Key Region Recognition Method, Device, Equipment and Medium Based on Multi-Objective Optimization

Abstract

The present application relates to a method, device, equipment and medium for identifying key regions based on multi-objective optimization. By obtaining a surrogate model corresponding to a target device to be designed, and randomly generating the initial positions and velocities of initial particles according to the surrogate model, design parameters and preset parameters related to the particle swarm optimization algorithm, where each particle corresponds to a parameter design region to be optimized, performing multiple iterative optimizations on the initial particle swarm, and at the same time saving the individual optimal positions and global optimal positions of each updated particle to an external archive, and solving the Pareto optimization solution according to all the individual optimal positions and global optimal positions after each historical iterative optimization, until the number of iterative optimizations meets the preset number of iterations, then obtaining a preset number of optimal particles according to the Pareto optimization solution in the external archive, that is, the parameter design region is the key region. Using this method can effectively improve the accuracy and efficiency of key region identification.

Description

Technical Field

[0001] The present application relates to the cross-technical field of engineering and computers, and in particular to a key area identification method, device, equipment and medium based on multi-objective optimization. Background Art

[0002] In large-scale projects, it is necessary to conduct scheme design in advance through experimental design methods. In order to reduce the cost of the project, etc., digital models will be constructed in advance for large-scale engineering projects (such as aircraft manufacturing). In the experimental sample space of the digital model, each indicator that affects the performance of the entity is called a key indicator, and the factors that affect the key indicators are called factors. The key indicators can be regarded as sub-models constructed by multiple factors, and the range of factor combinations that affect the performance of the entity is called the key area. Then, a response model between the key indicators and each factor can be constructed, and experimental design can be carried out in the key area through optimization algorithms to guide more accurate experiments. The original digital model obtained through mechanism analysis, mathematical derivation, etc. will have a certain error with the entity, and the entity needs to be tested to correct the original digital model.

[0003] Although the digital model is accurate, it still takes a long time to conduct experiments on the digital model, which is not conducive to the subsequent large-scale search of key areas. In order to improve efficiency, a proxy model can be constructed by sampling on the digital model. The proxy model is usually a black box function, which has no specific mathematical expression. The key area usually refers to the area in the function space that changes dramatically and has the most obvious impact on the response. Identifying the key area of ​​the proxy model is to search in the space of black box functions. A black box function refers to a function whose internal structure is unknown and whose analytical expression is unavailable. The study of such functions usually relies on limited input and output observation data.

[0004] However, black box functions are not analytic, and traditional analytical methods are difficult to apply. They need to rely on numerical approximation or random sampling techniques to determine the key areas. At the same time, the non-smoothness and nonlinear behavior of black box functions increase the difficulty of characterizing key areas. Conventional optimization or search methods are difficult to converge, and more complex algorithms need to be introduced. The search efficiency is affected by the objective function evaluation and the region division strategy. It is necessary to find a balance between global exploration and local development. In addition, the key areas are dynamic, requiring the algorithm to be sufficiently adaptable. Summary of the invention

[0005] Based on this, it is necessary to provide a key area identification method, device, equipment and medium based on multi-objective optimization that can quickly and accurately search for key areas in response to the above technical problems.

[0006] A key area identification method based on multi-objective optimization, the method comprising:

[0007] Obtain the digital model corresponding to the target device to be designed, and obtain the corresponding proxy model according to the digital model;

[0008] Obtain the design parameters related to the target device, where the design parameters include parameters in multiple dimensions and the value ranges of each parameter;

[0009] According to the proxy model, design parameters, and the preset parameters related to the particle swarm optimization algorithm, randomly generate the initial positions and velocities of the particles to construct an initial particle swarm, where each particle corresponds to a parameter design area to be optimized;

[0010] Perform multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of the particles according to the current states, individual optimal positions, and global optimal positions of the particles, evaluate the fitness of each updated particle using a multi-dimensional fitness evaluation mechanism, and mutate the updated particles under the preset mutation probability, and update the individual optimal positions and global optimal positions of the particles;

