A pre-hospital emergency facility site selection method and system based on improved NSGA-Ⅲ algorithm

Abstract

The present invention provides a pre-hospital emergency facility site selection method and system based on an improved NSGA-Ⅲ algorithm, the method comprising acquiring a data set; constructing a pre-hospital emergency facility site selection model and designing corresponding constraints; designing an improved NSGA-Ⅲ algorithm based on the evolutionary stage judgment of the decision space, the reference point selection strategy of the target space and the normal distribution crossover operator strategy, using the ARNX-NSGA-Ⅲ algorithm to perform global optimization on the pre-hospital emergency facility site selection model, and outputting the optimal compromise solution as the final pre-hospital emergency facility site selection parameter information. The present invention combines three key strategies to improve the convergence of the algorithm and the distribution performance of the solution, introduces a new perspective of multivariate emergency resource allocation, expands the multi-period model, and achieves a balanced effect between the service capability and cost-effectiveness of the emergency system, becoming an important basis for intelligent recommendation of emergency users, a key tool for data-driven decision-making, and a core guarantee for improving the accuracy of intelligent recommendation.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to a method and system for selecting a site for pre-hospital emergency facilities based on an improved NSGA-III algorithm. Background Art

[0002] As an indispensable subsystem of the social public safety emergency system, the efficient operation of the pre-hospital medical emergency system is crucial to protecting the life safety and health and well-being of the public. In particular, the location 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 installation of emergency facilities in public places, aiming to provide timely emergency treatment for patients with cardiac arrest outside the hospital and win precious rescue time. However, the actual application of these facilities is still in the exploratory and experimental stage in my country. Relevant studies focus on the deployment at the macro level or the deployment of a single facility, and the deployment strategies are mostly based on subjective cognitive standards. As a result, in actual cardiac arrests, which can be divided into pre-hospital cardiac arrest (OHCA) events according to the spatial location of the place of occurrence, the effectiveness of pre-hospital treatment has not yet reached expectations. In many cities, there is a serious mismatch between the distribution of emergency facilities and the actual needs of OHCA patients, and the accessibility of facilities is poor. As a result, although the number of emergency facilities is increasing, they cannot be fully and effectively utilized. On the one hand, it reduces economic benefits, and on the other hand, it becomes an important factor restricting the improvement of OHCA emergency efficiency.

[0004] How to scientifically plan the layout of pre-hospital cardiac arrest emergency facilities, build a rapid-response, wide-coverage, and easily accessible pre-hospital emergency system, and thereby guarantee the daily medical emergency needs of members of society and improve the quality of life of residents has become an issue that needs to be addressed urgently. Summary of the invention

[0005] The purpose of this application is to provide a pre-hospital emergency facility site selection method and system based on an improved NSGA-III algorithm to solve the above problems.

[0006] According to one aspect of the present application, a pre-hospital emergency facility site selection method based on an improved NSGA-III algorithm is proposed, the method comprising the following steps:

[0007] S1. Process and obtain a data set, where the data set includes parameter information corresponding to the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system. 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.

[0008] S2. According to the service capacity and total cost of the pre-hospital emergency system, a pre-hospital emergency facility site selection model is constructed and corresponding constraints are designed;

[0009] S3, based on the evolutionary stage judgment of the decision space, the reference point selection strategy of the target space and the normal distribution crossover operator strategy, the NSGA-Ⅲ algorithm is improved to obtain the ARNX-NSGA-Ⅲ algorithm;

[0010] S4. Use the ARNX-NSGA-Ⅲ algorithm to perform global optimization on the pre-hospital emergency facility site selection model and output the optimal compromise solution as the final pre-hospital emergency facility site selection parameter information.

[0011] In the above technical scheme, this application introduces three key strategies based on the NSGA-III algorithm to further explore and utilize the decision space information of the population, improve the efficiency of information exchange between individuals, thereby accelerating the convergence speed of the algorithm and improving the solution accuracy.

[0012] Furthermore, 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 represented by the number of residents who are not fully served and the number of residents who are doubly covered, respectively, using the objective function Z1 and the objective function Z2, where:

[0013]

[0014] In the formula, T represents the period division, V represents the set of demand points, represents the demand at demand point i during period t, Indicates that during time period t, demand point i has at least two candidate emergency points within radius r1 to provide services for it, W 2i ,j represents the set of alternative emergency points that can cover the demand point i with a distance less than the coverage radius r2, represents the maximum service capacity of emergency point j during period t, It represents the distance between alternative emergency point j and demand point i in time period t.

[0015] Furthermore, 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, which is specifically expressed by the objective function Z3:

[0016]

[0017] In the formula, T represents the period division, W represents the set of candidate emergency points, and h represents the maximum number of AEDs configured at each emergency point. Indicates that during time period t, there are more than 0 AEDs deployed in emergency point j. represents the number of AEDs in emergency point j during time period t, Fh (F o ) represents the loss cost of AED (ambulance), Indicates that during time period t, there are more than 0 ambulances parked in emergency point j. represents the number of ambulances included in the emergency point j during period t, Indicates the number of first aid personnel equipped for each AED during period t, represents the number of emergency personnel in each ambulance during period t, w t represents the time period t during which the emergency personnel work. represents the labor cost per hour of the emergency personnel during period t, It means that from the end of time period t to the beginning of time period t+1, an ambulance needs to be mobilized between the existing emergency center u and the emergency point j. It represents the number of ambulances mobilized between the existing emergency center u and the emergency point j from the end of time period t to the beginning of time period t+1. represents the distance between the emergency center u and the emergency point j from time period t to time period t+1, It represents the variable cost per unit distance of the ambulance in period t.

