Fractional order drug release parameter inversion method and system

Abstract

The application provides a fractional drug controlled release parameter inversion method and system, establishes a fractional diffusion model for describing drug release, sets to-be-inverted model parameters, and constructs a double-target evaluation function set including fitting error and release smoothness. An improved NSGA-III algorithm fusing a Levy flight strategy is used for iterative optimization of the model parameters. The algorithm introduces Levy flight disturbance in genetic operation to enhance global exploration capability, and uses a reference point correlation mechanism for environment selection to maintain diversity and uniform distribution of the solution set in a high-dimensional target space. Through the above process, a Pareto optimal parameter solution set capable of balancing multiple targets is finally obtained. The application effectively overcomes the defects of traditional single-target optimization, such as local fluctuation of the release curve and unclear physical meaning, and realizes efficient and stable inversion of the fractional order and initial concentration distribution parameters, thereby providing a more reliable and more interpretable parameter scheme for drug controlled release system design.

Description

Technical Field

[0001] This invention relates to the field of drug controlled release technology, and in particular to a fractional-order drug controlled release parameter inversion method and a fractional-order drug controlled release parameter inversion system. Background Technology

[0002] Currently, the design of drug controlled release systems is usually based on fractional diffusion differential equations to describe the release behavior of drugs in carrier materials, and numerical methods are used to simulate and analyze the release process. In the parameter design and inversion process, existing studies mostly adopt optimization methods with the single objective of minimizing the overall error between the release rate curve and the target curve, and adjust the model parameters accordingly.

[0003] However, in practical applications, the drug release process not only requires minimizing the overall release error but also necessitates considering multiple requirements such as the continuity, smoothness, and physical rationality of the release curve at different stages. Existing optimization methods based on a single objective function often struggle to simultaneously satisfy these multidimensional constraints during the inversion process, easily leading to problems such as local fluctuations and morphological distortion in the release curve, specifically manifested as phenomena lacking physical interpretation, such as "early peaks followed by later smoothing." The root of this limitation lies in the fact that traditional optimization models use error as the sole evaluation metric, failing to introduce systematic constraints on curve morphology, derivative trends, etc. This results in inversion results that may numerically approximate the target curve but lack sufficient practical physical meaning and release stability. Therefore, how to achieve synergistic constraints on the smoothness, continuity, and physical rationality of the release curve by introducing a multi-index comprehensive evaluation system while ensuring overall fitting accuracy, thereby obtaining more stable and reliable parameter inversion results, remains a key issue requiring further research.

[0004] Figures 1(a) and 1(b) show the release rate curves obtained using existing single-objective optimization techniques:

[0005] As can be seen, the release rate curve fluctuates greatly in the early stage, which reflects that the initial concentration and model order settings are unreasonable. However, the algorithm's optimization objective only optimizes the error size and cannot make the curve smoother. Therefore, smoothness needs to be added as a second optimization objective to ensure the rationality of the release.

[0006] Existing multi-objective algorithms (such as NSGA-II) are difficult to solve stably and efficiently when dealing with complex nonlinear, high-dimensional parameter inversion problems such as drug controlled release, and cannot provide reasonable drug design schemes. Summary of the Invention

[0007] In view of the above problems, the present invention is proposed to provide a fractional-order drug controlled-release parameter inversion method and a corresponding fractional-order drug controlled-release parameter inversion system to overcome or at least partially solve the above problems.

[0008] This invention discloses a fractional-order drug controlled-release parameter inversion method, the method comprising: A fractional-order diffusion model describing drug release behavior is established, and the set of model parameters to be inverted is determined; the set of model parameters includes the fractional derivative order and the initial drug concentration distribution parameters. Construct a set of objective functions for evaluating the quality of parameter inversion. The set of objective functions includes at least a fitting error function for characterizing the overall difference between the simulated release curve and the target release curve, and a release smoothness function for characterizing the smoothness of the release process. Based on the improved NSGA-III-MOCS algorithm, with the goal of simultaneously optimizing the values ​​of each objective function in the set of objective functions, it iterative optimization is performed in the solution space of the model parameter set until the termination condition is met, and the Pareto optimal solution set is obtained. Equilibrium solutions are selected from the Pareto optimal solution set, and the model parameters corresponding to the equilibrium solutions are used as the controlled release parameters of the drug controlled release system.