[0011] Save the individual optimal positions and global optimal positions of each updated particle to an external archive. In the external archive, solve the Pareto optimization solution according to all the individual optimal positions and global optimal positions after each historical iterative optimization, and save the solution result to the external archive;

[0012] Until the number of iterative optimizations meets the preset number of iterations, obtain the Pareto optimization solution from the external archive, obtain a preset number of optimal particles according to the Pareto optimization solution, and the parameter design area corresponding to the optimal particle is the key area, realizing the identification of the key area.

[0013] In one embodiment, when constructing the initial particle swarm:

[0014] Define the sampling space of the particles according to the value ranges of the design parameters in each dimension;

[0015] Adopt the Latin hypercube sampling method to generate multi-dimensionally uniformly distributed initial positions in the sampling space of the particles;

[0016] Randomly generate a preset number of initial particles in the sampling space of the particles according to the preset parameters related to the particle swarm optimization algorithm;

[0017] Randomly initialize the velocity of each initial particle to obtain the initial particle swarm.

[0018] In one embodiment, after generating the initial particle swarm, determine whether the initial positions of the initial particles satisfy the quantitative constraints, and adopt a repair strategy to adjust the positions of the initial particles that do not satisfy the quantitative constraints to positions that satisfy the quantitative constraints.

[0019] In one embodiment, during each iteration process, an algorithm improvement strategy is adopted to adaptively adjust the inertia weight and learning factor when updating the positions and velocities of each particle.

[0020] In one embodiment, the multi-dimensional fitness evaluation mechanism includes an information surface measure index and a gradient index;

[0021] When evaluating the fitness of each particle, the Latin hypercube sampling method is used to sample within the region represented by the particle, obtaining multiple sampling points, and calculating the function values of each sampling point;

[0022] Based on the calculation of each sampling point and function value, the information surface measure index and the gradient index are calculated, and the calculated results are used as the fitness of the corresponding particle.

[0023] In one embodiment, during the iterative optimization process of the particle swarm, according to the periodic restart strategy, at a preset period, a part of the particles are selected from the current particle swarm with a preset probability to re-initialize their positions and velocities.

[0024] In one embodiment, when solving the Pareto optimization solution based on all the individual optimal positions and the global optimal position after historical iterative optimization:

[0025] Based on the fitness, the particles corresponding to all the individual optimal positions and the global optimal position are non-dominated sorted, and the particles are divided into different front levels;

[0026] Calculate the crowding distance of each solution in the objective function, and sort the solutions in the first front in descending order according to the crowding distance;

[0027] Through the elite selection strategy, the elite solutions are selected from the sorted solution set, and the solution with the largest crowding distance is selected from the elite solutions as the optimal Pareto front solution.

[0028] The present application also provides a key area recognition device based on multi-objective optimization, and the device includes:

[0029] A surrogate model obtaining module, configured to obtain a digital model corresponding to a target device to be designed, and obtain a corresponding surrogate model according to the digital model;

[0030] A design parameter obtaining module, configured to obtain design parameters related to the target device, where the design parameters include parameters in multiple dimensions and the numerical range of each parameter;

[0031] An initial particle swarm construction module, configured to randomly generate the initial positions and velocities of particles according to the surrogate model, design parameters, and preset particle swarm optimization algorithm related parameters, and construct an initial particle swarm, where each particle corresponds to a parameter design region to be optimized;

[0032] An iterative optimization module, configured to perform multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of the particles according to the current states, individual optimal positions, and global optimal positions of the particles, evaluate the fitness of each updated particle using a multi-dimensional fitness evaluation mechanism, mutate the updated particles with a preset mutation probability, and update the individual optimal positions and global optimal positions of the particles;

[0033] A Pareto optimal solution solving module, configured to save the individual optimal positions and global optimal positions of each updated particle to an external archive. In the external archive, solve the Pareto optimal solution according to all the individual optimal positions and global optimal positions after each historical iterative optimization, and save the solution result to the external archive;

[0034] A key region identification completion module, configured to until the number of iterative optimizations meets a preset number of iterations, obtain the Pareto optimal solution from the external archive, obtain a preset number of optimal particles according to the Pareto optimal solution, and the parameter design region corresponding to the optimal particle is the key region, to realize the identification of the key region.