[0018] Furthermore, the site selection model and constraints of pre-hospital emergency facilities in step S2 are:

[0019] The site selection model of pre-hospital emergency facilities is expressed as:

[0020]

[0021] The corresponding constraints are expressed as:

[0022]

[0023]

[0024] 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 covered by r1 more than twice in the whole cycle is the largest; formula 3 indicates 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;

[0025] 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 location and number of AEDs at emergency point j remain unchanged every cycle; condition 3 means that the total number of AEDs equipped at all emergency points does not exceed the maximum limit, N h represents the maximum number of AEDs configured for all emergency points. Condition 4 ensures that the coverage radius r2 must cover all needs. Condition 5 indicates that if a demand point is not covered at least once, it cannot be covered twice. 1i,j represents the set of alternative emergency points that can cover demand point i with a distance less than the coverage radius r1; condition six ensures that demand point i is covered twice only when there are two or more emergency services within r1 of the demand point. Indicates that during time period t, demand point i has at least one (two) candidate emergency points providing services within radius r1; condition seven is defined as the service capacity of emergency point j to demand point i satisfying the function of the relevant distance; condition eight is expressed as the value constraint of the decision variable; condition nine is a non-negative constraint.

[0026] In the above technical solutions, this application optimizes the balance between the service capacity and cost-effectiveness of the emergency system, introduces a new perspective on the allocation of multiple emergency resources, and promotes a collaborative emergency mechanism for automatic external defibrillators and ambulances. At the same time, considering that the emergency demand presents a time-varying characteristic due to population mobility factors, the single-cycle model is expanded to a more flexible multi-cycle model.

[0027] Furthermore, the evolutionary stage of the decision space in step S3 is determined by calculating the entropy value of the population using the interquartile range and the standardized median. t , and calculate the entropy difference Δe between the two generations of populations t , compare the threshold γ and Δe to determine the evolutionary stage of the current population, where:

[0028] The difference between the upper quartile Q3 and the lower quartile Q1 is calculated to eliminate the interference of extreme values, and the ratio of the interquartile range to the total interval of the decision space (ub-lb) is standardized. The standardized IQR is expressed as follows:

[0029]

[0030] Introducing the difference measure based on the median mid—the standard median difference Δmid t As a statistic, the statistic is specifically expressed as:

[0031]

[0032] Then the entropy value e t , entropy difference Δe t and threshold γ are expressed as:

[0033]

[0034] Δe t =|e t -e t-1

[0035]

[0036] In the formula, D represents the dimension of the decision space, N represents the number of individuals in the population, and inf srepresents the standard interquartile range.

[0037] Furthermore, the normal distribution crossover operator strategy of step S3 includes introducing discrete recombination in the evolution strategy to the search space with more than one dimension, thereby establishing the NDX operator, which is expressed as:

[0038]

[0039] Among them, the two parent individuals are represented as μ is a random number uniformly distributed in the interval (0,1), and N represents the N individuals in the population.

[0040] Furthermore, the ARNX-NSGA-III algorithm of step S3 includes the following sub-steps:

[0041] S41, generate an initial solution that meets the constraints, and determine the initial reference point set Z and the number of reference points H according to the population size N p ;

[0042] S42, generate the initial population P, calculate the population evolution stage threshold γ and entropy value e 0 , evolutionary stage S 0 The default is "exploration", which initializes the total number of individuals associated with the reference point set Z sum = 0, initialize entropy difference Δe t <γ, the number of occurrences D sum =0;

[0043] S43, using the parent population P t , based on the normal distribution crossover and mutation operations, the offspring population Q is obtained t , merge the offspring population Q t and the parent population P t , and for the combined population R t Perform environmental selection to obtain a new population P t+1 ;

[0044] S44. Count the number of individuals Z associated with the reference point set sum , calculate the entropy value e t and the entropy difference Δe between two adjacent generations t , in response to Δe t <γ then D sum =D sum +1, if D sum >15%×MaxGen, enter the "exploration" stage, calculate the population number N and the number of reference points H p The difference k, in response to i≥|k|, determines whether the convergence condition is met. If so, selects the optimal compromise solution and outputs it.

[0045] Furthermore, step S44 also includes, in response to i<|k|, deleting k reference points with the least number of associated individuals, i=i+1, continuing to judge the size of i and |k| until i=|k|, judging whether the convergence condition is met, and if not, repeating the traversal and executing step S43;

[0046] and / or

[0047] In response to Δe t ≥γ or Δe t <γ when D sum =D sum +1, and D sum ≤15%×MaxGen, determine whether the convergence condition is met. If so, select the optimal compromise solution and output it before terminating the operation. If not, repeat the traversal and execute step S43.

[0048] In the above technical scheme, this application proposes the ARNX-NSGA-III algorithm based on the NSGA-III algorithm and combines three key strategies, which greatly improves the convergence and solution distribution performance of the NSGA-III algorithm.

[0049] Furthermore, the reference point screening steps include the following:

[0050] Step 1: According to the size of the population N, select a reference point set Z divided into p in each dimension, and the number of reference points is H p , the number of segments p must satisfy: H p ≥1.2N and H p-1 <1.2N;

[0051] Step 2: Determine the evolutionary stage of the population based on the ARNX-NSGA-Ⅲ algorithm;

[0052] Step 3: When the population as a whole is in the "exploration" stage, calculate the total number of individuals associated with each generation of reference point set Z sum ;

[0053] Step 4: When the population just enters the "exploration" stage, according to Z sum Keep the N reference points with the largest number of associated individuals to form a new reference point set Z n .