[0009] Optionally, a set of objective functions for evaluating the quality of parameter inversion is constructed, including: Construct and calculate the fitting error function, which characterizes the accuracy of parameter inversion by the root mean square error between the simulated release curve and the target release curve; A release smoothness function is constructed and calculated. The release smoothness function characterizes the smoothness of the release process by the energy term of the first derivative of the simulated release curve.

[0010] Optionally, based on the improved NSGA-III-MOCS algorithm, with the objective of simultaneously optimizing the values ​​of each objective function in the set of objective functions, iterative optimization is performed in the solution space of the model parameter set until the termination condition is met, obtaining the Pareto optimal solution set, including: Initialize the population within the solution space of the model parameter set; In each generation iteration, genetic operations are performed on the current parent population to generate the offspring population; Apply random perturbations based on Levy flight to individuals in the offspring population; The parent population is merged with the perturbed offspring population, and the objective function values ​​of all individuals in the merged population are calculated. The merged population is subjected to non-dominated sorting, and environmental selection is performed based on the reference point association mechanism to select the next generation population. The iterative process is repeated until the preset termination condition is met, and the final non-dominated solution set is taken as the Pareto optimal solution set.

[0011] Optionally, the merged population is subjected to non-dominated ranking, and environmental selection is performed based on a reference point association mechanism to select the next generation population, including: The merged population is sorted into multiple non-dominated levels by performing a non-dominated ranking. Individuals are selected into the next generation of the population in descending order of non-dominant hierarchy until the next complete hierarchy can no longer be accommodated, thus determining the critical level. Adaptive normalization is applied to the objective function values ​​of the currently selected individuals. Calculate the perpendicular distance from each individual to the line connecting each reference point, and associate each individual with the nearest reference point; The number of individuals associated with each reference point is counted. Individuals with fewer associated reference points and closest to the reference line are selected from the critical layer until the preset population size is filled.

[0012] Optionally, an equilibrium solution is selected from the Pareto optimal solution set, and the model parameters corresponding to the equilibrium solution are used as the controlled-release parameters of the drug controlled-release system, including: In the Pareto optimal solution set, the solution that achieves a balance between the two objectives of fitting error and release smoothness is selected as the balanced solution; The model parameters corresponding to the equilibrium solution are used as the controlled release parameters of the drug controlled release system.

[0013] This invention also discloses a fractional-order drug controlled-release parameter inversion system, the system comprising: The parameter configuration module is used to receive and set model parameters, algorithm parameters, and target release curves. The model building and numerical solution module is used to establish a fractional diffusion model describing drug release behavior, and to numerically solve the combination of input candidate parameters based on the fractional diffusion model, and output the simulated release curve. The objective function evaluation module is used to calculate a set of objective functions for evaluating the quality of parameter inversion based on the simulated release curve and the target release curve. The set of objective functions includes at least a fitting error function for characterizing the overall difference between the simulated release curve and the target release curve, and a release smoothness function for characterizing the smoothness of the release process. The multi-objective optimization module is used to iteratively optimize the objective function values ​​in the objective function set simultaneously based on the improved NSGA-III-MOCS algorithm until the termination condition is met, and to obtain and output the Pareto optimal solution set. The result processing module is used to receive the Pareto optimal solution set, select equilibrium solutions from the Pareto optimal solution set, and output and visualize the model parameters corresponding to the equilibrium solutions as the controlled release parameters of the drug controlled release system.