[0035] A computer device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0036] Obtain a digital model corresponding to a target device to be designed, and obtain a corresponding surrogate model according to the digital model;

[0037] Obtain design parameters related to the target device, where the design parameters include parameters in multiple dimensions and the value ranges of the parameters;

[0038] Randomly generate the initial positions and velocities of particles according to the surrogate model, design parameters, and preset particle swarm optimization algorithm related parameters, and construct an initial particle swarm, where each particle corresponds to a parameter design region to be optimized;

[0039] Perform multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of the particles according to the current states, individual optimal positions, and global optimal positions of the particles, evaluate the fitness of each updated particle using a multi-dimensional fitness evaluation mechanism, mutate the updated particles with a preset mutation probability, and update the individual optimal positions and global optimal positions of the particles;

[0040] Save the individual optimal positions and the global optimal position of each particle after update to an external archive. In the external archive, solve the Pareto optimization solution based on all the individual optimal positions and the global optimal position optimized in each historical iteration, and save the solution result to the external archive;

[0041] Until the number of iterative optimizations meets the preset number of iterations, obtain the Pareto optimization solution from the external archive, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, realizing the identification of the key region.

[0042] A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0043] Obtain the digital model corresponding to the target device to be designed, and obtain the corresponding surrogate model according to the digital model;

[0044] Obtain the design parameters related to the target device. The design parameters include parameters in multiple dimensions and the numerical range of each parameter;

[0045] According to the surrogate model, the design parameters, and the preset parameters related to the particle swarm optimization algorithm, randomly generate the initial positions and velocities of the particles, and construct an initial particle swarm. Among them, each particle corresponds to a parameter design region to be optimized;

[0046] Perform multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of the particles according to the current states, individual optimal positions, and global optimal positions of the particles, evaluate the fitness of each updated particle using a multi-dimensional fitness evaluation mechanism, and mutate the updated particles under the preset mutation probability, and update the individual optimal positions and the global optimal position of each particle;

[0047] Save the individual optimal positions and the global optimal position of each particle after update to an external archive. In the external archive, solve the Pareto optimization solution based on all the individual optimal positions and the global optimal position optimized in each historical iteration, and save the solution result to the external archive;

[0048] Until the number of iterative optimizations meets the preset number of iterations, obtain the Pareto optimization solution from the external archive, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, realizing the identification of the key region.

[0049] The above-mentioned key area recognition method, device, equipment and medium based on multi-objective optimization obtain the surrogate model corresponding to the target equipment to be designed, and randomly generate the initial positions and velocities of the particles according to the surrogate model, design parameters and the preset parameters related to the particle swarm optimization algorithm to construct an initial particle swarm, where each particle corresponds to a parameter design area to be optimized. The initial particle swarm is iteratively optimized multiple times, and at the same time, the individual optimal positions and the global optimal position of each updated particle are saved to the external archive, and the Pareto optimization solution is solved according to all the individual optimal positions and the global optimal position after each historical iterative optimization until the number of iterative optimizations meets the preset number of iterations. Then, a preset number of optimal particles are obtained according to the Pareto optimization solution in the external archive, and the parameter design area corresponding to the optimal particle is the key area, realizing the recognition of the key area. Using this method can effectively improve the accuracy and efficiency of key area recognition. Description of the Drawings

[0050] Figure 1 It is a schematic flowchart of the key area recognition method based on multi-objective optimization in an embodiment;