[0054] According to another aspect of the present application, a pre-hospital emergency facility site selection system based on an improved NSGA-III algorithm is proposed, the system comprising:

[0055] A data set processing module is configured to process and obtain a data set, wherein the data set includes parameter information corresponding to the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system, wherein 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;

[0056] A model building module is configured to build a pre-hospital emergency facility site selection model and design corresponding constraints based on the pre-hospital emergency system service capacity and the total cost of the pre-hospital emergency system;

[0057] The algorithm improvement module is configured to improve the NSGA-III algorithm based on the evolutionary stage judgment of the decision space, the reference point selection strategy of the target space, and the normal distribution crossover operator strategy to obtain the ARNX-NSGA-III algorithm;

[0058] The parameter optimization module is configured to use the ARNX-NSGA-Ⅲ algorithm to perform global optimization on the pre-hospital emergency facility site selection model, and output the optimal compromise solution as the final pre-hospital emergency facility site selection parameter information.

[0059] Compared with the prior art, the beneficial results of the present invention are:

[0060] (1) The present invention is based on the evolutionary stage judgment strategy of the decision space and the reference point selection strategy based on the target space, and improves the crossover operator, the core component of NSGA-III, to further mine and utilize the decision space information of the population, improve the efficiency of information exchange between individuals, thereby accelerating the convergence speed of the algorithm and improving the solution accuracy.

[0061] (2) In view of the strong time-varying characteristics of urban population distribution and in order to adapt to the temporal and spatial changes in emergency needs, the present invention takes into account the multi-period characteristics of emergency medical services and expands a single facility into two facilities to achieve joint emergency treatment. Based on the constructed pre-hospital emergency facility site selection model, effective resource allocation is achieved with the site selection of fixed emergency facilities AED as the main method and the relocation of mobile emergency facilities ambulances as the auxiliary method.

[0062] (3) The present invention introduces a new perspective of multi-dimensional emergency resource allocation and expands the multi-cycle model to achieve a balanced effect between the service capability and cost-effectiveness of the emergency system. It is an important basis for intelligent recommendation of emergency users, a key tool for data-driven decision-making, and the core of improving the accuracy of intelligent recommendation. It provides emergency users with an intelligent user emergency service system and builds a foundation for improving user services. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and are used together with the description to explain the principles of the present invention. It will be easy to recognize other embodiments and many expected advantages of the embodiments because they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar parts.

[0064] Figure 1is a flow chart of a method for selecting a site for pre-hospital emergency facilities based on an improved NSGA-III algorithm according to an embodiment of the present application;

[0065] Figure 2 It is a schematic diagram of the framework flow of the ARNX-NSGA-III algorithm according to one embodiment of the present application;

[0066] Figure 3 is a schematic diagram of ARNX-NSGA-III algorithm site selection coding according to an embodiment of the present application;

[0067] Figure 4 is a set of non-dominated solutions of a pre-hospital emergency facility location model based on an improved NSGA-III algorithm according to an embodiment of the present application;

[0068] Figure 5 It is an AED site selection result diagram of a pre-hospital emergency facility site selection model based on an improved NSGA-III algorithm according to an embodiment of the present application;

[0069] Figure 6 It is an ambulance site selection result diagram of a pre-hospital emergency facility site selection model based on an improved NSGA-III algorithm according to an embodiment of the present application;

[0070] Figure 7 It is a framework diagram of a pre-hospital emergency facility site selection optimization system based on an improved NSGA-III algorithm according to an embodiment of the present application. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical scheme 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 part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0072] refer to Figure 1 , Figure 1 The flowchart of the pre-hospital emergency facility site selection method based on the improved NSGA-III algorithm of the present application is shown. As shown in the figure, the method includes the following steps:

[0073] S101. Process and obtain a data set, where the data set includes parameter information corresponding to the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system. 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.

[0074] In some specific embodiments, in order to better abstract the site selection model of out-of-hospital cardiac arrest emergency facilities 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 in the region. All demand areas are clustered into demand points with a certain spatial resolution, that is, one demand point represents a demand area, and the number of demand points remains unchanged. The total demand in the study area remains basically consistent 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 predetermined 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 reallocated to new emergency points according to demand.

[0075] For the convenience of description, the sets and indexes 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:

[0076] Table 1: Collections and indexes

[0077]

[0078] Table 2: Model parameters

[0079]

[0080] Table 3: Decision variables

[0081]

[0082] In some specific embodiments, the service capacity of the pre-hospital cardiac arrest emergency system is characterized by the number of residents who achieve double coverage and the number of residents who are not fully served. The number of residents who achieve double coverage, in the site selection problem, when the demand point is within the maximum service radius of the facility point, the demand point is said to be fully covered. In view of the special properties of emergency facilities, it is necessary to fully consider that once a single coverage facility is occupied, it will be in a "busy" state for a long time and cannot serve other demand points, resulting in the original coverage area being in an "exposed" state. Therefore, the introduction of backup coverage is crucial to enhancing the system's response service capabilities, and the number of residents who achieve double coverage is characterized as:

[0083]

[0084] In the formula, T,t represents the period division, V,i represents the set of demand points, represents the demand at the demand point in period t, It means that during period t, demand point i has at least two candidate emergency points within radius r1 to provide services for it.