[0014] This invention has the following advantages: This invention establishes a dual-objective inversion model that simultaneously incorporates release error and release smoothness. From an evaluation mechanism perspective, it balances overall fitting accuracy with the physical rationality of the release process. Furthermore, it proposes an improved parameter inversion algorithm (NSGA-III-MOCS) that integrates the Lévy flight operator and the NSGA-III framework. This algorithm enhances global exploration capabilities by embedding the Lévy flight operator during the genetic evolution process and utilizes the reference point association mechanism of NSGA-III to replace traditional crowded distance calculations, effectively solving the problems of uneven solution set distribution and premature convergence in high-dimensional parameter spaces. Ultimately, this invention can achieve efficient simultaneous inversion of fractional derivative order and initial concentration distribution parameters. Through the reference point mechanism, it guides the optimal solution to a uniform distribution in the multidimensional objective space, providing diverse Pareto optimal parameter schemes for drug controlled-release design. Attached Figure Description

[0015] Figure 1(a) is a schematic diagram of the release rate curve optimized using the existing single-objective algorithm; Figure 1(b) is a schematic diagram of the release rate curve optimized using the existing single-objective algorithm; Figure 2 This is a flowchart of the fractional-order drug controlled-release parameter inversion method of the present invention; Figure 3 This is a schematic diagram showing the comparison between the linearly reduced release rate optimized using the method of this invention and the target release rate; Figure 4 This is a structural block diagram of the fractional-order drug controlled-release parameter inversion system of the present invention. Detailed Implementation

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] Reference Figure 2 The fractional-order drug controlled-release parameter inversion method provided in this embodiment of the invention may specifically include the following steps: (1) Model building and parameter initialization A one-dimensional time-fractional diffusion equation model describing the drug delivery mechanism in a carrier is established. The set of parameters to be inverted for the model is defined as X = [ [, C], which includes the order of fractional derivatives. (Value range 0 < ≤1) and the initial drug concentration distribution parameter C.

[0018] Initialize the population P in the solution space, setting the population size to N and the maximum number of iterations to T. Simultaneously, generate a series of structured reference points Z on the normalized multidimensional target space hyperplane to maintain the uniformity of solution distribution in subsequent evolution.

[0019] (2) Construction of the objective function Construct the objective optimization function Used to evaluate the quality of parameter inversion: (Fitting error): The root mean square error between the cumulative drug release curve obtained from numerical simulation and the target curve measured in experiments is calculated. The accuracy of the parameters is ensured by minimizing this error. (Release Smoothness): The energy term of the first derivative of the release rate curve is calculated. Minimizing this index suppresses numerical oscillations that may occur in fractional-order model calculations, ensuring that the inversion results conform to the continuity characteristics of the actual physical process.

[0020] (3) Multi-objective parameter optimization based on improved NSGA-III-MOCS An improved third-generation non-dominated sorting genetic algorithm (NSGA-III-MOCS) incorporating the Lévy flight mechanism is used for iterative optimization. The specific steps are as follows: ① Offspring generation (genetic manipulation): For the current parent population Perform simulated binary crossover (SBX) and polynomial mutation operations to generate an initial offspring population. .

[0021] ②Levi flight disturbance: To enhance the algorithm's ability to escape local optima, a preset probability is used. Perform a Lévy flight operation on the offspring individuals. For the selected individuals, generate a random step size of a Lévy distribution. Step and according to the formula Update the position to perform a long-range random search in the solution space.

[0022] ③ Population merging and non-dominated ranking: Parent generation With the perturbed offspring Merged into a mixed population (scale 2) N ).calculate The objective function values ​​of all individuals are calculated, and a fast non-dominated sort is performed on them to divide the individuals into different non-dominated levels.

[0023] ④ Environmental selection: Individuals are added to the new generation population in hierarchical order. Until it can no longer accommodate the next complete level (called the critical level) ).

[0024] Normalization: Adaptive normalization is performed on the target value of the currently selected individual.

[0025] Association operation: Calculate the vertical distance of each individual to the line connecting each reference point, and associate the individual with the nearest reference point.

