A medical resource allocation method based on fuzzy clustering evolutionary algorithm
By using a fuzzy clustering evolutionary algorithm to perform hierarchical simulation of medical resource allocation schemes, the optimization problem under uncertain circumstances was solved, achieving efficient and accurate medical resource allocation and improving the algorithm's search capability and computational efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- GUANGZHOU MEDICAL UNIV
- Filing Date
- 2022-11-20
- Publication Date
- 2026-07-21
AI Technical Summary
Existing evolutionary algorithms have failed to effectively handle context-based uncertainties in the medical resource allocation problem, resulting in large oscillations in the expected value of the objective function and inaccurate comparison of solutions, making it difficult to optimize and solve under uncertain environments.
A fuzzy clustering evolutionary algorithm is adopted to perform hierarchical simulation of medical resource allocation schemes through fuzzy clustering. The correlation coefficient and membership degree of clusters are calculated using rough set theory, which reduces the number of simulations and improves the accuracy and efficiency of calculation.
While ensuring computational accuracy, the algorithm minimizes computational resource consumption, improves efficiency and optimization capabilities, reduces fluctuations in fitness values, and facilitates a smooth optimization process.
Smart Images
Figure CN115881281B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of operations research technology, specifically relating to a medical resource allocation method based on fuzzy clustering evolutionary algorithm. Background Technology
[0002] With the development of technology, society has entered the era of big data. The modeling and parameter acquisition for many problems are obtained through statistical analysis of data. Therefore, optimization problems in real life are often affected by uncertainty. This uncertainty may stem from random model parameters, perturbations in the objective function, perturbations in decision variables, environmental influences, and so on. Due to differences in distribution, boundaries, and central tendency, these uncertainties may manifest in different forms, posing significant challenges to problem optimization.
[0003] The goal of studying the allocation of medical resources in uncertain environments is to find a solution that yields satisfactory results in various scenarios while controlling the risks of the allocation plan, thereby maximizing the expected value of the objective function.
[0004] Therefore, how to avoid the errors brought by uncertainty to the optimization problem of medical resource allocation, and how to optimize and solve the problem in an environment full of uncertainty, has become a hot topic in the field of evolutionary algorithm research. Evolutionary algorithms are population-based stochastic optimization methods that approximate the optimal solution of a problem through uncertainty mechanisms, and have become an important tool for solving uncertain optimization problems in recent years. Although existing research has explored evolutionary algorithms in uncertain environments, in most existing studies on uncertain evolutionary algorithms, uncertainty is usually manifested as noise added to the problem's objective function, or interference related to decision variables. Little attention has been paid to a special type of uncertainty in medical resource allocation problems—context-based uncertainty. An environment with context-based uncertainty is called a context-uncertain environment. In optimization problems under context-uncertain environments, the uncertainty of the external context has a very large impact on the results, even exceeding the impact of the quality of the solution. That is, a good solution in a negative external context may yield a far worse result than a poor solution in a positive external context. The medical resource allocation problem exhibits this special type of uncertainty. For example, in… Figure 2 In this scenario, suppose we need to designate five points along the route of medical resources, with the goal of minimizing the total time required to complete the transportation. It's easy to see that in most cases, Option 1 is more reasonable than Option 2, requiring a shorter total time.
[0005] This unique uncertainty not only leads to large oscillations in the approximation of the expected value of the objective function, making it difficult to stabilize, but also causes the comparison of solutions to become highly inaccurate during the optimization process, bringing great difficulties and challenges to the research of evolutionary algorithms. Summary of the Invention
[0006] To overcome the shortcomings of existing technologies, this invention provides a medical resource allocation method based on a fuzzy clustering evolutionary algorithm. First, the medical resource allocation optimization problem is modeled, and a fitness function is determined based on the optimization objective. Then, initial allocation schemes are randomly generated, and fuzzy clustering is performed on these schemes using rough set theory. Next, the weighted average of the Pearson correlation coefficients among all allocation schemes in each cluster is calculated according to probability to obtain the cluster correlation coefficient. Then, the weighted value of the correlation coefficient of each allocation scheme is calculated based on its membership to the cluster, resulting in the number of simulations. Based on the number of simulations, all allocation schemes are simultaneously evaluated in the same scenarios. Finally, the average fitness value of each allocation scheme in all simulated scenarios is calculated, and the allocation scheme is selected based on the average fitness value. This invention minimizes computational resource consumption and improves algorithm efficiency while ensuring computational accuracy.