[0085] The number of residents who are not fully served. Whether the demand point is covered depends on the distance between the facility point and the demand point. To determine whether the demand point is fully served, it is necessary to consider the established service capacity of the facility, such as the maximum demand that the emergency facility can serve. Usually, there is a negative correlation between the service capacity and the distance to the emergency point, that is, the closer the area is to the emergency point, the higher the service capacity it receives. Therefore, considering the backup coverage, the number of residents who are not fully served is characterized as:

[0086]

[0087] In the formula, T,t represents the period division, V,i represents the set of demand points, represents the demand at the demand point in period t, W 2i ,j represents the set of alternative emergency points that can cover the demand point i with a distance less than the coverage radius r2, represents the maximum service capacity of emergency point j during period t, It represents the distance between alternative emergency point j and demand point i in time period t.

[0088] The total cost of the pre-hospital cardiac arrest emergency system covers the loss cost of the emergency facilities, the variable cost of the ambulance, and the labor cost of the emergency personnel. In the model, the loss cost of the emergency facilities is broken down into the daily loss of the facilities. 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 during the cycle, the labor cost of the emergency personnel also changes accordingly. Therefore, the total cost of the pre-hospital cardiac arrest emergency system throughout the entire cycle is characterized as:

[0089]

[0090] Among them, T,t represents the period division, W,j represents the set of alternative emergency points, and h represents the maximum number of AEDs configured at each emergency point. Indicates that during time period t, there are more than 0 AEDs deployed in emergency point j. represents the number of AEDs in emergency point j during time period t, F h (F o ) represents the loss cost of AED (ambulance), Indicates that during time period t, there are more than 0 ambulances parked in emergency point j. represents the number of ambulances included in the emergency point j during period t, Indicates the number of first aid personnel equipped for each AED during period t, represents the number of emergency personnel in each ambulance during period t, w t represents the time period t during which the emergency personnel work. represents the labor cost per hour of the emergency personnel during period t, It means that from the end of time period t to the beginning of time period t+1, an ambulance needs to be mobilized between the existing emergency center u and the emergency point j. It represents the number of ambulances mobilized between the existing emergency center u and the emergency point j from the end of time period t to the beginning of time period t+1. represents the distance between the emergency center u and the emergency point j from time period t to time period t+1, It represents the variable cost per unit distance of the ambulance in period t.

[0091] S102. Based on the service capacity and total cost of the pre-hospital emergency system, a pre-hospital emergency facility site selection model is constructed and corresponding constraints are designed.

[0092] In some specific embodiments, the corresponding objective functions Z1 and Z2 are respectively characterized according to the number of residents who are not fully served and the number of residents who are double covered according to the system service capacity, and the objective function Z3 is constructed using the total cost of the emergency system. The model is expressed as follows:

[0093]

[0094]

[0095] Constraints:

[0096]

[0097] 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 covered by r1 more than twice in the whole cycle is the largest; Formula 3 indicates that the total cost of the whole cycle is the smallest, which includes the loss cost of AED and ambulance, the variable cost of ambulance and the labor cost of emergency personnel;

[0098] 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 location and number of AEDs at emergency point j remain unchanged every cycle; condition 3 means that the total number of AEDs equipped at all emergency points does not exceed the maximum limit, N h represents the maximum number of AEDs configured for all emergency points. Condition 4 ensures that the coverage radius r2 must cover all needs. Condition 5 indicates that if a demand point is not covered at least once, it cannot be covered twice. 1i ,j represents the set of alternative emergency points that can cover demand point i with a distance less than the coverage radius r1; condition six ensures that demand point i is covered twice only when there are two or more emergency services within r1 of the demand point. Indicates that during time period t, demand point i has at least one (two) candidate emergency points providing services within radius r1; condition seven is defined as the service capacity of emergency point j to demand point i satisfying the function of the relevant distance; condition eight is expressed as the value constraint of the decision variable; condition nine is a non-negative constraint.

[0099] S103. Based on the evolutionary stage judgment of the decision space, the reference point selection strategy of the target space and the normal distribution crossover operator strategy, an improved NSGA-Ⅲ algorithm is designed to obtain the ARNX-NSGA-Ⅲ algorithm.

[0100] In some specific embodiments, the evolution stage judgment based on the decision space specifically includes:

[0101] The interquartile range (IQR) is used to eliminate the interference of extreme values ​​by calculating the difference between the upper quartile (Q3) and the lower quartile (Q1) to quantitatively analyze the distribution characteristics of the group in the decision space. In order to achieve standardized comparison of each dimension, the ratio of the interquartile range to the total interval of the decision space (ub-lb) is standardized. The standardized IQR is defined as follows:

[0102]

[0103] And introduce the difference measure based on the median (mid) - the standard median difference (Δmid t ) is used as a statistic to reflect the standardized change in the median between two adjacent generations, which is used to assist in quantitatively evaluating the dynamic evolution of population distribution. The statistic is expressed as:

[0104]

[0105] Entropy value e t It is calculated by the standardized quartile difference and standardized median difference of the population. When the population is updated, it directly reflects the changes of the population in the decision space:

[0106]

[0107] Δe t =|e t -e t-1

[0108] The entropy difference between two adjacent generations of populations is Δe t , when Δe t The larger the value, the more significant the intergenerational difference in population entropy value, and the population is actively exploring the unknown potential solution space. t The closer the value is to 0, the lower the population diversity is and the population tends to converge.

