A Method and System for Locating Pre-Hospital Emergency Facilities Based on Improved PSO Algorithm

Abstract

The present invention provides a method and system for pre-hospital emergency facility location based on an improved PSO algorithm. Based on the periodic differences of different demand points, preliminary location plans for different emergency facilities are configured; the preliminary location plans are formed into a two-layer programming model focusing on the location of fixed emergency facilities and focusing on the selection of mobile emergency facilities. The upper-layer programming model determines the multi-objective configuration plan of the service capacity and total cost of the pre-hospital emergency system, and inputs the optimal compromise configuration plan into the lower-layer programming model; based on the improved PSO algorithm, the service effect of the emergency system in the lower-layer programming model is solved, and the optimization result is fed back to the upper-layer programming model to obtain the best configuration plan for the location of emergency facilities at demand points in different periods. Based on the hierarchical structure of the two-layer programming model and the improved algorithm, the present invention constructs a hierarchical and dynamically decision-making system that closely conforms to the characteristics of emergency medical services, provides a basic guarantee for intelligent recommendation for emergency users, and effectively improves the efficiency of emergency services.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly to a method and system for locating pre-hospital emergency facilities based on an improved PSO algorithm. Background Art

[0002] As an indispensable subsystem in the social public safety emergency system, the efficient operation of the pre-hospital medical emergency system is crucial for ensuring the public's life safety and health. In particular, the location problem of key emergency facilities such as Automatic External Defibrillators (AEDs) and ambulances has become a core issue in urban planning and urban development in recent years.

[0003] Many cities are actively promoting the addition of emergency facilities in public places, aiming to provide timely emergency treatment for patients with out-of-hospital cardiac arrest and win precious rescue time. However, the actual application of these facilities in China is still in the exploratory and experimental stage. Relevant research mostly focuses on macro-level deployment or the deployment of single facilities, and most deployment strategies are based on subjective cognitive criteria. As a result, in the case of out-of-hospital cardiac arrest (OHCA) events where actual cardiac arrests can be divided according to the spatial location of the occurrence site, the effectiveness of pre-hospital treatment has not yet reached the expected level. There are serious mismatches between the distribution of emergency facilities and the actual needs of OHCA patients in many cities, and the accessibility of facilities is poor. This has led to the phenomenon that although the number of emergency facilities is increasing day by day, they cannot be fully and effectively utilized. On the one hand, it reduces economic benefits, and on the other hand, it has instead become an important factor restricting the improvement of OHCA emergency efficiency.

[0004] Therefore, there is an urgent need to propose a solution that can not only meet the scientific planning of the layout of pre-hospital cardiac arrest emergency facilities, dynamically construct a pre-hospital emergency system with rapid response, wide coverage, and easy access, but also, after the demand changes, can quickly respond to the needs of patients, provide medical services in a timely manner, pursue the highest possible service level, and maximize the comprehensive satisfaction of patients with waiting time and subsequent treatment costs. Summary of the Invention

[0005] The purpose of this application is to provide a method and system for locating pre-hospital emergency facilities based on an improved PSO algorithm, so as to combine the network layout optimization plan of fixed emergency facilities AEDs and mobile emergency facilities ambulances, provide a theoretical reference for the location design of pre-hospital cardiac arrest emergency facilities in Chinese cities, and effectively improve the current quality of pre-hospital emergency services.

[0006] According to one aspect of this application, a method for locating pre-hospital emergency facilities based on an improved PSO algorithm is proposed. The method includes the following steps:

[0007] S1. Based on the periodic differences of different demand points, configure the preliminary site selection plans for different first-aid facilities, where the first-aid facilities include fixed first-aid facilities and mobile first-aid facilities;

[0008] S2. Transform the preliminary site selection plan into a two-layer programming model that focuses on the site selection of fixed first-aid facilities and the selection of mobile first-aid facilities. Among them, the two-layer programming model includes an upper-layer programming model and a lower-layer programming model. The upper-layer programming model determines the multi-objective configuration plan of the pre-hospital first-aid system service capacity and the total cost of the pre-hospital first-aid system, and inputs the optimal compromise configuration plan into the lower-layer programming model;

[0009] S3. Solve the service effect of the first-aid system in the lower-layer programming model based on the improved PSO algorithm, and feedback the optimization result to the upper-layer programming model to obtain the best configuration plan for the site selection of first-aid facilities for different periodic demand points.

[0010] In the above technical solution, based on the hierarchical structure of the two-layer programming model, this application constructs a hierarchical dynamic decision-making system, and the overall design of the model closely adheres to the characteristics of first-aid medical services. Among them, the upper-layer model focuses on the balance between the service capacity and cost-benefit of the first-aid system, and the lower-layer design considers the first-aid service effect from the perspective of residents. By comprehensively evaluating the first-aid efficiency with satisfaction, combined with the network layout optimization plan of fixed first-aid facilities AED and mobile first-aid facilities ambulances, it provides a theoretical reference for the site selection design of pre-hospital cardiac arrest first-aid facilities in Chinese cities, effectively improving the current quality of pre-hospital first-aid services.

[0011] Furthermore, the improved PSO algorithm includes the following sub-steps:

[0012] S31. Set parameters, including population size , problem dimension , inertia weight , learning factor , maximum number of iterations and search space boundary ;

[0013] S32. Randomly initialize the position and velocity of the particles, and calculate the individual optimum and population optimum ;

[0014] S33. Adjust the inertia weight of the particle individuals using the dynamic inertia weight index strategy, and calculate the reverse solution of the particle relative to the dynamic center of gravity based on the dynamic center-of-gravity reverse learning strategy;

[0015] S34. Update the position of the particle when the fitness of the reverse solution of the particle is better than the fitness of the current solution, i.e., , update the position of the particle and the fitness . Update the personal best when the current fitness is better than the historical personal best , update the personal best , update the particle velocity , and update the particle position using the sine-cosine perturbation strategy , represents the current iteration number;

[0016] S35. Loop through steps S33 - S34 until the convergence condition is met, and output the optimal solution.

[0017] Furthermore, the dynamic inertia weight exponential strategy combines the exponential law to reduce the inertia weight, specifically expressed as: , where represents the inertia weight of the current iteration; represents the minimum value of the inertia weight; represents the maximum value of the inertia weight; represents the current iteration number; represents the total number of iterations.

[0018] Furthermore, the dynamic barycenter reverse learning strategy introduces the dynamic random selection of the number of solutions participating in the barycenter calculation. Specifically, the barycenter of the dynamic random solution set is expressed as , then the reverse solution with respect to the barycenter is expressed as , where , is a subset composed of solutions, is a subset and

[0019] is a solution vector in the subset is set in the -dimensional search space. For the th iteration, the update strategy for the th dimension position of the particle

[0020]

[0021] is as follows: represents the velocity of the particle in the th generation and the th dimension; represents the particle in the th generation and the The position in dimension Indicates the position of the particle in the dimension in generation Indicates a random number in the interval [0, 1].

[0022] In the above technical solution, in view of the defects of the premature convergence of the PSO algorithm to the local optimal solution and the deficiency in balancing between local and global exploration, etc., this application introduces a dynamic center of gravity reverse learning strategy, a dynamic inertia weight exponential decay strategy, and a sine-cosine perturbation strategy, achieving significant effects in solving optimization, having high stability, and having significant advantages in comprehensive global search ability and optimization efficiency.

[0023] Furthermore, the lower-level planning model includes a response time satisfaction function and a treatment cost satisfaction function. Among them, the resident's satisfaction with the response time gradually decays with the increase of time, and the extension of the first aid time leads to an increase in the subsequent treatment cost. Then, the first aid response time satisfaction function is expressed as:

[0024]

[0025] In the formula, represents the shortest waiting time acceptable to the resident, represents the longest waiting time acceptable to the resident for the first aid service, represents the time when the resident obtains the first aid service;

[0026] The treatment cost satisfaction function is expressed as:

[0027]

[0028] In the formula, represents the number of patients; represents the response delay time of the first aid service; and respectively represent the probabilities of the patient's condition being serious and general when calling the first aid service; and respectively represent the amounts by which the subsequent treatment costs for serious and general condition patients increase at least for each minute of delay in the response of the first aid service.