[0007] The technical solution adopted by this invention to solve its technical problem includes the following steps:
[0008] Step 1: Model the problem of medical resource allocation;
[0009] The problem of medical resource allocation based on directed graph networks is solved by considering cities that need resources as nodes C = {c1, c2, ..., c} in the network. n The transportation path can be viewed as an edge A = {a1, a2, ..., a} pointing from one node to another. m Medical resources originate from city C1 and are ultimately transported to their destination city C. n ; where, through each path a i The time required d i and cost p i It is uncertain; there are rewards for early delivery of medical resources, and penalties for failure to deliver within the agreed time; the ultimate goal is to ensure that, while visiting every city, the resources finally reach the destination city c. n The allocation scheme that minimizes costs is as follows:
[0010] minE[∑p i +P] (1)
[0011] Where P represents the additional reward or penalty for transportation, calculated as follows:
[0012]
[0013] Where D represents the total time spent on the transportation plan, and T... l and T u These are the lower and upper bounds of the agreed time, respectively; γ and δ are the reward factor and penalty factor, respectively; and α is the severity parameter set according to the actual situation.
[0014] Step 2: Randomly generate initial allocation schemes, and perform fuzzy clustering of the allocation schemes using rough set theory based on the Euclidean distance between them; treat each allocation scheme as an individual.
[0015] Given a population set X = {x1, x2, ..., x...} n} Divide into c clusters {V1,V2,…,V c In the context of}, assume a given universe of discourse U = X = {x1, x2, ..., x}. n Let R be an equivalence relation on U, and let the given partition be denoted as . Is it assigned to cluster center v? i The set of individuals belonging to the same cluster; then the set The upper approximation set and the lower approximation set are respectively:
[0016]
[0017] In the formula, Represents the equivalence relation R j The element x is contained below j The equivalence class of x j Describes a set X that belongs to set X. Element;
[0018] Boundary region BN under equivalence relation R R for:
[0019]
[0020] Based on the above definitions, and according to the average of the lower approximation set and the weighted domain, the following fuzzy centroid update formula is defined, which simultaneously considers the influence of fuzzy membership degree and the upper and lower approximation sets:
[0021]
[0022] in
[0023]
[0024] Here, J(V) i Let be the fuzzy centroid of the i-th cluster, m be the fuzziness factor, and u be the fuzzy centroid. ij Represents individual x jFor cluster V i Membership degree;
[0025] parameter and Let R be the roughness and approximate accuracy of the i-th cluster, respectively, satisfying:
[0026]
[0027] Based on the fuzzy centroid update formula given in formula (5), each individual x is obtained through multiple iterations. j For cluster V i final membership degree u ij ;
[0028] Step 3: Calculate the weighted average of the Pearson correlation coefficients among all allocation schemes in each cluster according to probability, and obtain the cluster correlation coefficient;
[0029] By calculating u in each cluster ij All individuals x ≠ 0 j The correlation coefficient between them yields cluster V. i The weighted average correlation coefficient; where the correlation coefficient between two individuals is obtained using the Pearson correlation coefficient formula:
[0030]
[0031] In the formula, X and Y represent the simulated fitness values of two individuals, respectively, and σ X ,σ Y Let μ represent the standard deviation of the fitness values of the two individuals. X ,μ Y These represent the mean fitness of the two individuals, respectively.
[0032] Cluster V i The set of all elements in a is denoted as A. i ={x j |u ij If ≠0, then cluster V i The weighted correlation coefficient is:
[0033]
[0034] Step 4: Calculate the correlation coefficient weighting value of the allocation scheme based on the membership degree of the cluster to obtain the number of simulations required for fitness evaluation of each allocation scheme during the optimization process;
[0035] The correlation coefficient of an individual is calculated using the weighted correlation coefficient of the cluster, and the corresponding number of simulations is set; the individual x j The set of all the clusters to which it belongs is denoted as B. j ={V i |uij If x ≠ 0, then individual x j The weighted correlation coefficient is calculated using formula (9):
[0036]
[0037] Then, based on the weighted average of the individual correlation coefficients, determine the number of simulations required for fitness evaluation during the optimization process for that individual; set the corresponding number of simulations based on the reciprocal of the correlation coefficient, letting...