[0109] Under ideal conditions, for any finite interval R, all N individuals in the population are evenly distributed within R. At this time, the shortest distance between an individual in the population and its nearest neighbor is |R| / N, which is 1 / N after standardization. The standard interquartile range is inf s is 0.5. Propose a threshold γ and select inf s The Δe value obtained when the change is less than 1 / N and Δmid≈0 is used as the threshold γ. Further considering the linear relationship between the threshold γ and the decision space dimension (D), the threshold γ is finally defined as:

[0110]

[0111] When Δe t >γ, indicating that the algorithm is in the "exploration" stage. In order to avoid the premature convergence that occurs in the early stage of evolution, we set Δe t When the number of occurrences of <γ is greater than 15% of the maximum evolutionary generation (MaxGen), the population is considered to have entered the "exploration" stage.

[0112] In some specific embodiments, as the evolutionary process progresses, individuals tend to be associated with reference lines that run through the true Pareto frontier. Even if the Pareto frontier surface of the problem being solved is unknown, the total number of individuals in each generation of the population associated with the reference point can be counted, and the importance of each reference point can be evaluated based on this, thereby eliminating redundant reference points to optimize the overall configuration, eliminating the interference of invalid reference points on group selection, and improving the efficiency of the algorithm. The reference point selection strategy of the target space uses the number of reference points to adapt to the population size N, and dynamically selects reference points with higher importance according to the population in the target space evolution stage. The specific steps of reference point screening include:

[0113] Step 1: According to the size of the population N, select a reference point set Z divided into p in each dimension, and the number of reference points is H p , the number of segments p must satisfy: H p ≥1.2N and H p-1 <1.2N.

[0114] Step 2: Determine the evolutionary stage of the population based on the evolutionary stage of the decision space.

[0115] Step 3: When the population as a whole is in the "exploration" stage, calculate the total number of individuals associated with each generation of reference point set Z sum .

[0116] Step 4: When the population just enters the "exploration" stage, according to Z sum Keep the N reference points with the largest number of associated individuals to form a new reference point set Z n .

[0117] In some specific embodiments, the normal distribution crossover operator strategy introduces normal distribution into the simulated binary crossover (SBX) operator, sets its development and exploration probabilities to be consistent with the SBX operator, replaces the expansion factor β with 1.481·|N(0,1)|, and introduces discrete recombination in the evolution strategy to the search space greater than one dimension, thereby establishing the NDX operator, which is described as follows:

[0118]

[0119] Among them, the first parent individual is represented by The second parent individual is represented by μ is a random number uniformly distributed in the interval (0,1).

[0120] S104. Use the ARNX-NSGA-Ⅲ algorithm to perform global optimization on the pre-hospital emergency facility site selection model, and output the optimal compromise solution as the final pre-hospital emergency facility site selection parameter information.

[0121] Continue to refer Figure 2 , Figure 2 The flowchart of the ARNX-NSGA-III algorithm of the embodiment of the present application is shown. As shown in the figure, the improved NSGA-III algorithm includes the following steps:

[0122] Step 201: Generate an initial solution that satisfies the constraints of the out-of-hospital cardiac arrest emergency facility site selection model.

[0123] Step 202: Generate reference point Z and initialize the number of reference points H p , determine the initial reference point set Z and the number of reference points H according to the population size N p , which is used to guide the optimization process.

[0124] Step 203: Initialize the population P, create a set of candidate solutions, and calculate the population evolution stage threshold γ to distinguish different advanced stages.

[0125] Step 204: Sort each dimension of the decision vector and obtain the median mid.

[0126] Step 205: Calculate the entropy value e. The evolution stage S defaults to "exploration". Calculate the entropy value e 0 , evolutionary stage S 0 The default is "exploration", which initializes the total number of individuals associated with the reference point set Z sum = 0, initialize entropy difference Δe t <γ, the number of occurrences D sum =0.

[0127] Step 206: Select NDX crossover operator and polynomial mutation operator to evolve the population. Iterate and update the population. t Perform normal distribution crossover and mutation operations to obtain the offspring population Q t , merge the offspring population Q t and the parent population P t , and obtain the merged population R t .

[0128] Step 207: Population standardization and Pareto non-dominated sorting: standardize the population and sort the population according to the Pareto non-dominated relationship.

[0129] Step 208: Determine the next generation based on the reference point Z and the niche retention strategy, and use the reference point and the niche retention strategy to determine the next generation population.

[0130] Step 209: Count the reference point set Z sum The number of associated individuals, count the individuals associated with each reference point.

[0131] Step 210: Calculate the entropy value e t and the entropy difference Δe between two adjacent generations t , calculate the entropy of the current population, and calculate the entropy of the two adjacent generations of populations.

[0132] Step 211: Determine the entropy difference Δe t Is it less than the evolution stage threshold γ? If so, then D sum =D sum +1, go to step 213, if not, go to step 212.

[0133] Step 212: Determine whether the maximum number of iterations has been reached. If not, re-execute step 206. If so, select the optimal compromise solution and end the operation.

[0134] Step 213: Determine D sum Whether it meets the condition of greater than 10% × MaxGen, if it meets D sum >10%×MaxGen, enter the "exploration" stage, calculate the population N and the number of reference points H p The difference k, i = 0, execute step 214, if D sum ≤10%×MaxGen, execute step 212.

[0135] Step 214: Determine whether i is less than |k|, if not, execute step 212, if so, execute step 215.

[0136] Step 215: Delete the k reference points with the least number of associated individuals, i=i+1, and return to execute step 214.