[0029] Even further, the lower-level planning model and the corresponding constraint conditions are expressed as:

[0030] Formula Four

[0031] Constraint conditions:

[0032] Condition Ten

[0033] Condition Eleven

[0034] Condition Twelve

[0035] Condition Thirteen

[0036] Condition Fourteen

[0037] Condition Fifteen

[0038] Condition Sixteen

[0039] Condition Seventeen

[0040] Condition Eighteen

[0041] Condition Nineteen

[0042] Condition Twenty

[0043] Condition Twenty - One

[0044] Condition Twenty - Two

[0045] The objective function formula four indicates that the comprehensive satisfaction of patients with waiting time and the subsequent treatment cost is maximized; the constraint condition ten indicates the covered radius The covered demand should reach at least the proportion of the total demand; the constraint condition eleven indicates that the sum of the actual service volumes of each cycle's first - aid points at the level does not exceed times its service capacity; the constraint condition twelve restricts that the number of first - aid points with ambulances allowed to be opened in each cycle does not exceed the maximum limit; the constraint condition thirteen stipulates that the number of ambulances configured at the selected first - aid points is the number specified by the first - aid point type; the constraint condition fourteen stipulates that the total number of ambulances at all first - aid points in each cycle does not exceed the maximum limit; the formula condition fifteen indicates that the number of lacking or redundant ambulances in each cycle is transferred out or in from the existing first - aid centers; the formula condition sixteen indicates that after the first - aid point experiences ambulance re - positioning within the time period it remains balanced with the number of ambulances at the current first - aid point within the time from the alternative first - aid point The travel time is affected by the driving speeds of different types of vehicles; Condition 19 of the formula indicates that the travel time of the ambulance from the emergency point to the demand point is equal to the ratio of the road distance between the emergency point and the demand point to the vehicle driving speed; Condition 20 of the formula defines the maximum service capacity of the emergency point ; Condition 21 of the formula is the value constraint of the decision variable; Condition 22 of the formula is the non - negative constraint.

[0046] Furthermore, the service capacity of the pre - hospital emergency system is defined as the number of residents corresponding to the area covering the demand points. Then, the service capacity of the pre - hospital emergency system is represented by the number of residents not fully served and the number of residents with double coverage through the objective function and the objective function respectively, where:

[0047]

[0048]

[0049] In the formula, represents the period division, represents the set of demand points, represents the demand volume of the demand point during the period, represents that during the period, there are at least two candidate emergency points within the radius providing services for the demand point represents the set of alternative emergency points that can cover the demand point at a distance less than the coverage radius ; represents the maximum service capacity of the emergency point during the period, represents the road distance between the alternative emergency point and the demand point during the

[0050] Furthermore, the total cost of the pre - hospital emergency system includes the loss cost of the emergency facilities themselves, the variable cost of the ambulances, and the labor cost of the emergency personnel. Among them, its objective function is specifically expressed as:

[0051]

[0052] In the formula, represents the period division, Denote the set of alternative emergency points, Denote the maximum limit number of AEDs configured at each emergency point, Denote Time period, the number of AEDs configured at the emergency point is more than 0, Denote Time period, the number of AEDs included in the emergency point Denote the loss cost of AED (ambulance), Denote Time period, the number of ambulances parked at the emergency point is more than 0, Denote Time period, the number of ambulances included in the emergency point Denote Time period, the number of emergency personnel equipped for each AED, Denote Time period, the number of emergency personnel equipped for each ambulance, Denote Time period, the working hours of emergency personnel, Denote Time period, the labor cost per hour of emergency personnel, Denote the time period end to the time period beginning, it is necessary to transfer ambulances between the existing emergency center and the emergency point Denote the time period end to the time period beginning, the number of ambulances transferred between the existing emergency center and the emergency point Denote the time period to the time period within, the distance between the emergency center and the emergency point Denote Time period, the variable cost per unit distance of the ambulance.

[0053] Furthermore, the upper-level planning model and the corresponding constraint conditions are as follows:

[0054] The upper-level planning model is expressed as:

[0055] Formula One

[0056] Formula Two ​​​​​

[0057] Formula 3

[0058] The corresponding constraints are expressed as:

[0059] Condition 1

[0060] Condition 2

[0061] Condition three

[0062] Condition 4

[0063] Condition five

[0064] Condition six

[0065] Condition 7

[0066] Condition 8

[0067] Condition nine

[0068] Among them, formula 1 indicates that the demand that is not served in the whole cycle is the smallest; formula 2 indicates that the demand that is served in the whole cycle is the smallest. The demand for more than two times is the largest; Formula 3 indicates that the total cost of the whole cycle is the smallest, including the wear and tear costs of AED and ambulance, the variable cost of ambulance and the labor cost of emergency personnel;

[0069] Condition 1 means that the number of AEDs equipped at each emergency point does not exceed the maximum limit, and condition 2 ensures that the emergency point The location and number of AEDs remain unchanged every cycle; Condition 3 means that the total number of AEDs equipped at all emergency points does not exceed the maximum limit, Indicates the maximum number of AEDs configured for all emergency points. Condition 4 ensures the coverage radius All requirements must be covered; Condition 5 means that if a requirement point is not covered at least once, it cannot be covered twice. Indicates that the coverage radius can be less than Distance to cover demand points The set of alternative emergency points; Condition 6 ensures that only when the demand point When there are two or more emergency rescues, the demand point It was only covered twice. express Time period, demand point In radius There is at least one (two) candidate emergency point providing services for it; condition seven is defined as an emergency point For demand points The service capacity meets a functional relationship related to distance; Condition Eight represents the value constraint of the decision variable; Condition Nine is the non - negative constraint.

[0070] In the above - mentioned technical solution, this application optimizes the balance between the service capacity and cost - effectiveness of the first - aid system, introduces a new perspective on the allocation of multiple first - aid resources, and promotes a collaborative first - aid mechanism for two facilities, namely automated external defibrillators and ambulances. At the same time, considering the time - varying characteristics of first - aid demands caused by population mobility factors, the single - cycle model is extended to a more flexible multi - cycle model. The model dynamically adjusts the positions of ambulances at alternative first - aid points in different time periods, thereby improving the efficiency of pre - hospital cardiopulmonary arrest emergency medical services and effectively coping with the resource - allocation challenges caused by demand changes.

[0071] According to another aspect of this application, a pre - hospital first - aid facility location system based on an improved PSO algorithm is proposed. The system includes:

[0072] A preliminary location module, configured to configure preliminary location plans for different first - aid facilities based on the periodic differences of different demand points. The first - aid facilities include fixed first - aid facilities and mobile first - aid facilities;

[0073] An optimal compromise module, configured to form a two - layer programming model that focuses on the location of fixed first - aid facilities and focuses on the selection of mobile first - aid facilities from the preliminary location plan. Among them, the two - layer programming model includes an upper - layer programming model and a lower - layer programming model. The upper - layer programming model determines a multi - objective configuration plan for the service capacity of the pre - hospital first - aid system and the total cost of the pre - hospital first - aid system, and inputs the optimal compromise configuration plan into the lower - layer programming model;

[0074] A best configuration module, configured to solve the service effect of the first - aid system of the lower - layer programming model based on the improved PSO algorithm, and feedback the optimization result to the upper - layer programming model to obtain the best configuration plan for the location of first - aid facilities for different - cycle demand points.