[0038]
[0039] Where λ is a control parameter set according to the problem; after the calculation is completed, t is... j Round the value to the nearest integer.
[0040] Step 5: Based on the number of simulations, all allocation schemes are evaluated synchronously in the same scenario. The average fitness value of each allocation scheme in all scenarios that have been simulated is calculated. The allocation schemes are sorted from smallest to largest according to the average fitness value, and the allocation scheme with the smallest average fitness value is selected to obtain the best allocation scheme.
[0041] The beneficial effects of this invention are as follows:
[0042] 1) The hierarchical simulation method based on fuzzy clustering proposed in this invention reduces the number of simulations by utilizing the correlation coefficients between solutions in optimization problems under uncertain circumstances. By leveraging the inherent consistency between the uncertainty of rough set theory and the uncertainty of the problem, fuzzy clustering is performed on the population, and the number of simulations is hierarchically set for individuals based on the correlation coefficients between solutions in different clusters after clustering. This method minimizes computational resource consumption and improves algorithm efficiency while ensuring computational accuracy.
[0043] 2) This invention applies a fuzzy clustering evolutionary algorithm to the optimization problem of medical resource allocation, verifying the algorithm's effectiveness through examples and promoting the construction of smart cities. The medical resource allocation problem is characterized by significant uncertainty, leading to large fluctuations in the fitness values of allocation schemes. To address this, this invention employs a hierarchical simulation method based on fuzzy clustering to set appropriate simulation iterations for the correlation coefficients between allocation schemes during the evolutionary process, thereby improving the algorithm's optimization efficiency. Attached Figure Description
[0044] Figure 1 This is a flowchart of the method of the present invention.
[0045] Figure 2 A diagram illustrating the allocation of medical resources. Detailed Implementation
[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0047] For special uncertain environments, this study combines evolutionary algorithms with fuzzy clustering methods. Based on the high correlation between solutions under uncertain conditions, a hierarchical simulation method based on fuzzy clustering is proposed to reduce the number of simulations and improve algorithm efficiency. The proposed algorithm is then applied to the problem of optimizing medical resource allocation under uncertain circumstances.
[0048] like Figure 1 As shown, this invention proposes a medical resource allocation method based on fuzzy clustering evolutionary algorithm. It combines fuzzy clustering method with evolutionary algorithm and applies it to the medical resource allocation optimization problem, which can improve the algorithm's search ability and optimization efficiency at the same time.
[0049] 1. A model is constructed for the optimization problem of medical resource allocation, and a fitness function is determined based on the optimization objective. This invention considers the optimization of medical resource allocation based on directed graph networks. The optimization objective is to find the allocation scheme that minimizes the cost of reaching the destination city while ensuring that every city is traversed.
[0050] 2. Randomly generate initial allocation schemes, and perform fuzzy clustering of the allocation schemes based on the Euclidean distance between them using rough set theory.
[0051] 3. Calculate the weighted average of the Pearson correlation coefficients among all allocation schemes in each cluster according to probability, and obtain the cluster correlation coefficient.
[0052] 4. Calculate the correlation coefficient weighted value of the allocation scheme based on the membership degree of the cluster to obtain the number of simulations required for fitness evaluation of each allocation scheme during the optimization process.
[0053] 5. Based on the number of simulations, all allocation schemes are evaluated simultaneously under the same scenario. Although the uncertainty of the scenario has a significant impact on the fitness value, making it difficult to approximate the expected fitness value, it is not actually necessary to calculate the accurate expected fitness value when selecting an allocation scheme during the optimization process. Instead, a correct comparison of the merits of different allocation schemes within the population is sufficient to ensure the optimization process proceeds smoothly and ultimately yields an optimal allocation scheme.
[0054] 6. Calculate the average fitness value of each allocation scheme across all scenarios in which simulations were performed, and select an allocation scheme based on the average fitness value. Specific implementation examples:
[0056] This invention addresses the problem of medical resource allocation. Addressing the limitations and shortcomings of existing methods, it designs an algorithm based on the characteristics of the problem itself, improving the search capability and optimization efficiency of evolutionary algorithms. The algorithm is then applied to real-world medical resource allocation problems. Furthermore, in line with the needs of the new technological revolution and to achieve the cross-disciplinary integration of information science and biomedicine, theoretical research is guided by application requirements.