[0026] Niche preservation: Count the number of individuals associated with each reference point. Prioritize individuals from the critical layer. Select individuals with smaller associated reference point values ​​and closest to the reference line until the population size is filled. N .

[0027] (4) Output of parameter inversion results After reaching the maximum number of iterations, the final Pareto optimal solution set is output.

[0028] Select an inflection point solution from the solution set as the recommended parameter combination. This is a balance point that reduces fitting error without incurring excessive smoothness costs, and use it as the final inversion parameter of the drug controlled release system.

[0029] The following example illustrates the operation of the method of the present invention.

[0030] This example uses the "linearly decreasing release" objective to describe the complete process of software from startup to output results.

[0031] Step 1: System Initialization and Target Setting In the interactive interface, select "Linear Decreasing Release" as the target mode. The system then uses the formula... Generate target release rate curve data. Simultaneously, set algorithm parameters: for example, population size N=400, maximum number of iterations T=200, and fractional order. The search range is set to [0.1, 1.0], and the probability of Levi's flight detection is... =0.1.

[0032] Step 2: Population Generation and Preliminary Assessment The software randomly generates initial parameter combinations (parent population) within the parameter space. The system calls the "modeling module" to calculate the release curve corresponding to each set of parameters using a fractional difference scheme, and calculates the error between the curve and the target curve. and smoothness .

[0033] Step 3: Iterative optimization loop (NSGA-III-MOCS) The software enters an automated iteration process, with each generation performing the following operations: 1. Genetic evolution: Crossover and mutation of the parent population to generate transitional offspring.

[0034] 2. Lévy Flight Perturbation: The algorithm randomly selects 10% of individuals and applies a Lévy flight step size to their positions. For example, if an individual's order parameter was originally... After random perturbation, it mutates into This allows us to explore new regions of solution space.

[0035] 3. Model calculation: Substitute the new parameters after perturbation into the fractional diffusion equation and recalculate the release curve and the target function value.

[0036] 4. Environment selection: Merge the parent generation and the offspring generation and perform a non-dominated sort.

[0037] 5. Survival of the fittest: Prioritize the retention of individuals with high non-dominant levels; in the critical layer, retain those individuals that are closest to the reference point and whose surrounding area is relatively sparse, to ensure the diversity of the solution set.

[0038] Step 4: Convergence Determination and Result Output The program stops calculating after 200 iterations. At this point, the population has converged to the Pareto front.

[0039] Step 5: Final Result Analysis The software outputs a Pareto optimal solution set. A solution is selected from this set (the one that best balances error and smoothness).

[0040] Results: The optimal parameter combination output by the software is shown in Table 1. Table 1. Linear reduction of initial drug concentration and model order

[0041] The results of comparing the linearly decreasing release rate with the target release rate are as follows: Figure 3 At this point, the simulated release curve highly overlaps with the target linear curve, and the fitting error is <10. -3 Furthermore, there was no obvious burst release phenomenon in the initial stage of release (excellent smoothness index). This result verifies that the parameters obtained by inversion can guide the preparation process and achieve the expected linear drug release effect.

[0042] It should be noted that, for the sake of simplicity, the method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of the present invention are not limited to the described order of actions, because according to the embodiments of the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily essential to the embodiments of the present invention.

[0043] The fractional-order drug controlled-release parameter inversion system provided in this embodiment of the invention may specifically include the following modules: The parameter configuration module is used to receive and set model parameters, algorithm parameters, and target release curves. The model building and numerical solution module is used to establish a fractional diffusion model describing drug release behavior, and to numerically solve the combination of input candidate parameters based on the fractional diffusion model, and output the simulated release curve. The objective function evaluation module is used to calculate a set of objective functions for evaluating the quality of parameter inversion based on the simulated release curve and the target release curve. The set of objective functions includes at least a fitting error function for characterizing the overall difference between the simulated release curve and the target release curve, and a release smoothness function for characterizing the smoothness of the release process. The multi-objective optimization module is used to iteratively optimize the objective function values ​​in the objective function set simultaneously based on the improved NSGA-III-MOCS algorithm until the termination condition is met, and to obtain and output the Pareto optimal solution set. The result processing module is used to receive the Pareto optimal solution set, select equilibrium solutions from the Pareto optimal solution set, and output and visualize the model parameters corresponding to the equilibrium solutions as the controlled release parameters of the drug controlled release system.