[0075] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0076] (1) The present invention proposes a dynamic center reverse - learning strategy, a dynamic inertia - weight exponential - decay strategy, and a sine - cosine perturbation strategy for the defects of the PSO algorithm in premature convergence to local optimal solutions and its deficiency in balancing local and global exploration, achieving significant effects in solving optimization, and having high stability and better performance advantages.

[0077] (2) The present invention introduces a new perspective on the allocation of multiple first-aid resources, realizes the combined rescue of two facilities. At the same time, considering the characteristics of the dynamic change of first-aid needs in real life, the single-cycle model is extended to a multi-cycle model, and based on the hierarchical structure of the bilevel programming model, a hierarchical dynamic decision-making system is constructed. The overall design of the model closely adheres to the characteristics of emergency medical services. Among them, the upper-layer model focuses on the balance between the service capacity and cost-effectiveness of the first-aid system, and the lower-layer design considers the first-aid service effect from the perspective of residents. The first-aid efficiency is evaluated through comprehensive satisfaction, so as to improve the first-aid service efficiency and quality.

[0078] (3) The present invention evaluates the first-aid efficiency through comprehensive satisfaction, combines the network layout optimization scheme of fixed first-aid facilities AED and mobile first-aid facilities ambulances, provides a theoretical basis for the site selection design of pre-hospital cardiac arrest first-aid facilities in Chinese cities, and also lays a basic guarantee for the intelligent recommendation of first-aid users. Brief Description of the Drawings

[0079] The drawings are included to provide a further understanding of the embodiments and are incorporated into and form a part of this specification. The drawings illustrate the embodiments and, together with the description, are used to explain the principles of the present invention. Other embodiments and many of the intended advantages of the embodiments will be readily apparent as they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. Like reference numerals refer to corresponding like parts.

[0080] Figure 1 is a flowchart of a pre-hospital first-aid facility site selection method based on an improved PSO algorithm according to an embodiment of the present application;

[0081] Figure 2 is a schematic diagram of the framework process of pre-hospital first-aid facility site selection based on an improved PSO algorithm according to an embodiment of the present application;

[0082] Figure 3 is a schematic diagram of the site selection coding of the upper-layer planning model according to an embodiment of the present application;

[0083] Figure 4 is the non-dominated solution set of the upper-layer planning model according to an embodiment of the present application;

[0084] Figure 5 is a diagram of the AED site selection result of the upper-layer planning model according to an embodiment of the present application;

[0085] Figure 6 is a diagram of the ambulance site selection result of the pre-hospital first-aid facility site selection model based on an improved PSO algorithm according to an embodiment of the present application;

[0086] Figure 7 It is a framework diagram of a pre - hospital emergency facility location optimization system based on an improved PSO algorithm according to an embodiment of the present application. Detailed implementation manners

[0087] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0088] Reference Figure 1 , Figure 1 shows a flowchart of the pre - hospital emergency facility location method based on the improved PSO algorithm of the present application. As shown in the figure, the method includes the following steps:

[0089] S101. Based on the periodic differences of different demand points, configure preliminary location plans for different emergency facilities, where the emergency facilities include fixed emergency facilities and mobile emergency facilities.

[0090] In some specific embodiments, in order to better abstract the out - of - hospital cardiac arrest emergency facility location model into a mathematical model, the following assumptions are made: The locations of all demand areas are known, and they are divided into different area types according to the characteristics of demand changes within the area. All demand areas are clustered into demand points at a certain spatial resolution, that is, one demand point represents one demand area, and the number of demand points remains unchanged. The total demand in the research area remains basically the same in each cycle. The demand of all demand points in each cycle is known, and the demand is defined as the population of the area. The locations of all alternative emergency points are known, and they are divided into different types of alternative emergency points according to location characteristics. Different types of emergency points are equipped with a fixed number of AEDs or ambulances. The location of the existing emergency center is known, and all ambulances return to the emergency center at the end of each cycle. At the beginning of a new cycle, they are re - allocated to new emergency points according to the demand.

[0091] For the convenience of description, the sets and indices in the model are shown in Table 1, the model parameters are shown in Table 2, and the model decision variables are shown in Table 3:

[0092] Table 1: Sets and indices

[0093]

[0094] Table 2: Model parameters

[0095]

[0096] Table 3: Decision variables

[0097]

[0098] S102. Fit the preliminary site selection plan into a two - layer programming model focusing on the location of fixed first - aid facilities and the selection of mobile first - aid facilities. Among them, the two - layer programming model includes an upper - layer programming model and a lower - layer programming model. The upper - layer programming model determines the multi - objective configuration plan of the pre - hospital first - aid system service capacity and the total cost of the pre - hospital first - aid system, and inputs the optimal compromise configuration plan into the lower - layer programming model.

[0099] In some specific embodiments, the two - layer programming problem proposed in this application is in the form of multiple objectives in the upper layer and a single objective in the lower layer, and its mathematical model is:

[0100]

[0101] In the formula, represents the upper - layer programming model, represents the lower - layer programming model, represents the induced domain of the two - layer programming problem, that is, the influence of the optimal solution set of the lower - layer problem on the upper - layer variable

[0102] When solving the upper - layer multi - objective programming problem, a set of Pareto optimal solutions will be obtained, and these solutions reflect the optimal trade - off between different objectives. If all the upper - layer optimal solutions are directly used to solve the lower - layer problem, it will inevitably cause too high a computational cost. Therefore, in this application, the best - compromise solution method is adopted at the interface of the upper and lower layer models, that is, a relatively optimal solution is selected from the upper - layer Pareto optimal solution set as the input of the lower - layer model. Specifically, in this application, each solution is normalized on each objective function to ensure that objective functions with different dimensions can be evaluated on the same comparison basis. Subsequently, the normalized values of each objective function are accumulated to obtain a comprehensive performance index. By comparing this comprehensive performance index, the solution with the best comprehensive performance is selected as the optimal compromise solution, that is, the optimal compromise configuration plan.

[0103] Specifically, in the design of the upper - layer objective function of the two - layer programming model, it mainly focuses on two key aspects: one is the service capacity provided by the first - aid system; the other is the economy of the first - aid system. The service capacity provided by the first - aid system is characterized by the number of residents with dual coverage and the number of residents not fully served.

[0104] ​The number of residents achieving dual coverage. In the site selection problem, when a demand point is within the maximum service radius of a facility point, the demand point is said to be fully covered. Given the special nature of first aid facilities, it is necessary to fully consider the situation where a single coverage facility, once occupied, will be in a "busy" state for a long time and unable to serve other demand points, resulting in the original covered area being in an "exposed" state. Therefore, introducing backup coverage is crucial for enhancing the response service capacity of the system. Then, the number of residents achieving dual coverage is characterized as: , where represents the cycle division, represents the set of demand points, represents the demand volume of the demand point during the represents the demand point within the radius having at least two candidate first aid points providing services for it.

[0105] The number of residents not fully served. Judging whether a demand point is covered depends on the distance between the facility point and the demand point. And judging whether a demand point is fully served requires considering the established service capacity of the facility, such as the maximum demand volume that a first aid facility can serve. Usually, there is a negative correlation between the service capacity and the distance to the first aid point, that is, the closer the area is to the first aid point, the higher the service capacity it receives. Therefore, considering the backup coverage, the number of residents not fully served is characterized as: , where represents the cycle division, represents the set of demand points, represents the demand volume of the demand point during the represents the set of alternative first aid points that can cover the demand point at a distance less than the coverage radius , represents the maximum service capacity of the first aid point during the represents the travel distance between the alternative first aid point and the demand point during the

[0106] The economy of the first aid system is reflected by the total cost of the first aid system. The total cost of the pre-hospital cardiac arrest first aid system covers the loss cost of the first aid facility itself, the variable cost of the ambulance, and the labor cost of the first aid personnel. In the model, the loss cost of the first aid facility itself is refined into the daily loss of the facility. In addition, the variable cost of the ambulance varies according to the specific usage in different time periods. As the number of ambulances increases or decreases within the cycle, the labor cost of the first aid personnel also changes accordingly. Thus, the total cost of the pre-hospital cardiac arrest first aid system over the entire cycle is characterized as:

[0107]

[0108] Among them, represents the cycle division, represents the set of alternative first aid points, represents the maximum limit number of AEDs configured at each first aid point, represents time period, there are more than 0 AEDs configured at the first aid point within, represents time period, the number of AEDs included in the first aid point is, represents the loss cost of the AED (ambulance), represents time period, there are more than 0 ambulances parked within the first aid point within, represents time period, the number of ambulances included in the first aid point is, represents time period, the number of first aid personnel equipped for each AED, represents time period, the number of first aid personnel equipped for each ambulance, represents time period, the working hours of the first aid personnel, represents time period, the labor cost per hour of the first aid personnel, represents the time period end to the time period beginning, it is necessary to transfer ambulances between the existing first aid center and the first aid point , represents the time period end to the time period beginning, the number of ambulances transferred between the existing first aid center and the first aid point is, represents the time period to the time period within the emergency center and the emergency point distance, represents during a period, the variable cost per unit distance of the ambulance.