[0051] Figure 2 It is a schematic diagram of the steps in the particle swarm optimization process in an embodiment;

[0052] Figure 3 It is a structural block diagram of the key area recognition device based on multi-objective optimization in an embodiment;

[0053] Figure 4 It is an internal structure diagram of a computer device in an embodiment. Detailed Embodiments

[0054] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0055] In view of the many problems existing in the prior art when searching for key areas using surrogate models, such as Figure 1 As shown, a key area recognition method based on multi-objective optimization is provided, which specifically includes the following steps:

[0056] Step S100, obtain the digital model corresponding to the target equipment to be designed, and obtain the corresponding surrogate model according to the digital model.

[0057] Step S110, obtain the design parameters related to the target equipment, where the design parameters include parameters in multiple dimensions and the numerical ranges of the parameters.

[0058] Step S120: According to the surrogate model, design parameters, and preset parameters related to the particle swarm optimization algorithm, randomly generate the initial positions and velocities of the particles to construct an initial particle swarm. Herein, each particle corresponds to a parameter design region to be optimized.

[0059] Step S130: Conduct multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of the particles according to the current states, individual best positions, and global best positions of the particles. Use a multi-dimensional fitness evaluation mechanism to evaluate the fitness of each updated particle, and mutate the updated particles under a preset mutation probability, and update the individual best positions and global best positions of the particles.

[0060] Step S140: Save the individual best positions and global best positions of each updated particle to an external archive. In the external archive, solve the Pareto optimization solution according to all the individual best positions and global best positions after each historical iterative optimization, and save the solution result to the external archive.

[0061] Step S150: Until the number of iterative optimizations meets the preset number of iterations, obtain the Pareto optimization solution from the external archive, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, thereby realizing the identification of the key region.

[0062] In this application, first obtain the digital model corresponding to the target device to be designed, and obtain the corresponding surrogate model according to the simulation data of the digital model to achieve accurate fitting of the digital model. Characterize the key region through a multi-objective function, and then use an improved adaptive particle swarm optimization algorithm to solve the key region in the surrogate model. In this way, multiple key regions that meet the requirements of subsequent experimental design can be obtained through one solution, and then specific values of each design parameter are selected from the key regions for subsequent experiments. While ensuring the accuracy of the experiment, it greatly saves costs such as time and economy.

[0063] In step S100, the target device to be designed may include large mechanical devices such as aircraft and radars. The digital model can be an existing one, that is, obtain the corresponding digital model according to the type of the target device to be designed.

[0064] Furthermore, when obtaining the corresponding surrogate model based on the digital model, various existing algorithms can be adopted, and the algorithm type can be selected according to the current design requirements. When modeling small-sample data and uncertainty quantification is required, Gaussian process regression is generally sampled to construct the surrogate model, such as when constructing the dynamic models of engines or robots. For problems with high-dimensional data, moderate data volume, and obvious non-linear characteristics, support vector machines can be used to construct the surrogate model. For example, to simulate the relationship between complex material properties (such as thermal conductivity, elastic modulus) and process parameters.

[0065] In step S110, the design parameters of the target device to be designed are obtained, which are the design requirements of the target device. Among them, it includes various types of parameters, that is, parameters in multiple dimensions, and a value range for each parameter. Taking the target device to be designed as an aircraft or a radar as an example for illustration.

[0066] The radar system consists of multiple sub-models, and each sub-model can be transformed into a digital model. Taking the radar anti-jamming sub-model as an example, it is necessary to focus on the influence of parameters such as the signal-to-interference ratio, intermittent period, duty cycle, and interference bandwidth on the angular tracking accuracy of the radar. According to domain knowledge, the reasonable value ranges of parameters such as the signal-to-interference ratio, intermittent period, duty cycle, and interference bandwidth can be obtained. For example, for a weather radar, the signal-to-interference ratio ranges from 15 dB to 40 dB, the intermittent period ranges from 100 μs to 5 ms, the duty cycle ranges from 0.1% to 10%, and the interference bandwidth ranges from 1 MHz to 10 MHz.

