically, the mathematical expression for absolute synergistic benefits is:

[0187] ,

[0188] Based on the above calculation example, collaborative operation time The time was 488.3 minutes, with no coordinated reference time. The absolute synergistic effect is 665.2 minutes. ≈176.9 minutes (approximately 2.9 hours), indicating that the collaborative mechanism can shorten rescue time by nearly 3 hours. It is important to emphasize that... The higher the value, the more significant the synergistic value.

[0189] Relative synergistic benefits This is the core performance indicator after removing the impact of the accident's own scale, and its mathematical expression is:

[0190] ,

[0191] Based on the above calculation example, relative synergistic benefits .

[0192] According to embodiments of the present invention, a multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization is proposed. This invention achieves the comprehensive minimization of resource pre-configuration costs and response costs under worst-case scenarios by constructing a two-stage robust optimization model and an iterative solution algorithm for the main problem and sub-problems, ensuring the strong robustness of the rescue plan in the face of uncertainties such as demand and travel time. The method establishes a joint command mechanism based on departmental weights, effectively coordinating the actions of multiple departments such as fire fighting and medical services, significantly improving task coordination and response speed. Simultaneously, by quantifying the benefits of collaboration, the significant advantage of collaborative rescue over independent action in shortening rescue time is scientifically evaluated, providing reliable data support for rescue decision-making and improving the efficiency, reliability, and adaptability of railway tunnel emergency rescue.

[0193] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0194] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0195] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0196] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization, characterized in that: Includes the following steps: Step S1: Obtain basic data of railway tunnels, including tunnel structure information, resource prepositioning point information, departmental responsibility information, and historical accident data; Step S2: Based on the aforementioned railway tunnel basic data, construct a two-stage robust optimization model, which includes: The first-stage contingency plan decision model aims to minimize the sum of the resource pre-positioning cost and the second-stage response cost under the worst-case scenario, and determines the resource pre-positioning plan accordingly. The second-stage response decision model has the objective function of minimizing the sum of rescue time cost and resource shortage penalty cost under a given resource pre-configuration plan and specific accident scenario, and generating a dynamic rescue scheduling plan. The worst-case scenario is defined by a parameterized uncertainty set U, constructed based on the historical accident data, which describes the uncertainty of resource demand and travel time. Step S3: Based on the two-stage robust optimization model, the main problem-sub-problem iterative algorithm is used to solve the problem. The main problem optimizes the resource pre-setting scheme, and the sub-problems find the worst scenario and calculate its response cost. After iterative convergence, the optimal resource pre-setting scheme and dynamic rescue scheduling scheme are output. Step S4: Based on the optimal resource pre-configuration scheme and the dynamic rescue scheduling scheme, execute multi-department collaborative rescue decisions and output rescue instructions.

2. The multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization according to claim 1, characterized in that, In step S1, The tunnel structure information includes a tunnel structure diagram, which includes tunnel length, slope, cross-sectional dimensions, and emergency exit location information. The resource prepositioning point information includes a set of potential rescue bases, a set of rescue resource types, and resource prepositioning costs. The departmental responsibility information includes the set of departments, the basic response time of each department, and the decision-making weight of each department.

3. The multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization as described in claim 1, characterized in that, Step S2, in which the two-stage robust optimization model is constructed, specifically includes: Step S21: Construct an uncertainty set U, which is used to describe the uncertainty parameters of the accident scenario, including resource demand and travel time; Step S22: Construct the first-stage contingency plan decision model. The objective function of the first-stage contingency plan decision model is to minimize the pre-set resource cost and the worst-case response cost. Its mathematical expression is: ， In the formula, Indicates the pre-set cost of resources. This represents the cost of pre-setting one unit of resource r at rescue base j; This represents the quantity of pre-positioned resources r at rescue base j; y and q are... , , ; This represents the response cost under the worst-case scenario; Given a pre-defined scheme q and a specific scenario At that time, the maximum cost of the second-stage response decision; Step S23: Construct the second-stage response decision model. The objective function of the second-stage response decision model is to minimize the rescue time cost and the resource shortage penalty cost. Its mathematical expression is: ， In the formula, For the time cost of rescue; For travel time; The number of resources dispatched; The cost of penalizing resource shortages; This is the penalty weighting coefficient; Resource demand; This refers to the actual amount of resources used. This is the penalty function.