[0109] Then the upper - level model is expressed as:

[0110] Formula One

[0111] Formula Two

[0112] Formula Three

[0113] Constraints:

[0114] Condition One

[0115] Condition Two

[0116] Condition Three

[0117] Condition Four

[0118] Condition Five

[0119] Condition Six

[0120] Condition Seven

[0121] Condition Eight

[0122] Condition Nine

[0123] Formula One represents that the un - served demand in the whole cycle is the smallest; Formula Two represents that the demand covered more than twice in the whole cycle is the largest; Formula Three represents that the total cost in the whole cycle is the smallest, which includes the loss cost of AED and ambulances, the variable cost of ambulances and the labor cost of emergency personnel; Condition One means that the number of AEDs equipped at each emergency point does not exceed the maximum limit, and Condition Two ensures that the location and number of AEDs at the emergency point remain unchanged every cycle; Condition Three means that the total number of AEDs equipped at all emergency points does not exceed the maximum limit,

[0124] represents the maximum limit number of AEDs configured for all emergency points, and Condition Four ensures the coverage radius ​​All requirements must be covered; Condition Five states that if a requirement point is not covered at least once, it cannot be covered twice. Indicates that it can cover the requirement point at a distance less than the coverage radius of the alternative first-aid points; Condition Six ensures that a requirement point is covered twice only when there are two or more first-aids within the of the requirement point; When there are two or more first-aids, the requirement point is covered twice. Indicates time period, and there is at least one (two) candidate first-aid point within the radius of the requirement point to provide services for it; Condition Seven is defined as the service capacity of the first-aid point for the requirement point to meet the functional formula related to the distance; Condition Eight represents the value constraint of the decision variable; Condition Nine is the non-negativity constraint. Specifically, in the design of the lower-level objective function, focus on constructing the satisfaction function from the perspective of residents, that is, consider the effect of first-aid services from the perspective of residents. Specifically, it includes constructing the satisfaction function of the first-aid response time and the satisfaction function of the subsequent treatment cost.

[0125] From the perspective of residents, constructing the satisfaction function of residents' first-aid response time not only examines the efficiency of first-aid services, which is the key to evaluating the efficacy of pre-hospital cardiac arrest first-aid, but also has crucial significance for improving the coverage rate and success rate of first-aid services. Assuming that if the first-aid service is provided within the shortest waiting time

[0126] acceptable to residents, the satisfaction of residents is defined as 1; if the first-aid service is provided outside the longest waiting time acceptable to residents, the satisfaction of residents is defined as 0; if the first-aid service activity occurs within the time period, the satisfaction of residents with the first-aid response time gradually decays as time increases. Thus, the satisfaction function of residents with the first-aid response time is given as: The timeliness of pre-hospital first-aid services has an important impact on the subsequent treatment costs of patients. For every minute the first-aid time is extended, the subsequent medical costs of patients will increase accordingly. Thus, the function of waiting time and subsequent medical costs is constructed as:

[0127]

[0128] Among them,

[0129]

[0130] where represents the number of patients; represents the delay time of the first-aid service response; and respectively represent the probabilities of the patient's serious and general conditions when calling for emergency services; and respectively represent the amounts by which the subsequent treatment costs for patients with serious and general conditions increase at least for each one-minute delay in the emergency service response.

[0131] Then the lower-level model is expressed as:

[0132] Formula Four

[0133] Constraints:

[0134] Condition Ten

[0135] Condition Eleven

[0136] Condition Twelve

[0137] Condition Thirteen

[0138] Condition Fourteen

[0139] Condition Fifteen

[0140] Condition Sixteen

[0141] Condition Seventeen

[0142] Condition Eighteen

[0143] Condition Nineteen

[0144] Condition Twenty

[0145] Condition Twenty-One

[0146] Condition Twenty-Two

[0147] The objective function Formula Four represents the maximum comprehensive satisfaction of the patient with the waiting time and the patient with the subsequent treatment costs. Constraint Ten means that the demand covered by the coverage radius should reach at least proportion of the total demand. Constraint Eleven means that the sum of the actual service volumes of the emergency points in each cycle under the level does not exceed of their service capabilities.times. Constraint twelve restricts the number of emergency points with ambulances that can be opened per period to not exceed the maximum limit. Constraint thirteen stipulates that the number of ambulances configured at the selected emergency points is the number specified by the emergency point type. Constraint fourteen stipulates that the total number of ambulances at all emergency points per period does not exceed the maximum limit. Formula condition fifteen indicates that the number of missing or redundant ambulances per period is transferred out of or into the existing emergency centers, and formula condition sixteen indicates that the emergency point During the time period After the relocation of ambulances, it remains balanced with the number of ambulances at this point within the time . Constraint seventeen represents the limit on the total number of emergency personnel per period. Formula condition eighteen indicates that the travel time from the alternative emergency point to the demand point is affected by the driving speeds of different types of vehicles. Formula condition nineteen indicates that the travel time of the ambulance from the emergency point to the demand point is equal to the ratio of the road distance between the emergency point and the demand point to the vehicle driving speed. Formula condition twenty defines the maximum service capacity of the emergency point . Formula condition twenty - one is the value constraint of the decision variable. Formula condition twenty - two is the non - negative constraint.

[0148] In the construction of the bi - level programming model of this application, considering the strong time - variability of the urban population distribution, to adapt to the spatio - temporal changes of emergency needs, taking into account the multi - period characteristics of emergency medical services, a single facility is expanded into two facilities to achieve joint emergency rescue. Based on the bi - level programming model, an effective resource allocation is realized with the fixed emergency facility AED site selection as the main and the relocation of mobile emergency facilities ambulances as the supplement. In addition, from the perspective of residents, the model realizes the goals of minimizing the siting cost of the emergency system, maximizing the comprehensive service capacity, and maximizing the satisfaction from the perspective of residents, which has practical significance.

[0149] S103, Solve the service effect of the emergency system of the lower - level programming model based on the improved PSO algorithm, and feedback the optimization result to the upper - level programming model to obtain the optimal configuration plan for the emergency facility site selection for different - period demand points.

[0150] In some specific embodiments, the lower - level programming model is solved using the improved PSO algorithm, and the optimal solution of the mobile emergency facility ambulance site selection is fed back to the upper - level programming model. The improved PSO algorithm includes the following sub - steps:

[0151] S1031, Set parameters, including the population size , the problem dimension , the inertia weight , the learning factor , maximum number of iterations and search space boundaries ;

[0152] S1032, randomly initialize the positions and velocities of the particles , calculate the individual optimum and the population optimum ;

[0153] S1033, use the dynamic inertia weight exponential strategy to adjust the inertia weight of each particle, and calculate the particle relative to the dynamic center of gravity reverse solution ;

[0154] S1034, in response to the fitness of the reverse solution of the particle being better than the fitness of the current solution, that is , update the position and fitness of the particle, that is , , in response to the current fitness being better than the historical individual optimum, that is , update the individual optimum , update the particle velocity , and update the particle position using the sine-cosine perturbation strategy ;

[0155] S1035, loop through steps S1033 - S1034 until the convergence condition is met, and output the optimal solution.