[0067] In step S120, an optimized particle swarm optimization algorithm is used to solve the key area based on the surrogate model and the design parameters of the target device to be designed. Among them, the preset parameters related to the particle swarm optimization algorithm include the conventional parameters that need to be set in the particle swarm optimization algorithm, such as the number of iterations, the number of particles in the particle swarm, etc.

[0068] In this embodiment, for some problems existing in the existing particle swarm optimization algorithm and the disadvantages when directly applying it to the search for the key area. For example, in fitness evaluation, using a single or limited index is difficult to reflect the complexity of the multi-dimensional optimization goal. In terms of parameter setting, such as the inertia weight in the particle swarm optimization algorithm remains fixed and cannot be dynamically adjusted according to different stages, which limits the search and balance performance. When dealing with complex constraint conditions, using simple penalty functions or position adjustment methods cannot effectively meet the constraint requirements. The archive management and elite strategy are simple, lacking non-dominated sorting and crowding degree calculation, which affects the quality and diversity of the non-dominated solution set. At the same time, the maintenance of population diversity is insufficient, which easily causes the population to converge prematurely to the local optimal solution, and there is a lack of search methods for hyper-rectangular regions. That is to say, the existing particle swarm optimization algorithm cannot be directly applied to the search for the key area.

[0069] Further explanations are provided here. The key region actually corresponds to multiple feasible design solutions. It can be understood that the design solutions of the device are actually specific values of numerous relevant parameters. A good design solution can meet various requirements while also having good performance. During the preliminary design stage, only the selectable ranges of the relevant parameters can be given, which means there are countless design solutions. The key region refers to further determining a smaller range within the selectable ranges of the parameters. In fact, this range also includes multiple values. Then, different values of the parameters are selected within the key region according to the space-filling design method, so as to obtain multiple design solutions with better performance and meeting the constraints.

[0070] Further explanations are provided here. The key region actually corresponds to multiple feasible design solutions. The design solutions of the device can be regarded as composed of specific value combinations of numerous relevant parameters. An excellent design solution should not only meet various requirements but also have good performance. In the initial stage of design, usually only the selectable ranges of the parameters can be given, which means there may be countless design solutions. The so-called key region refers to further determining a smaller range within the selectable ranges of the parameters. This range still contains multiple possible parameter combinations. In the key region, by using the space-filling design method to select different parameter values, multiple design solutions with excellent performance and meeting the constraint conditions can be obtained.

[0071] Furthermore, in the optimized particle swarm optimization algorithm, a particle coding method is proposed to characterize the regions in the numerical ranges of the design parameters, enabling it to adaptively adjust.

[0072] In this embodiment, when constructing the initial particle swarm: Define the sampling space of the particles according to the numerical ranges of the design parameters in each dimension, use the Latin hypercube sampling method to generate the initial positions with multi-dimensional uniform distribution in the sampling space of the particles, randomly generate a preset number of initial particles in the sampling space of the particles according to the preset relevant parameters of the particle swarm optimization algorithm, and randomly initialize the velocity of each initial particle to obtain the initial particle swarm.

[0073] Specifically, assume there is a d dimensional black-box function , where is the decision variable vector. Since the analytical expression of the function cannot be obtained, only by sampling the input can the corresponding function values be obtained. Based on the black-box function, the particles are designed and initialized. In the high-dimensional space, each particle is represented as a hyper-rectangular region, and its position vector is defined as:

[0074] (1)

[0075] In formula (1), is the particle i at the starting coordinate of the d -th dimension, is the window size (region length) of this dimension, d is the dimension of the problem. The velocity vector of the particle is defined as:

[0076] (2)

[0077] In formula (2), is the velocity of the particle i at the starting coordinate of the d -th dimension, is the velocity of the window size of the d -th dimension.