[0057] 1. Modeling the medical resource allocation problem. This embodiment considers the medical resource allocation problem based on a directed graph network, treating the cities that need resources as nodes C = {c1, c2, ..., c} in the network. n The transportation path can be viewed as an edge A = {a1, a2, ..., a} pointing from one node to another. m The medical resources will depart from the starting city c1, which has the richest stockpile, and will be distributed along the route before finally being transported to the destination city c. n This addresses the local shortage of medical resources. Specifically, it involves each path a... i The time required d i and cost p i It's uncertain. There's a reward for early delivery of medical resources, and a penalty for failure to deliver within the agreed time. The ultimate goal is to find a way to reach the destination city c while ensuring that every city is visited. n The allocation scheme with the lowest cost:
[0058]
[0059] Where P represents the additional reward or penalty for transportation, calculated as follows:
[0060]
[0061] Where D represents the total time spent on the transportation plan, and T... l and T u These are the lower and upper bounds of the agreed time, respectively; γ and δ are the reward factor and penalty factor, respectively; and α is the severity parameter set according to the actual situation.
[0062] 2: Using rough set theory, fuzzy clustering is performed on individuals based on the Euclidean distance between them. In this step, this project considers the given population set X = {x1, x2, ..., x...} n} Divide into c clusters {V1,V2,…,V c In the context of}, suppose the given universe of discourse is U = X = {x1, x2, ..., x}. n Let R be an equivalence relation on U, and let the given partition be denoted as . Is it assigned to cluster center v?i The set of individuals belonging to the same cluster. Then the set... The upper approximation set and the lower approximation set are respectively:
[0063]
[0064] Boundary region BN under equivalence relation R R for:
[0065]
[0066] Based on the above definitions, and according to the average of the lower approximation set and the weighted domain, this project will define the following fuzzy centroid update formula, which simultaneously considers the influence of fuzzy membership degree and the upper and lower approximation sets:
[0067]
[0068] in
[0069]
[0070] Here, J(V) i Let be the fuzzy centroid of the i-th cluster, m be the fuzziness factor, and u be the fuzzy centroid. ij Represents individual x j For cluster V i Membership degree. Parameter and These are the roughness and approximate accuracy of the i-th cluster, respectively, satisfying...
[0071]
[0072] Based on the fuzzy centroid update formula given in formula (5), each individual x is obtained through multiple iterations. j For cluster V i final membership degree u ij .
[0073] 3: By calculating u in each cluster ij All individuals x ≠ 0 j The correlation coefficient between them yields cluster V. i The weighted average correlation coefficient. The correlation coefficient between two individuals is obtained using the Pearson correlation coefficient formula:
[0074]
[0075] Cluster V i The set of all elements in a is denoted as A. i ={x j |u ij If ≠0, then cluster V iThe weighted correlation coefficient is:
[0076]
[0077] 4: Calculate the correlation coefficient of individuals using the weighted correlation coefficient of the cluster, and set the corresponding number of simulations. Let individual x... j The set of all the clusters to which it belongs is denoted as B. j ={V i |u ij If x ≠ 0, then individual x j The weighted correlation coefficient is calculated using formula (9):
[0078]
[0079] Then, the number of simulations required for fitness evaluation during the optimization process is determined based on the weighted average of the individual correlation coefficients. For individuals with high correlation coefficients, only a small number of simulations are needed to accurately evaluate the quality of the solution; therefore, t j It should be set relatively small. For individuals with low correlation coefficients, more simulations are needed to make accurate assessments, therefore t... j It should be set relatively large. Specifically, the number of simulations should be set according to the reciprocal of the correlation coefficient, letting...
[0080]
[0081] Here, λ is a control parameter set according to the problem. Since the number of simulations must be an integer, the value must be rounded after the calculation.
[0082] 5. Based on the number of simulations, all allocation schemes are evaluated simultaneously under the same scenario. Although the uncertainty of the scenario has a significant impact on the fitness value, making it difficult to approximate the expected fitness value, it is not actually necessary to calculate the accurate expected fitness value when selecting an allocation scheme during the optimization process. Instead, a correct comparison of the merits of different allocation schemes within the population is sufficient to ensure the optimization process proceeds smoothly and ultimately yields an excellent allocation scheme.
[0083] 6: Calculate the average fitness value of each allocation scheme in all scenarios that have been simulated, sort the allocation schemes according to the average fitness value, and select the allocation scheme with the highest ranking.