[0156] Specifically, in step S1033, the inertia weight controls the tendency of the particle to maintain the current flight direction, determining the balance between the global search and the local search of the algorithm. The exponentially decreasing inertia weight strategy has high flexibility and high adaptability. It reduces the inertia weight according to an exponential law. The rapid decrease in the early stage supports the algorithm to explore widely, and the slowdown of the decrease rate in the later stage helps the algorithm to turn to precise development. Based on this, this application designs a dynamic inertia weight exponential decreasing strategy, that is: , where is the inertia weight of the current iteration; is the minimum value of the inertia weight; is the maximum value of the inertia weight; is the current iteration number; is the total number of iterations.

[0157] Reverse learning increases the possibility of the algorithm jumping out of the local optimum trap by evaluating the reverse positions of the solutions, thereby exploring new potential solution spaces and increasing the probability of finding the global optimum solution. The reverse solution is generated by calculating the center of gravity of the solution set and using this as a reference. Suppose there is a solution set , where each solution is a dimensional vector, and the centroid of the solution set can be defined as: . Based on the centroid reverse learning, this application proposes a dynamic centroid reverse learning strategy. During the iteration process, the calculation of the centroid no longer fixedly selects all solutions, but dynamically and randomly selects the number of solutions participating in the centroid calculation. Specifically, the solution set is defined as follows: , where is a subset composed of solutions, and is a solution vector in the subset . Then the reverse solution of with respect to the centroid can be defined as: . This application adopts the dynamic centroid reverse learning strategy to perform reverse perturbation on the population individuals at the initial stage of iteration, significantly improving the global search efficiency of the particles in the vast search space and endowing them with the ability to jump out of the local optimal solution. Having diverse search experiences helps to discover better solutions in the exploration and exploitation stages, thereby improving the overall performance of the algorithm and the efficiency of problem-solving.

[0158] Specifically, in step S1034, the particle position update formula directly determines the way the particles explore the search space and the convergence behavior of the algorithm. In the case of a complex solution space, the position update strategy of the standard PSO algorithm easily makes the particles converge to the local optimal solution prematurely. To balance local exploration and global exploration, this application proposes a novel particle position update formula. The core idea is to introduce randomness by utilizing the variation characteristics of the sine and cosine functions, thereby increasing the diversity of the particle search space and improving the global search ability of the algorithm. Assume that in the dimensional search space, for the th iteration, the position update strategy of the th particle in the th dimension is as follows:

[0159]

[0160] where represents the velocity of the particle in the th generation in the th dimension; is the position of the particle in the th generation in the th dimension; represents the position of the particle in the th generation in the th dimension; is a random number in the interval [0,1].

[0161] Continue to refer to Figure 2 , Figure 2 which shows a schematic diagram of the framework process for the location selection of pre - hospital emergency facilities based on the improved PSO algorithm according to the embodiments of the present application. As shown in the figure, the algorithm includes the upper - level planning model ARNX - NSGA - Ⅲ algorithm of steps 201 - 215 and the lower - level scale model AMPSO algorithm of steps 216 - 225, specifically including the following steps:

[0162] Step 201: Generate an initial solution that satisfies the upper - and lower - layer constraints.

[0163] Step 202: Generate reference points and initialize the number of reference points , and determine the initial reference point set and the number of reference points according to the population size for guiding the optimization process.

[0164] Step 203: Initialize the population , create a set of candidate solutions, and calculate the population evolution stage threshold to distinguish different advanced stages.

[0165] Step 204: Sort each dimension of the decision vector and obtain the median .

[0166] Step 205: Calculate the entropy value , the evolution stage is defaulted to "exploration", calculate the entropy value , the evolution stage is defaulted to "exploration", initialize the total number of individuals associated with the reference point set = 0, initialize the entropy difference , the number of occurrences = 0.

[0167] Step 206: Select the NDX crossover operator and polynomial mutation operator to evolve the population. Iteratively update the population, perform normal - distribution crossover and mutation operations on the parent population to obtain the offspring population , merge the offspring population and the parent population to obtain the merged population .

[0168] Specifically, the normal - distribution crossover operator strategy introduces the normal distribution into the Simulated Binary Crossover (SBX) operator, sets its exploitation and exploration probabilities to be the same as those of the SBX operator, and uses to replace the spread factor and introduce discrete recombination in the evolutionary strategy for search spaces of more than one dimension, thereby establishing the NDX operator, which is described as follows: , where the first parent individual is denoted as , and the second parent individual is denoted as , is a random number uniformly distributed in the interval (0, 1).

[0169] Step 207: Population standardization and Pareto non-dominated sorting. Standardize the population and sort the population according to the Pareto non-dominated relationship.

[0170] Step 208: Determine the next generation based on the reference point and the niche reservation strategy. Use the reference point and the niche reservation strategy to determine the next generation population.

[0171] Step 209: Count the number of individuals associated with the reference point set . Count the individuals associated with each reference point.

[0172] Specifically, the reference point selection strategy in the objective space utilizes the reference point number to adaptively adjust the population size , and dynamically selects reference points with higher importance according to the evolutionary stage of the population in the objective space. The specific steps for screening reference points are as follows:

[0173] Step 1: According to the size of the population , select a reference point set where each dimension is divided into , the number of reference points is , and the number of divided segments needs to satisfy: and .

[0174] Step 2: Determine the evolutionary stage of the population according to the judgment of the evolutionary stage in the decision space.

[0175] Step 3: When the population as a whole is in the "exploration" stage, calculate the sum of the number of individuals associated with the reference point set in each generation.

[0176] Step 4: When the population just enters the "exploitation" stage, according to , retain the reference points with the largest number of associated individuals to form a new reference point set .

[0177] Step 210: Calculate the entropy value and the entropy difference , calculate the entropy value of the current population and the entropy values of the populations of two adjacent generations.

[0178] Step 211: Determine the entropy difference Is it less than the evolution stage threshold , if so, , execute Step 213, if not, execute Step 212.

[0179] Specifically, use the interquartile range (IQR) to exclude the interference of extreme values by calculating the difference between the upper quartile ( ) and the lower quartile ( ) to quantitatively analyze the distribution characteristics of the population in the decision space. To achieve standardized comparison of each dimension, the ratio of the interquartile range to the total interval of the decision space is standardized. The standardized IQR is defined as follows: , and introduce a difference measure based on the median ( ) - the standard median difference ( ) as a statistic to reflect the standardized change in the median between two adjacent generations and assist in quantitatively evaluating the dynamic evolution of the population distribution. The statistic is expressed as: . The entropy value is calculated from the standardized interquartile difference and the standardized median difference of the population. When the population is updated, it directly reflects the change of the population in the decision space: , . The entropy value difference between two adjacent generations of the population , when the value is larger, it indicates that the intergenerational difference in the population entropy value is more significant, and the population is actively exploring the unknown potential solution space. On the contrary, when the value tends to 0, it indicates that the population diversity decreases and the population tends to converge.

[0180] Step 212: Determine whether the maximum number of iterations is reached. If not, re - execute Step 206. If so, select the optimal compromise solution and execute the initial operation of the lower - layer model at the beginning of 216.

[0181] Step 213: Determine whether it satisfies the condition of being greater than . If it satisfies , enter the "exploration" stage, calculate the difference between the population and the number of reference points , , execute Step 214. If , execute Step 212.