[0044] In an optional embodiment of the present invention, the parameter configuration module is further configured to: Receive and set the parameters of the model to be inverted, including the fractional derivative order and the initial drug concentration distribution parameters; Receive and set algorithm parameters, including population size, maximum number of iterations, Lévy flight parameters, and number of reference point splits; Import or generate the target release curve as the optimization target.

[0045] In an optional embodiment of the present invention, the objective function evaluation module is further configured to: Construct and calculate the fitting error function, which characterizes the accuracy of parameter inversion by the root mean square error between the simulated release curve and the target release curve; A release smoothness function is constructed and calculated. The release smoothness function characterizes the smoothness of the release process by the energy term of the first derivative of the simulated release curve.

[0046] In an optional embodiment of the present invention, the multi-objective optimization module is further configured to: Initialize the population within the solution space of the model parameter set; In each generation iteration, genetic operations are performed on the current parent population to generate the offspring population; Apply random perturbations based on Levy flight to individuals in the offspring population; The parent population is merged with the perturbed offspring population, and the objective function values ​​of all individuals in the merged population are calculated. The merged population is subjected to non-dominated sorting, and environmental selection is performed based on the reference point association mechanism to select the next generation population. The iterative process is repeated until the preset termination condition is met, and the final non-dominated solution set is taken as the Pareto optimal solution set.

[0047] In an optional embodiment of the present invention, the multi-objective optimization module is further configured to: The merged population is sorted into multiple non-dominated levels by performing a non-dominated ranking. Individuals are selected into the next generation of the population in descending order of non-dominant hierarchy until the next complete hierarchy can no longer be accommodated, thus determining the critical level. Adaptive normalization is applied to the objective function values ​​of the currently selected individuals. Calculate the perpendicular distance from each individual to the line connecting each reference point, and associate each individual with the nearest reference point; The number of individuals associated with each reference point is counted. Individuals with fewer associated reference points and closest to the reference line are selected from the critical layer until the preset population size is filled.

[0048] Combination Figure 4 The system architecture diagram of the present invention is shown below. The module composition, module functions, and relationships between modules of the present invention are as follows: (1) Parameter configuration module Function: Responsible for receiving user-input control parameters and algorithm hyperparameters. Specifically includes: Model parameter settings: fractional derivative order upper and lower bounds of the search and initial concentration distribution The number of discretized nodes.

[0049] Algorithm parameter settings: Set population size N Maximum number of iterations T Levi's flight parameters and reference point segmentation number H .

[0050] Target curve selection: Import the expected ideal drug release rate curve (constant release, linearly decreasing release, nonlinear release).

[0051] Relationship with other modules: Provides the initial population and search space constraints to the subsequent "Multi-objective Optimization Module"; provides objective comparison data to the "Objective Function Evaluation Module".

[0052] (2) Model building and numerical solution module Functionality: This module includes a built-in numerical solver for a one-dimensional time-fractional diffusion equation based on Caputo fractional derivatives. It is used for physical simulations.

[0053] Operating mechanism: The finite difference method combined with a cubic B-spline function is used to process the input candidate parameters. Combination into release rate j(t) The time-varying sequence.

[0054] Relationship with other modules: Receives candidate solutions from the "Multi-Objective Optimization Module" and transmits the calculated release curve data to the "Objective Function Evaluation Module".

[0055] (3) Objective function evaluation module Function: Responsible for calculating the fitness value of candidate solutions and quantifying the quality of parameters.

[0056] This module contains two independent evaluation functions. (Fitting error): Calculate the root mean square error between the simulated release curve and the target curve.