Claims
1. A method for allocating medical resources based on a fuzzy clustering evolutionary algorithm, characterized in that, Includes the following steps: Step 1: Model the problem of medical resource allocation; This problem addresses the allocation of medical resources using directed graph networks, treating cities that require resources as nodes in the network. C = { c 1, c 2,… c n The transportation path can be viewed as an edge pointing from one node to another. A = { a 1, a 2,… a m }; among which medical resources come from c 1. Departure, ultimately transporting resources to the destination city. c n ; Among them, through each path a i Time required d i and cost p i It's uncertain; there are rewards for early delivery of medical resources, and penalties for failure to deliver within the agreed time; the ultimate goal is to ensure that, while visiting every city, the resources finally reach the destination city. c n The allocation scheme that minimizes costs is as follows: (1) in P Additional rewards or penalties for transportation are calculated as follows: (2) in D The total time spent on the transportation plan, T l and T u These are the lower and upper bounds of the agreed time, respectively. γ and δ These are reward factors and penalty factors, α The severity parameter of the epidemic is set according to the actual situation; Step 2: Randomly generate initial allocation schemes, and perform fuzzy clustering of the allocation schemes using rough set theory based on the Euclidean distance between them; treat each allocation scheme as an individual. Given a population set X = { x 1, x 2,…, x n } divided into c Clusters { V 1, V 2,…, V c In the context of}; assuming a given universe of discourse U = X = { x 1, x 2,…, x n }, R yes U An equivalence relation on the given partition is denoted as . , Is it assigned to the cluster center? The set of individuals belonging to the same cluster; then the set The upper approximation set and the lower approximation set are respectively: (3) In the formula, Representing equivalence relations R j Containing elements x j equivalence class, Represents a set X The middle belongs to the set Element; In equivalence relation R The boundary domain below for: (4) Based on the above definitions, and according to the average of the lower approximation set and the weighted domain, the following fuzzy centroid update formula is defined, which simultaneously considers the influence of fuzzy membership degree and the upper and lower approximation sets: (5) in (6) here, J ( V i ) is the first i The fuzzy centroid of a cluster, m As a fuzzy factor, u ij Represents an individual x j Cluster V i Membership degree; parameters and They are the first i The roughness and approximate accuracy of each cluster satisfy: (7) Based on the fuzzy centroid update formula given in formula (5), each individual centroid is obtained through multiple iterations. x j Cluster V i final membership degree u ij ; Step 3: Calculate the weighted average of the Pearson correlation coefficients among all allocation schemes in each cluster according to probability, and obtain the cluster correlation coefficient; By calculating in each cluster u ij ≠ All individuals of 0 x j The correlation coefficient between them yields the clusters. V i The weighted average correlation coefficient; where the correlation coefficient between two individuals is obtained using the Pearson correlation coefficient formula: (8) In the formula, These represent the simulated fitness values of the two individuals, respectively. These represent the standard deviations of the fitness values of the two individuals, , These represent the mean fitness of the two individuals, respectively. Cluster V i The set of all elements in is denoted as A i = { x j | u ij ≠ If 0}, then the cluster V i The weighted correlation coefficient is: (9) Step 4: Calculate the correlation coefficient weighting value of the allocation scheme based on the membership degree of the cluster to obtain the number of simulations required for fitness evaluation of each allocation scheme during the optimization process; The correlation coefficient of an individual is calculated using the weighted correlation coefficient of the cluster, and the corresponding number of simulations is set; the individual... x j The set of all the clusters to which a member belongs is denoted as B j = { V i | u ij ≠ 0}, then the individual x j The weighted correlation coefficient is calculated using formula (9): (10) Then, based on the weighted average of the individual correlation coefficients, determine the number of simulations required for fitness evaluation during the optimization process for that individual; set the corresponding number of simulations based on the reciprocal of the correlation coefficient, letting... (11) in, λ These are control parameters set according to the problem; after the calculation is completed... Round the value to the nearest integer. Step 5: Based on the number of simulations, simultaneously evaluate all allocation schemes in the same scenario, calculate the average fitness value of each allocation scheme in all scenarios that have been simulated, sort the allocation schemes from smallest to largest according to the average fitness value, and select the allocation scheme with the smallest average fitness value to obtain the best allocation scheme.