[0182] Specifically, in the ideal state, for any one - dimensional finite interval All individuals in the population are evenly distributed within , and at this time, the shortest distance between an individual in the population and its nearest neighboring individual is . After standardization, it is , and the standard interquartile range is 0.5. A threshold is determined. Select whose change is less than and to obtain the value as the threshold . Further consider the linear relationship between the threshold and the decision space dimension . Finally, define the threshold as: . When , it indicates that the algorithm is in the "exploration" stage. To avoid the interference of a small number of premature convergence situations in the early stage of evolution on the judgment, it is set that when appears more than 10% of the maximum number of generations , it is considered that the population enters the "investigation" stage.

[0183] Step 214: Determine whether is less than . If not, execute Step 212. If so, execute Step 215.

[0184] Step 215: Delete the reference points with the fewest associated individuals, , and return to execute Step 214.

[0185] Step 216: Initialize the parameters and randomly initialize the positions and velocities of the particles. The parameters specifically include the population size , the problem dimension , the inertia weight , the learning factor , the maximum number of iterations , the search space boundary , randomly initialize the position and velocity of the particles.

[0186] Step 217: Determine the individual optimum and the population optimum. Calculate the fitness of each particle and determine the individual optimum of each particle and the global optimum of the entire population.

[0187] Step 218: Dynamic inertia weight exponential decay strategy. Use the dynamic inertia weight exponential decay strategy to adjust the exploration and exploitation capabilities of the algorithm. At the beginning of the iteration, starting from the first generation To the maximum number of iterations , adjust the inertia weight according to the number of iterations .

[0188] Step 219: Boundary adjustment. Perform boundary adjustment to ensure that the particle positions do not exceed the search space boundaries.

[0189] Step 220: Dynamic center of gravity reverse learning strategy. Use the dynamic center of gravity reverse learning strategy to generate new candidate solutions and determine the reverse solutions with respect to the center of gravity . Calculate the reverse solutions of the particles relative to the center of gravity to enhance population diversity and prevent premature convergence.

[0190] Step 221: Judgment . If satisfied, update the current particle position and the current fitness, that is, update the current particle position and the current fitness to check and update the current particle position and fitness.

[0191] Step 222: Continue judgment . If satisfied, update the individual best and the global best and update the particle velocity, that is, update the individual best , and at the same time update the particle velocity.

[0192] Step 223: Update the particle positions using the sine-cosine perturbation strategy. Perform position updates on each particle using the sine-cosine perturbation strategy. If the fitness of a certain particle is better than the current global best, update the global best.

[0193] Step 224: Judge whether the maximum number of iterations is reached. If so, output the result and execute Step 225. Otherwise, return to execute Step 218

[0194] Step 225: Judge whether the termination condition is satisfied. If so, end the operation. If not, return to execute Step 202.

[0195] Embodiment

[0196] Suppose a total of 796 demand points and 363 alternative first-aid points are determined in a certain street. One day is divided into four periods, namely: , , and , and five representative types of places are set, namely residential areas , public places , office places , night entertainment places and schools . Taking the residential area as an example, the design ideas for the demand changes in different cycles are as follows:

[0197]

[0198] In the formula, represents the total population in the research area; represents the cycle total population of the type of location; represents the demand volume of the type of demand point in the th cycle; represents the population flow coefficient of the th cycle type of

[0199] Table 4: Detailed parameters of some demand points

[0200]

[0201] Table 5: Detailed parameters of some alternative first aid points

[0202]

[0203] The upper-level planning problem focuses on the siting decision of fixed first aid facilities AED. Considering the upper limit constraint of the AED first aid facilities configured at the first aid points, an integer coding method is adopted, and the length of each chromosome is set to be twice the number of alternative first aid points . For this purpose, the first half is encoded in binary to indicate whether to select the corresponding alternative first aid point, and the second half is encoded by the integer set to specify the number of AEDs configured at the corresponding first aid point. For example, when the solution is in the form of "1101002110", it means that the 1st, 2nd, and 4th alternative first aid points are considered. Specifically, 2 AEDs are configured at the 2nd first aid point and 1 AED is configured at the 4th first aid point. The coding situation is as shown. Figure 3 shown.

[0204] The lower-level planning problem focuses on the siting decision of mobile first aid facilities ambulances. Since the number of first aid points with ambulances allowed to be opened in each cycle is a certain value, an integer coding method is adopted, and the length of each chromosome is set to be equal to the number of first aid points with ambulances allowed to be opened throughout the cycle , the value range of each gene is . For example, assume , and cycles respectively allow 1, 1, and 2 emergency points to park ambulances. When the solution form is " 313102807 ", it means cycle opens No. 313, cycle opens No. 10, cycle opens No. 28 and No. 07.

[0205] According to statistics, in a certain city in 2023, a total of 101,831 pre-hospital emergency tasks were accepted, and the permanent population of the whole city was 5.327 million. According to the actual research results, the fixed loss cost of AED is 8 yuan per day, and the fixed loss cost of ordinary ambulances is 30 yuan per day. When there is only AED at the emergency point, the coverage radii and take 300m and 800m respectively. When the emergency point includes an ambulance, the coverage radii and take 800m and 2500m respectively. The specific settings of other example parameters are shown in Table 6-7.

[0206] Table 6: Parameters of NSGA-III algorithm in the example

[0207]

[0208] Table 7: Parameters of AMPSO algorithm in the example

[0209]

[0210] Use the NSGA-III algorithm and the AMPSO algorithm to solve the pre-hospital cardiac arrest emergency facility location model, set the number of double-layer iterations to 5, and the obtained solutions are as follows:

[0211] Table 8: Solution results of the double-layer programming model after 5 iterations

[0212]

[0213] Combining the objective function values of the upper and lower layer models, it is finally confirmed that the solution generated in the 4th generation is the best result. In the 4th generation, the Pareto solution set calculated by the upper layer model is as Figure 4 shown, and the partial solutions intercepted are shown in Table 9. It can be seen that the total cost of the pre-hospital cardiac arrest emergency system will increase with the increase in the number of residents with dual coverage and the number of residents who are fully served.

[0214] Table 9: Partial non-dominated solutions of the model

[0215]

[0216] Figure 5 It shows the AED site selection result diagram of the pre - hospital emergency facility site selection model based on the improved PSO algorithm according to the embodiments of the present application. Among them, the third group of solutions is selected as the optimal solution by the optimal compromise solution method, and the corresponding AED site selection results and the configured quantity are shown in Table 10 and Figure 5 as shown below.

[0217] Table 10: Site selection results of the model

[0218]

[0219] Continuing to refer to Figure 6 , Figure 6 it shows the ambulance site selection result diagram of the pre - hospital emergency facility site selection model based on the improved PSO algorithm according to the embodiments of the present application. After giving the optimal compromise solution, through the iteration of the lower - layer model, it is solved that: at time, alternative emergency points No. 104 and No. 126 are selected to be equipped with ambulances; at time, a total of 5 alternative emergency points, namely No. 75, No. 99, No. 115, No. 136 and No. 144, are selected to be equipped with ambulances; at time, alternative emergency points No. 98 and No. 104 are re - selected; at time, alternative emergency points No. 59 and No. 138 are selected. The corresponding ambulance site selection results are as Figure 6 shown below.

[0220] During the entire cycle demonstrated by this solution, within the range of , the proportion of achieving double - coverage demand is about 90%. This efficient coverage performance benefits from the configuration of emergency personnel around each fixed AED emergency facility. This strategy transforms the round - trip distance from the place where cardiac arrest occurs to the emergency point into a one - way distance, effectively expanding the service radius of AED first aid. Therefore, on the premise of the same configured quantity, the solution obtained by the model constructed in this paper significantly improves the service efficiency of the pre - hospital cardiac arrest first - aid system. Relatively speaking, the strategy of equipping professional emergency personnel leads to a significant increase in the total cost of the system, with the single - day cost reaching as high as 71,842 yuan. If it is assumed that half of the equipped emergency personnel are volunteers, then without sacrificing service efficiency, the total cost of the system can be reduced by about 43%. If the proportion of volunteers is further increased to 90%, the total cost of the system can be significantly reduced to 16,042 yuan. Therefore, in the process of configuring emergency facilities, improving first - aid efficiency requires multi - aspect cooperation.