[0057] (Release Smoothness): The energy term of the first derivative of the release rate curve is used to penalize the violent oscillations in the early stages of release.

[0058] Relationship with other modules: Receives simulation data from the "Model Building and Numerical Solution Module" and outputs... Return to the "Multi-objective Optimization Module".

[0059] (4) Multi-objective optimization module Function: Runs the improved NSGA-III-MOCS algorithm. This module combines the evolutionary mechanism of genetic algorithms with the Lévy flight strategy of cuckoo search.

[0060] Hybrid Evolution Submodule: Performs SBX crossover and polynomial mutation to produce offspring.

[0061] Lévy perturbation submodule: Apply a long-tailed random step-size perturbation conforming to the Lévy distribution to a subset of individuals, as shown in the formula. This prevents the algorithm from getting trapped in local optima.

[0062] Environment Selection Submodule: Based on the reference point mechanism, it performs non-dominated sorting and association operations to select evenly distributed Pareto optimal frontier individuals from the merged population.

[0063] Relationship with other modules: The "Modeling Module" and "Evaluation Module" are called in a loop until the iteration termination condition is met.

[0064] (5) Result Processing Module Function: Responsible for processing the final Pareto optimal solution set.

[0065] Data Export: Output the optimal parameter combination .

[0066] Graphical plotting: Plot the Pareto front and the corresponding optimal release curve comparison chart.

[0067] Relationship with other modules: Receives the final output of the optimization module and displays the results.

[0068] As the system implementation is basically similar to the method implementation, it is described in a relatively simple way. For relevant details, please refer to the description of the method implementation.

[0069] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0070] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0071] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for inverting fractional-order drug controlled-release parameters, characterized in that, The method includes: A fractional-order diffusion model describing drug release behavior is established, and the set of model parameters to be inverted is determined; the set of model parameters includes the fractional derivative order and the initial drug concentration distribution parameters. Construct a set of objective functions for evaluating the quality of parameter inversion. The set of objective functions includes at least a fitting error function for characterizing the overall difference between the simulated release curve and the target release curve, and a release smoothness function for characterizing the smoothness of the release process. Based on the improved NSGA-III-MOCS algorithm, with the goal of simultaneously optimizing the values ​​of each objective function in the set of objective functions, it iterative optimization is performed in the solution space of the model parameter set until the termination condition is met, and the Pareto optimal solution set is obtained. Equilibrium solutions are selected from the Pareto optimal solution set, and the model parameters corresponding to the equilibrium solutions are used as the controlled release parameters of the drug controlled release system.

2. The method according to claim 1, characterized in that, Construct a set of objective functions for evaluating the quality of parameter inversion, including: Construct and calculate the fitting error function, which characterizes the accuracy of parameter inversion by the root mean square error between the simulated release curve and the target release curve; A release smoothness function is constructed and calculated. The release smoothness function characterizes the smoothness of the release process by the energy term of the first derivative of the simulated release curve.

3. The method according to claim 1, characterized in that, Based on the improved NSGA-III-MOCS algorithm, with the objective of simultaneously optimizing the values ​​of each objective function in the set of objective functions, it iterative optimization is performed in the solution space of the model parameter set until the termination condition is met, obtaining the Pareto optimal solution set, including: Initialize the population within the solution space of the model parameter set; In each generation iteration, genetic operations are performed on the current parent population to generate the offspring population; Apply random perturbations based on Levy flight to individuals in the offspring population; The parent population is merged with the perturbed offspring population, and the objective function values ​​of all individuals in the merged population are calculated. The merged population is subjected to non-dominated sorting, and environmental selection is performed based on the reference point association mechanism to select the next generation population. The iterative process is repeated until the preset termination condition is met, and the final non-dominated solution set is taken as the Pareto optimal solution set.