[0137] Example

[0138] Assume that a street has identified 796 demand points and 363 alternative emergency points. A day is divided into four periods: T1 (03:00-09:00), T2 (09:00-17:00), T3 (17:00-22:00) and T4 (22:00-03:00), and five representative types of places are set, namely residential area A1, public place A2, office place A3, night entertainment place A4 and school A5. Taking the residential area as an example, the design ideas for the changes in demand in different periods are as follows:

[0139]

[0140] In the formula, Q represents the total population in the study area; q t (A l ) represents the tth period A l (l=1,2,3,4,5) total population of type of place; Indicates that the tth period belongs to A l The demand of type demand point i; q0(·) represents the static population of the region or demand point; α l,t Represents the tth cycle A l Population mobility coefficient of type of place; η l is the correction coefficient of the type of place in the tth period. Due to limited space, Tables 4 and 5 only show the detailed parameters of some demand points and alternative points respectively.

[0141] Table 4: Detailed parameters of some demand points

[0142]

[0143] Table 5: Detailed parameters of some alternative first aid points

[0144]

[0145] The pre-hospital emergency facility site selection model based on the improved NSGA-Ⅲ algorithm focuses on the site selection decision of fixed emergency facilities AED, taking into account the upper limit constraint (h) on the configuration of AED emergency facilities at the emergency point. For this reason, the integer coding method is adopted to set the length of each chromosome equal to twice the number of alternative emergency points (Num). The first half uses binary coding {0,1} to indicate whether the corresponding alternative emergency point is selected, and the second half uses the integer set {0,1,2,...,h} to encode the number of AEDs configured at the corresponding emergency point. For example, when the solution is expressed as "1101002110", it means that alternative emergency points No. 1, No. 2, and No. 4 are taken into consideration. Specifically, emergency point No. 2 is equipped with 2 AEDs and emergency point No. 4 is equipped with 1 AED. The coding situation is as follows Figure 3shown.

[0146] According to statistics, in 2023, a city received 101,831 pre-hospital emergency tasks, with a permanent population of 5.327 million. According to the actual survey results, the fixed loss cost of AED is F h The fixed loss cost of an ordinary ambulance is 8 yuan / day. o The coverage radius is 300m and 800m respectively when the first aid point only has AED, and the coverage radius is 800m and 2500m respectively when the first aid point also has ambulance. The other example parameter settings are shown in Table 6.

[0147] Table 6: ARNX-NSGA-III algorithm parameters in the example

[0148]

[0149] refer to Figure 4 , Figure 4 The non-dominated solution set of the pre-hospital emergency facility location selection model based on the improved NSGA-III algorithm according to the embodiment of the present application is shown. After solving the pre-hospital emergency facility location optimization model based on the improved NSGA-III algorithm, the calculated Pareto solution set is as follows: Figure 4 As shown in Table 7, the intercepted partial solution shows that the total cost of the pre-hospital cardiac arrest emergency system will increase with the increase in the number of residents achieving dual coverage and the number of residents fully served.

[0150] Table 7: Partial non-dominated solutions of the model

[0151]

[0152] Figure 5 The AED site selection result diagram of the pre-hospital emergency facility site selection model based on the improved NSGA-Ⅲ algorithm according to the embodiment of the present application is shown, wherein 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 configuration quantity are shown in Tables 8 and Figure 5 shown.

[0153] Table 8: Site selection results of the model

[0154]

[0155] Continue to refer Figure 6 , Figure 6The ambulance site selection result diagram of the pre-hospital emergency facility site selection model based on the improved NSGA-Ⅲ algorithm according to the embodiment of the present application is shown. After the optimal compromise solution is given, the algorithm is iterated to solve: at time T1, No. 104 and No. 126 alternative emergency points are selected to equip ambulances, at time T2, No. 75, No. 99, No. 115, No. 136 and No. 144 are selected to equip ambulances, at time T3, No. 98 and No. 104 alternative emergency points are re-selected, and at time T4, No. 59 and No. 138 alternative emergency points are selected. The corresponding ambulance site selection results are shown as follows: Figure 6 shown.

[0156] Further references Figure 7 As an implementation of the above method, in the second aspect, the present application provides an embodiment of a pre-hospital emergency facility site selection system 700 based on an improved NSGA-Ⅲ algorithm. Figure 1 Corresponding to the method embodiment shown, the system can be specifically applied to various electronic facilities. The system 700 includes a data set processing module 701, a model building module 702, an algorithm improvement module 703 and a parameter optimization module 704 which are interconnected, wherein:

[0157] A data set processing module 701 is configured to process and obtain a data set, wherein the data set includes parameter information corresponding to the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system, wherein 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;

[0158] A model building module 702 is configured to build the pre-hospital emergency facility site selection model and design corresponding constraints;

[0159] The algorithm improvement module 703 is configured to design and improve the NSGA-III algorithm based on the evolutionary stage judgment of the decision space, the reference point selection strategy of the target space and the normal distribution crossover operator strategy to obtain the ARNX-NSGA-III algorithm;

[0160] The parameter optimization module 704 is configured to use the ARNX-NSGA-III algorithm to perform global optimization on the pre-hospital emergency facility site selection model, and output the optimal compromise solution as the final pre-hospital emergency facility site selection parameter information.

[0161] Although the principles of the present invention are 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 merely explanations of the exemplary implementations of the present invention, and are not intended to limit the scope of the present invention. The details in the embodiments do not constitute limitations on the scope of the present invention, and any obvious changes such as equivalent transformations, simple replacements, etc. based on the technical solution of the present invention, without departing from the spirit and scope of the present invention, fall within the protection scope of the present invention.