[0221] Further referring to Figure 7, as an implementation of the above method, in a second aspect, the present application provides an embodiment of a pre-hospital emergency facility location system 700 based on an improved PSO algorithm. This system embodiment corresponds to the Figure 1 method embodiment shown, and this system can be specifically applied to various electronic facilities. The system 700 includes a preliminary location module 701, an optimal trade-off module 702, and an optimal configuration module 703 that are communicatively connected to each other, where:

[0222] The preliminary location module 701 is configured to configure preliminary location plans for different emergency facilities based on the periodic differences of different demand points. The emergency facilities include fixed emergency facilities and mobile emergency facilities;

[0223] The optimal trade-off module 702 is configured to fit the preliminary location plan into a two-layer programming model that focuses on the location of fixed emergency facilities and the selection of mobile emergency facilities. Among them, the two-layer programming model includes an upper-layer programming model and a lower-layer programming model. The upper-layer programming model decides on a multi-objective configuration plan for the service capacity of the pre-hospital emergency system and the total cost of the emergency system, and inputs the optimal trade-off configuration plan into the lower-layer programming model;

[0224] The optimal configuration module 703 is configured to solve the service effect of the emergency system of the lower-layer programming model based on the improved PSO algorithm, and feedback the optimization result to the upper-layer programming model to obtain the optimal configuration plan for the location of emergency facilities for different periodic demand points.

[0225] Although the principles of the present invention have been described in detail above in conjunction with the preferred embodiments of the present invention, those skilled in the art should understand that the above embodiments are only explanations of the illustrative implementation manners of the present invention and do not limit the scope of the present invention. The details in the embodiments do not constitute a limitation on the scope of the present invention. Without departing from the spirit and scope of the present invention, any obvious changes such as equivalent transformations and simple substitutions based on the technical solutions of the present invention all fall within the protection scope of the present invention.

Claims

1. A pre-hospital emergency facility site selection method based on an improved PSO algorithm, characterized in that: The method comprises: S1, based on the periodic differences of different demand points, configure preliminary site selection plans for different emergency facilities, wherein the emergency facilities include fixed emergency facilities and mobile emergency facilities; S2, fitting the preliminary site selection plan into a two-level planning model that focuses on the site selection of fixed emergency facilities and focuses on the selection of mobile emergency facilities, wherein the two-level planning model includes an upper-level planning model and a lower-level planning model, the upper-level planning model determines a multi-objective configuration plan for the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system, and inputs the optimal compromise configuration plan into the lower-level planning model; S3, solving the emergency system service effect of the lower-level planning model based on the improved PSO algorithm, and feeding back the optimization result to the upper-level planning model to obtain the best configuration plan for the location of emergency facilities for different periodic demand points; The improved PSO algorithm includes the following sub-steps: S31, setting parameters, the parameters including population size , Problem Dimension , inertia weight , learning factor , maximum number of iterations and search space boundaries ; S32, randomly initialize the position of particles and speed , calculate the individual optimal and population optimal ; S33, using the dynamic inertia weight index strategy to adjust the inertia weight of individual particles, and calculating the particle weight based on the dynamic center of gravity reverse learning strategy Relative to dynamic center of gravity The reverse solution of ; S34, in response to the fitness of the particle's reverse solution being better than the fitness of the current solution , update the particle's position and fitness , in response to the current fitness being better than the historical individual optimal , update the individual optimal , update particle velocity , and use the sine-cosine perturbation strategy to update the particle position , Indicates the current iteration number, Represents particles exist Daizhongdi The speed of the dimension, Represents particles exist Daizhongdi The location of the dimension; S35, looping through the steps S33-S34 until the convergence condition is met, and outputting the optimal solution; The lower-level planning model includes a satisfaction function for emergency response time and a satisfaction function for treatment costs, wherein residents' satisfaction with response time gradually decays over time, and prolonged emergency time leads to increased treatment costs in the later stages; If emergency services are provided at the shortest waiting time acceptable to residents If the emergency service is provided within the longest waiting time acceptable to the residents, the residents’ satisfaction is defined as 1; If the emergency service is provided outside the city, the residents’ satisfaction is defined as 0; if the emergency service activity occurs in During the time period, residents' satisfaction with the emergency response time gradually decreases as time goes by, thus giving the emergency response time satisfaction function; The treatment cost satisfaction function is expressed as: In the formula, represents the number of patients; represents the delay in emergency service response; and They represent the probability of the patient's condition being serious and general when calling emergency services; and Respectively, they represent the minimum amount of increase in subsequent treatment costs for patients with serious and general conditions when emergency service response is delayed by one minute; The service capacity of the pre-hospital emergency system is defined as the number of residents corresponding to the coverage area of ​​the demand point. The service capacity of the pre-hospital emergency system is calculated by the number of residents who are not fully served and the number of residents who are double covered, respectively, using the objective function And the objective function represents, where: In the formula, Indicates period division; represents a set of demand points; express Time period, demand point Quantity of demand; express Time period, demand point In radius There are at least two candidate first aid points within the territory to provide services for it; Indicates that the coverage radius can be less than Distance to cover demand points A collection of alternative first aid points; express Time period, alternative emergency points Maximum service capacity; express Time period, alternative emergency points And demand point The distance of the journey; The total cost of the pre-hospital emergency system includes the loss cost of the emergency facilities, the variable cost of the ambulance and the labor cost of the emergency personnel, where its objective function is Specifically expressed as: In the formula, Indicates period division; Indicates a collection of alternative first aid points; Indicates the maximum number of AEDs that can be configured at each emergency point; express Time period, alternative emergency points There are more than 0 AEDs configured inside; express Time period, alternative emergency points The number of AEDs included; represents the loss cost of AED; represents the attrition cost of the ambulance; express Time period, alternative emergency points There are more than 0 ambulances parked inside; express Time period, alternative emergency points the number of ambulances included; express The number of first aid personnel assigned to each AED during the period; express The number of emergency personnel in each ambulance during the period; express Time period, the length of time the emergency personnel worked; express Time period, the labor cost per hour of emergency personnel; Indicates time period End of time period Initially, it is necessary to go to an existing emergency center With alternative first aid points to mobilize ambulances between; Indicates time period End of time period Initially, in the existing emergency center With alternative first aid points the number of ambulances to be mobilized between Indicates time period To time period Inside, Emergency Center With alternative first aid points distance; express The variable cost per unit distance of an ambulance during each period.

2. The pre-hospital emergency facility site selection method based on the improved PSO algorithm according to claim 1, characterized in that: The dynamic inertia weight index strategy combines the exponential law to reduce the inertia weight, which is specifically expressed as: , where Indicates the inertia weight of the current iteration; Indicates the minimum value of inertia weight; Indicates the maximum value of inertia weight; Indicates the current iteration number; Indicates the total number of iterations.

3. The pre-hospital emergency facility site selection method based on the improved PSO algorithm according to claim 1, characterized in that: The dynamic center of gravity reverse learning strategy introduces a dynamic random selection of the number of solutions participating in the center of gravity calculation. Specifically, the dynamic random solution set The center of gravity is expressed as ,but About the Center of Gravity The reverse solution of Expressed as , where Is The subset of solutions, For subset A solution vector in .

4. The pre-hospital emergency facility site selection method based on the improved PSO algorithm according to claim 1, characterized in that: The sine-cosine perturbation strategy is set at In the dimensional search space, for the Iterations, particles No. The location update strategy is as follows: in, Indicates 1 to A positive integer between Indicates 1 to A positive integer between Represents particles exist Daizhongdi The speed of the dimension; Represents particles exist Daizhongdi The location of the dimension; Represents particles exist Daizhongdi The location of the dimension; Represents a random number in the range 0-1.