4. The method according to claim 3, characterized in that, The merged population is subjected to non-dominated ranking, and environmental selection is performed based on the reference point association mechanism to select the next generation population, including: The merged population is sorted into multiple non-dominated levels by performing a non-dominated ranking. Individuals are selected into the next generation of the population in descending order of non-dominant hierarchy until the next complete hierarchy can no longer be accommodated, thus determining the critical level. Adaptive normalization is applied to the objective function values ​​of the currently selected individuals. Calculate the perpendicular distance from each individual to the line connecting each reference point, and associate each individual with the nearest reference point; The number of individuals associated with each reference point is counted. Individuals with fewer associated reference points and closest to the reference line are selected from the critical layer until the preset population size is filled.

5. The method according to claim 1, characterized in that, Equilibrium solutions are selected from the Pareto optimal solution set, and the model parameters corresponding to the equilibrium solutions are used as the controlled-release parameters of the drug controlled-release system, including: In the Pareto optimal solution set, the solution that achieves a balance between the two objectives of fitting error and release smoothness is selected as the balanced solution; The model parameters corresponding to the equilibrium solution are used as the controlled release parameters of the drug controlled release system.

6. A fractional-order drug controlled-release parameter inversion system, characterized in that, The system includes: The parameter configuration module is used to receive and set model parameters, algorithm parameters, and target release curves. The model building and numerical solution module is used to establish a fractional diffusion model describing drug release behavior, and to numerically solve the combination of input candidate parameters based on the fractional diffusion model, and output the simulated release curve. The objective function evaluation module is used to calculate a set of objective functions for evaluating the quality of parameter inversion based on the simulated release curve and the target release curve. The set of objective functions includes at least a fitting error function for characterizing the overall difference between the simulated release curve and the target release curve, and a release smoothness function for characterizing the smoothness of the release process. The multi-objective optimization module is used to iteratively optimize the objective function values ​​in the objective function set simultaneously based on the improved NSGA-III-MOCS algorithm until the termination condition is met, and to obtain and output the Pareto optimal solution set. The result processing module is used to receive the Pareto optimal solution set, select equilibrium solutions from the Pareto optimal solution set, and output and visualize the model parameters corresponding to the equilibrium solutions as the controlled release parameters of the drug controlled release system.

7. The system according to claim 6, characterized in that, The parameter configuration module is also used for: Receive and set the parameters of the model to be inverted, including the fractional derivative order and the initial drug concentration distribution parameters; Receive and set algorithm parameters, including population size, maximum number of iterations, Lévy flight parameters, and number of reference point splits; Import or generate the target release curve as the optimization target.

8. The system according to claim 6, characterized in that, The objective function evaluation module is also used for: Construct and calculate the fitting error function, which characterizes the accuracy of parameter inversion by the root mean square error between the simulated release curve and the target release curve; A release smoothness function is constructed and calculated. The release smoothness function characterizes the smoothness of the release process by the energy term of the first derivative of the simulated release curve.

9. The system according to claim 6, characterized in that, The multi-objective optimization module is also used for: Initialize the population within the solution space of the model parameter set; In each generation iteration, genetic operations are performed on the current parent population to generate the offspring population; Apply random perturbations based on Levy flight to individuals in the offspring population; The parent population is merged with the perturbed offspring population, and the objective function values ​​of all individuals in the merged population are calculated. The merged population is subjected to non-dominated sorting, and environmental selection is performed based on the reference point association mechanism to select the next generation population. The iterative process is repeated until the preset termination condition is met, and the final non-dominated solution set is taken as the Pareto optimal solution set.

10. The system according to claim 9, characterized in that, The multi-objective optimization module is also used for: The merged population is sorted into multiple non-dominated levels by performing a non-dominated ranking. Individuals are selected into the next generation of the population in descending order of non-dominant hierarchy until the next complete hierarchy can no longer be accommodated, thus determining the critical level. Adaptive normalization is applied to the objective function values ​​of the currently selected individuals. Calculate the perpendicular distance from each individual to the line connecting each reference point, and associate each individual with the nearest reference point; The number of individuals associated with each reference point is counted. Individuals with fewer associated reference points and closest to the reference line are selected from the critical layer until the preset population size is filled.

Images