Claims

1. A pre-hospital emergency facility site selection method based on an improved NSGA-Ⅲ algorithm, characterized in that: The method comprises: S1. Process and obtain a data set, wherein the data set includes parameter information corresponding to the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system, wherein 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; S2. Constructing a pre-hospital emergency facility site selection model and designing corresponding constraints based on the pre-hospital emergency system service capacity and the total cost of the pre-hospital emergency system; S3, based on the evolutionary stage judgment of the decision space, the reference point selection strategy of the target space and the normal distribution crossover operator strategy, the NSGA-Ⅲ algorithm is improved to obtain the ARNX-NSGA-Ⅲ algorithm; S4, using the ARNX-NSGA-III algorithm to perform global optimization on the pre-hospital emergency facility site selection model, and outputting the optimal compromise solution as the final pre-hospital emergency facility site selection parameter information; The ARNX-NSGA-III algorithm includes the following sub-steps: S41, generate an initial solution that meets the constraints, and determine the initial reference point set Z and the number of reference points H according to the population size N p ; S42, generate the initial population P, calculate the population evolution stage threshold γ and entropy value e 0 , evolutionary stage S 0 The default is "exploration", which initializes the total number of individuals associated with the reference point set Z sum = 0, initialize entropy difference Δe t <γ, the number of occurrences D sum =0; S43, using the parent population P t , based on the normal distribution crossover and mutation operations, the offspring population Q is obtained t , merge the offspring population Q t and the parent population P t , and for the combined population R t Perform environmental selection to obtain a new population P t+1 ; S44. Count the number of individuals Z associated with the reference point set sum , calculate the entropy value e t and the entropy difference Δe between two adjacent generations of populations t , determine Δe t Is it less than the evolution stage threshold γ? If so, then D sum =D sum +1, execute step S46, if not, execute step S45; S45, judging whether the convergence condition is met, if not, re-execute step S43, if yes, select the optimal compromise solution and end the operation; S46, Judgement D sum Whether it meets the condition of being greater than a%×MaxGen, if it meets D sum >a%×MaxGen, enter the "exploration" stage, calculate the population N and the number of reference points H p The difference k, i = 0, execute step S47, if D sum ≤a%×MaxGen, execute step S45, wherein a represents a parameter with a value of 10-20; S47, determine whether i is less than |k|, if not, execute step S45, if yes, execute step S48; S48, delete k reference points with the least number of associated individuals, i=i+1, and return to execute step S47; The normal distribution crossover operator strategy includes introducing discrete recombination in evolutionary strategies to search spaces with more than one dimension, thereby establishing the NDX operator, which is expressed as: Among them, the two parent individuals are represented as μ is a random number uniformly distributed in the interval (0,1); The pre-hospital emergency facility site selection model and the constraints in step S2 are: The site selection model of pre-hospital emergency facilities is expressed as: The corresponding constraints are expressed as: 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 covered by r1 more than twice in the whole cycle is the largest; formula 3 indicates 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; in the formula, T represents the period division, V represents the set of demand points, represents the demand at demand point i during period t, Indicates that during time period t, demand point i has at least two candidate emergency points within radius r1 to provide services for it, W 2i ,j represents the set of alternative emergency points that can cover the demand point i with a distance less than the coverage radius r2, represents the maximum service capacity of emergency point j during period t, represents the distance between the alternative emergency point j and the demand point i during the period t; T represents the period division, W represents the set of alternative emergency points, h represents the maximum number of AEDs configured at each emergency point, Indicates that during time period t, there are more than 0 AEDs deployed in emergency point j. represents the number of AEDs in emergency point j during time period t, F h represents the loss cost of AED, F o represents the wear and tear cost of the ambulance, Indicates that during time period t, there are more than 0 ambulances parked in emergency point j. represents the number of ambulances included in the emergency point j during period t, Indicates the number of first aid personnel equipped for each AED during period t, represents the number of emergency personnel in each ambulance during period t, w t represents the time period t during which the emergency personnel work. represents the labor cost per hour of the emergency personnel during period t, It means that from the end of time period t to the beginning of time period t+1, an ambulance needs to be mobilized between the existing emergency center u and the emergency point j. It represents the number of ambulances mobilized between the existing emergency center u and the emergency point j from the end of time period t to the beginning of time period t+1. represents the distance between the emergency center u and the emergency point j from time period t to time period t+1, It represents the variable cost per unit distance of the ambulance during period t; 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 location and number of AEDs at emergency point j remain unchanged every cycle; condition 3 means that the total number of AEDs equipped at all emergency points does not exceed the maximum limit, N h represents the maximum number of AEDs configured for all emergency points. Condition 4 ensures that the coverage radius r2 must cover all needs. Condition 5 indicates that if a demand point is not covered at least once, it cannot be covered twice. 1i ,j represents the set of alternative emergency points that can cover demand point i with a distance less than the coverage radius r1; condition six ensures that demand point i is covered twice only when there are two or more emergency services within r1 of the demand point. Indicates that in period t, demand point i has at least one candidate emergency point within radius r1 to provide service for it. Indicates that during period t, demand point i has at least two candidate emergency points providing services within radius r1; condition seven is defined as the service capacity of emergency point j to demand point i that satisfies the function of the relevant distance; condition eight is expressed as the value constraint of the decision variable; condition nine is a non-negative constraint.

2. The pre-hospital emergency facility site selection method based on the improved NSGA-III algorithm according to claim 1, characterized in that: The reference point screening steps include the following: Step 1: According to the size of the population N, select a reference point set Z divided into p in each dimension, and the number of reference points is H p , the number of segments p satisfies H p ≥1.2N and H p-1 <1.2N; Step 2: Determine the evolutionary stage of the population based on the ARNX-NSGA-III algorithm; Step 3: When the population as a whole is in the "exploration" stage, calculate the total number of individuals associated with each generation of reference point set Z sum ; Step 4: When the population just enters the "exploration" stage, according to Z sum Keep the N reference points with the largest number of associated individuals to form a new reference point set Z n .