4. The multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization according to claim 3, characterized in that, The construction of the uncertain set U in step S21 specifically includes: Step S211: Using the partitioned budget uncertainty set form, determine the nominal value and deviation range of the uncertainty parameter based on the historical accident data; Step S212: Determine the zoning uncertainty budget parameters based on the historical accident data, including the uncertainty budget of fire resource demand, the uncertainty budget of medical resource demand, the uncertainty budget of travel time in the core area, and the uncertainty budget of travel time in the outer area, and control the conservatism of the uncertainty set U; Step S213: Based on the nominal value, the deviation range, and the partition uncertainty budget parameter, generate the polyhedral representation of the uncertainty set U, the mathematical expression of which is: , In the formula, For resource demand, For resource demand The nominal value, ; This represents the maximum deviation in resource demand. This is the lower bound of resource demand. ; For travel time, This is the nominal value of the travel time. This represents the maximum deviation in travel time. This is the lower bound of the passage time. , This is the upper bound of the travel time. ; A collection of dedicated firefighting resources; A collection of medical-specific resources; This is a collection of accident points in the core area of ​​the tunnel. This is a collection of accident sites in the area surrounding the tunnel. Budgeting for uncertainties in fire protection resource needs; Budgeting for the uncertainty of healthcare resource needs; Budgeting for uncertain travel times in the core area; Budgeting for the uncertainty of travel time in the outer areas.

5. The multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization according to claim 1, characterized in that, Step S3 uses a main problem-subproblem iterative algorithm to solve the problem, specifically including: Step S31: Initialize the main problem, and set the initial worst-case scenario set. Set to an empty set and initialize the upper bound of the algorithm. and the lower bound of the algorithm ; Step S32: Solve the main problem to obtain the current resource pre-configuration scheme. and current target value And update the lower bound of the algorithm. ; Step S33: Based on the current resource provisioning scheme, solve the sub-problem to find the worst-case scenario under the current provisioning scheme. and the corresponding second-phase response cost And update the upper bound of the algorithm. In the formula, The upper bound before the update. The pre-allocated resource quantity obtained from solving the current round master problem; Step S34: Determine the convergence condition, if If the conditions are met, then the optimal resource pre-configuration scheme and the dynamic rescue scheduling scheme will be output; otherwise, the worst-case scenario will be output. Add to the worst-case scenario set and return to step S32; where, This is the preset convergence tolerance.

6. The multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization according to claim 5, characterized in that, The specific steps in step S33 for solving the subproblem include: Step S331: Based on the current resource provisioning scheme, construct a sub-problem model. The sub-problem model is a minimax problem, the objective of which is to determine the worst-case scenario that maximizes the response cost of the second stage. Its mathematical expression is: ， In the formula, The output of the subproblem; This refers to the time cost of resource scheduling. Penalty cost items for resource shortages Weighting for resource shortage penalties; For the scene The amount of resource shortage at the next accident point k relative to resource r; For the scene Below, the resource requirement of incident point k for resource r; For the scene Below is the unit resource travel time cost from rescue base j to accident site k; For the inner minimization operator, For resource dispatch quantity variable; For resource usage variables; Step S332: Perform dual transformation on the subproblem model, and use strong duality theory to transform the inner minimization problem into a maximization problem, thereby transforming the two-layer problem into a single-layer mixed integer linear programming problem; Step S333: Solve the single-layer problem after dual transformation to obtain the worst-case scenario. Second-stage optimal response cost .

7. The multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization according to claim 2, characterized in that, The specific steps in step S4 for implementing multi-department collaborative rescue decision-making include: Step S41: Based on the dynamic rescue dispatch scheme, allocate rescue tasks to multiple departments, including fire departments, medical departments, traffic police departments, railway operation departments, and emergency management departments; Step S42: Based on the departmental decision-making weights, construct a joint command and decision-making mechanism to coordinate the rescue operations of the multiple departments; Step S43: Monitor and dynamically adjust rescue efficiency in real time, wherein the rescue efficiency The calculation formula is: ， In the formula, To improve the efficiency of collaboration; This represents the environmental complexity impact coefficient. The coefficient representing the influence of carbon monoxide concentration; This represents the influence coefficient of resource sufficiency. This represents the impact coefficient on communication efficiency.

8. The multi-department collaborative emergency rescue method for railway tunnels based on two-stage robust optimization according to claim 1, characterized in that, It also includes: Step S5: Quantifying the benefits of multi-departmental collaboration. Step S5 includes: Step S51: Calculate the time without a cooperating reference The calculation formula is: ， In the formula, This represents the total response time in the non-cooperative mode, where... This represents the number of departments in the department set. This serves as the base response time for each department; The total casualty rescue time in the non-cooperative mode, where m refers to the number of casualty types. This refers to the specific number of wounded in category j; This is the basic rescue time for Category j injured persons; This represents the number of effective rescue teams in a non-cooperative mode. Step S52: Calculate collaborative operation time The calculation formula is: ， In the formula, For coordinated response time, For coordinated rescue time; among them, ， In the formula, To the degree of coordination; Let be the departmental decision weight for the i-th department; ， Number of available rescue teams; Step S53: Based on the aforementioned non-cooperative reference time and the aforementioned collaborative operation time Calculate the synergistic benefits, which include absolute synergistic benefits and relative synergistic benefits. The mathematical expression for absolute synergistic benefits is: ； The mathematical expression for relative synergistic benefits is: 。

Images