5. The pre-hospital emergency facility site selection method based on the improved PSO algorithm according to claim 1, characterized in that: The upper-level planning model and the corresponding constraints are: The upper-level planning model is expressed as: Formula 1 Formula 2 Formula 3 The corresponding constraints are expressed as: Condition 1 Condition 2 Condition 3 Condition 4 Condition 5 Condition 6 Condition Seven Condition Eight Condition 9 Among them, formula 1 indicates that the demand that is not served in the whole cycle is the smallest; formula 2 indicates that the demand that is served in the whole cycle is the smallest. The demand for more than two times is the largest; Formula 3 shows that the total cost of the whole cycle is the smallest, including the loss cost of AED and ambulance, the variable cost of ambulance and the labor cost of emergency personnel; where, Indicates period division; represents a set of demand points; express Time period, demand point Quantity of demand; express Time period, demand point In radius There are at least two candidate first aid points within the territory to provide services for it; Indicates that the coverage radius can be less than Distance to cover demand points A collection of alternative first aid points; express Time period, alternative emergency points Maximum service capacity; express Time period, alternative emergency points And demand point The distance of the journey; Indicates a collection of alternative first aid points. Indicates the maximum number of AEDs that can be configured at each emergency point; express Time period, alternative emergency points There are more than 0 AEDs configured inside; express Time period, alternative emergency points The number of AEDs included; represents the loss cost of AED; represents the attrition cost of the ambulance; express Time period, alternative emergency points There are more than 0 ambulances parked inside; express Time period, alternative emergency points the number of ambulances included; express The number of first aid personnel assigned to each AED during the period; express The number of emergency personnel in each ambulance during the period; express Time period, the length of time the emergency personnel worked; express Time period, the labor cost per hour of emergency personnel; Indicates time period End of time period Initially, it is necessary to go to an existing emergency center With alternative first aid points to mobilize ambulances between; Indicates time period End of time period Initially, in the existing emergency center With alternative first aid points the number of ambulances to be mobilized between Indicates time period To time period Inside, Emergency Center With alternative first aid points distance; express The variable cost per unit distance of the ambulance during the period; Condition 1 means that the number of AEDs equipped at each emergency point does not exceed the maximum limit, and condition 2 ensures that there are alternative emergency points. The location and number of AEDs remain unchanged every cycle; Condition 3 means that the total number of AEDs equipped at all emergency points does not exceed the maximum limit, Indicates the maximum number of AEDs configured for all emergency points. Condition 4 ensures the coverage radius All requirements must be covered; Condition 5 means that if a requirement point is not covered at least once, it cannot be covered twice. Indicates that the coverage radius can be less than Distance to cover demand points The set of alternative emergency points; Condition 6 ensures that only when the demand point When there are two or more emergency rescues, the demand point It was only covered twice. express Time period, demand point In radius There is at least one candidate emergency point providing services for it. express Time period, demand point In radius There are at least two candidate first aid points providing services for it; condition seven is defined as the candidate first aid point For demand points The service capacity satisfies the function of the distance; Condition eight is expressed as the value constraint of the decision variable; Condition nine is the non-negative constraint.

6. A pre-hospital emergency facility site selection system based on an improved PSO algorithm, characterized in that: The system comprises: A preliminary site selection module is configured to configure preliminary site selection plans for different emergency facilities based on periodic differences of different demand points, wherein the emergency facilities include fixed emergency facilities and mobile emergency facilities; an optimal compromise module, configured to fit the preliminary site selection scheme into a two-layer planning model focusing on the site selection of fixed emergency facilities and the selection of mobile emergency facilities, wherein the two-layer planning model includes an upper-layer planning model and a lower-layer planning model, the upper-layer planning model determines a multi-objective configuration scheme of the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system, and selects the optimal compromise configuration scheme and inputs it into the lower-layer planning model; An optimal configuration module is configured to solve the emergency system service effect of the lower-level planning model based on the improved PSO algorithm, and feed back the optimization result to the upper-level planning model to obtain the optimal configuration plan for the location of emergency facilities for different periodic demand points; The improved PSO algorithm includes the following sub-steps: S31, setting parameters, the parameters including population size , Problem Dimension , inertia weight , learning factor , maximum number of iterations and search space boundaries ; S32, randomly initialize the position of particles and speed , calculate the individual optimal and population optimal ; S33, using the dynamic inertia weight index strategy to adjust the inertia weight of individual particles, and calculating the particle weight based on the dynamic center of gravity reverse learning strategy Relative to dynamic center of gravity The reverse solution of ; S34, in response to the fitness of the particle's reverse solution being better than the fitness of the current solution , update the particle's position and fitness , in response to the current fitness being better than the historical individual optimal , update the individual optimal , update particle velocity , and use the sine-cosine perturbation strategy to update the particle position , Indicates the current iteration number, Represents particles exist Daizhongdi The speed of the dimension, Represents particles exist Daizhongdi The location of the dimension; S35, looping through the steps S33-S34 until the convergence condition is met, and outputting the optimal solution; The lower-level planning model includes a satisfaction function for emergency response time and a satisfaction function for treatment costs, wherein residents' satisfaction with response time gradually decays over time, and prolonged emergency time leads to increased treatment costs in the later stages; If emergency services are provided at the shortest waiting time acceptable to residents If the emergency service is provided within the longest waiting time acceptable to the residents, the residents’ satisfaction is defined as 1; If the emergency service is provided outside the city, the residents’ satisfaction is defined as 0; if the emergency service activity occurs in During the time period, residents' satisfaction with the emergency response time gradually decreases as time goes by, thus giving the residents' satisfaction function with the emergency response time; The treatment cost satisfaction function is expressed as: In the formula, represents the number of patients; represents the delay in emergency service response; and They represent the probability of the patient's condition being serious and general when calling emergency services; and Respectively, they represent the minimum amount of increase in subsequent treatment costs for patients with serious and general conditions when emergency service response is delayed by one minute; The service capacity of the pre-hospital emergency system is defined as the number of residents corresponding to the coverage area of ​​the demand point. The service capacity of the pre-hospital emergency system is calculated by the number of residents who are not fully served and the number of residents who are double covered, respectively, using the objective function And the objective function represents, where: In the formula, Indicates period division; represents a set of demand points; express Time period, demand point Quantity of demand; express Time period, demand point In radius There are at least two candidate first aid points within the territory to provide services for it; Indicates that the coverage radius can be less than Distance to cover demand points A collection of alternative first aid points; express Time period, alternative emergency points Maximum service capacity; express Time period, alternative emergency points And demand point The distance of the journey; The total cost of the pre-hospital emergency system includes the loss cost of the emergency facilities, the variable cost of the ambulance and the labor cost of the emergency personnel, where its objective function is Specifically expressed as: In the formula, Indicates period division; Indicates a collection of alternative first aid points; Indicates the maximum number of AEDs that can be configured at each emergency point; express Time period, alternative emergency points There are more than 0 AEDs configured inside; express Time period, alternative emergency points The number of AEDs included; represents the loss cost of AED; represents the attrition cost of the ambulance; express Time period, alternative emergency points There are more than 0 ambulances parked inside; express Time period, alternative emergency points the number of ambulances included; express The number of first aid personnel assigned to each AED during the period; express The number of emergency personnel in each ambulance during the period; express Time period, the length of time the emergency personnel worked; express Time period, the labor cost per hour of emergency personnel; Indicates time period End of time period Initially, it is necessary to go to an existing emergency center With alternative first aid points to mobilize ambulances between; Indicates time period End of time period Initially, in the existing emergency center With alternative first aid points the number of ambulances to be mobilized between Indicates time period To time period Inside, Emergency Center With alternative first aid points distance; express The variable cost per unit distance of an ambulance during each period.

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