3. A multi-objective optimization system based on an improved NSGA-Ⅲ algorithm, characterized in that: The system comprises: a data set processing module configured to process and obtain a data set, wherein the data set includes parameter information corresponding to the service capacity of the pre-hospital emergency system and the total cost of the pre-hospital emergency system, wherein 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; A model building module, configured to build a pre-hospital emergency facility site selection model and design corresponding constraints; The algorithm improvement module is configured to improve the NSGA-III algorithm based on the evolutionary stage judgment of the decision space, the reference point selection strategy of the target space, and the normal distribution crossover operator strategy to obtain the ARNX-NSGA-III algorithm; A parameter optimization module is configured to use the ARNX-NSGA-III algorithm to perform global optimization on the pre-hospital emergency facility site selection model, and output an optimal compromise solution as final pre-hospital emergency facility site selection parameter information; The algorithm improvement module configuration implements the following steps: S41, generate an initial solution that meets the constraints, and determine the initial reference point set Z and the number of reference points H according to the population size N p ; S42, generate the initial population P, calculate the population evolution stage threshold γ and entropy value e 0 , evolutionary stage S 0 The default is "exploration", which initializes the total number of individuals associated with the reference point set Z sum = 0, initialize entropy difference Δe t <γ, the number of occurrences D sum =0; S43, using the parent population P t , based on the normal distribution crossover and mutation operations, the offspring population Q is obtained t , merge the offspring population Q t and the parent population P t , and for the combined population R t Perform environmental selection to obtain a new population P t+1 ; S44. Count the number of individuals Z associated with the reference point set sum , calculate the entropy value e t and the entropy difference Δe between two adjacent generations of populations t , determine Δe t Is it less than the evolution stage threshold γ? If so, then D sum =D sum +1, execute step S46, if not, execute step S45; S45, judging whether the convergence condition is met, if not, re-execute step S43, if yes, select the optimal compromise solution and end the operation; S46, Judgement D sum Whether it meets the condition of being greater than a%×MaxGen, if it meets D sum >a%×MaxGen, enter the "exploration" stage, calculate the population N and the number of reference points H p The difference k, i = 0, execute step S47, if D sum ≤a%×MaxGen, execute step S45, wherein a represents a parameter with a value of 10-20; S47, determine whether i is less than |k|, if not, execute step S45, if yes, execute step S48; S48, delete k reference points with the least number of associated individuals, i=i+1, and return to execute step S47; The normal distribution crossover operator strategy includes introducing discrete recombination in evolutionary strategies to search spaces with more than one dimension, thereby establishing the NDX operator, which is expressed as: Among them, the two parent individuals are represented as μ is a random number uniformly distributed in the interval (0,1); The site selection model of the pre-hospital emergency facilities and the constraint conditions in step S2 are respectively: The site selection model of the pre-hospital emergency facilities is expressed as: The corresponding constraints are expressed as: 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 covered by r1 more than twice in the whole cycle is the largest; formula 3 indicates 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; in the formula, T represents the period division, V represents the set of demand points, represents the demand at demand point i during period t, Indicates that during time period t, demand point i has at least two candidate emergency points within radius r1 to provide services for it, W 2i ,j represents the set of alternative emergency points that can cover the demand point i with a distance less than the coverage radius r2, represents the maximum service capacity of emergency point j during period t, represents the distance between the alternative emergency point j and the demand point i during the period t; T represents the period division, W represents the set of alternative emergency points, h represents the maximum number of AEDs configured at each emergency point, Indicates that during time period t, there are more than 0 AEDs deployed in emergency point j. represents the number of AEDs in emergency point j during time period t, F h represents the loss cost of AED, F o represents the wear and tear cost of the ambulance, Indicates that during time period t, there are more than 0 ambulances parked in emergency point j. represents the number of ambulances included in the emergency point j during period t, Indicates the number of first aid personnel equipped for each AED during period t, represents the number of emergency personnel in each ambulance during period t, w t represents the time period t during which the emergency personnel work. represents the labor cost per hour of the emergency personnel during period t, It means that from the end of time period t to the beginning of time period t+1, an ambulance needs to be mobilized between the existing emergency center u and the emergency point j. It represents the number of ambulances mobilized between the existing emergency center u and the emergency point j from the end of time period t to the beginning of time period t+1. represents the distance between the emergency center u and the emergency point j from time period t to time period t+1, It represents the variable cost per unit distance of the ambulance during period t; 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 location and number of AEDs at emergency point j remain unchanged every cycle; condition 3 means that the total number of AEDs equipped at all emergency points does not exceed the maximum limit, N h represents the maximum number of AEDs configured for all emergency points. Condition 4 ensures that the coverage radius r2 must cover all needs. Condition 5 indicates that if a demand point is not covered at least once, it cannot be covered twice. 1i ,j represents the set of alternative emergency points that can cover demand point i with a distance less than the coverage radius r1; condition six ensures that demand point i is covered twice only when there are two or more emergency services within r1 of the demand point, Indicates that in period t, demand point i has at least one candidate emergency point within radius r1 to provide service for it. Indicates that during period t, demand point i has at least two candidate emergency points providing services within radius r1; condition seven is defined as the service capacity of emergency point j to demand point i that satisfies the function of the relevant distance; condition eight is expressed as the value constraint of the decision variable; condition nine is a non-negative constraint.

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