[0078] In this embodiment, in order to ensure the uniformity of the initial particle distribution and cover the entire search space, Latin Hypercube Sampling (LHS) is adopted to uniformly generate the starting positions and window sizes of the particles within the range of each dimension. For the j -th dimension, the starting position and window size are initialized as:

[0079] (3)

[0080] (4)

[0081] In formulas (3) and (4), and are respectively the lower bound and upper bound of the j -th dimension (i.e., the value range of the parameter), and are the minimum and maximum values of the window size, U ( a , b ) represents a uniform distribution on the interval a , b .

[0082] In this embodiment, after generating the initial particle swarm, it is judged whether the initial positions of the initial particles satisfy the quantitative constraints, and a repair strategy is adopted to adjust the positions of the initial particles that do not satisfy the quantitative constraints to positions that satisfy the quantitative constraints.

[0083] Specifically, assuming that the constraints are known, the quantitative constraints are the mathematical relationships between the factors of each dimension (i.e., the design parameters mentioned above), that is, it is necessary to make the particles satisfy the constraints during initialization, and also need to satisfy the constraints during subsequent iterations and mutations.

[0084] Specifically, the repair strategy is to re-initialize the particles that do not meet the constraints and force them to meet the constraints.

[0085] Furthermore, the constraints are divided into simple linear constraints and complex non-linear constraints. When generating the initial particle swarm, solve the constraint satisfaction for the simple linear constraints to obtain a reduced search space, and check the particles obtained after initialization to verify whether they meet all the simple linear constraint conditions. When iterating to t the i +1 generation, if the particle j dimensional position or window size exceeds the boundary, the boundary correction is performed in the following way:

[0086] (5)

[0087] (6)

[0088] In formula (5), and represent the minimum and maximum values of the value range of the j th dimension.

[0089] For complex constraints and particles that do not meet the above simple constraints, a penalty term is imposed in the fitness calculation to reduce the priority of this solution in the optimization process. For particles that do not meet the constraints, randomly regenerate the position parameters of the particles so that they are within the allowed region; dynamically adjust its position parameters and to avoid falling into the region that does not meet the constraints:

[0090] (7)

[0091] In formula (7), is the penalty coefficient, usually taking a large positive value, indicates that a penalty term is added when the inequality constraint is violated, p is the number of inequality constraints, the definition of refers to formula (1), represents the objective function without considering the constraints,

[0092] In other embodiments, in addition to using Latin Hypercube Sampling (LHS), other methods such as Sobol sequence sampling or random uniform sampling can also be adopted to generate the positions of the initial particle swarm. These methods further enhance the diversity of the particle swarm and the global search ability of the optimization algorithm by providing different particle distribution characteristics, providing better initial conditions for complex optimization problems.

[0093] In step S130, during the iterative optimization process, it generally includes updating the particle position and velocity, calculating the fitness of the updated particle, obtaining the individual optimal position of the updated particle and the global optimal particle in the particle swarm to assist the particle in updating in the next iterative optimization.

[0094] In this embodiment, in each iteration process, in order to improve the performance of the algorithm, an algorithm improvement strategy is also adopted to adaptively adjust the inertia weight and learning factors 、 during the update of each particle.

[0095] Specifically, the inertia weight is gradually adjusted by the number of iterations t to balance the global exploration and local development capabilities. The adjustment formula is:

[0096] (8)

[0097] In formula (8), and are respectively the maximum and minimum values of the inertia weight, is the maximum number of iterations, t is the current number of iterations, is a small value to avoid function divergence.

[0098] Specifically, the learning factors 、 are also dynamically adjusted by the number of iterations t , set the initial values and , and adjust according to the learning factor adjustment strategy. The dynamic adjustment of the learning factors and the learning factor enhances the dependence of the particle on the individual optimal and global optimal, improving the optimization effect.

[0099] Furthermore, the following formula is used to adjust the learning factor :

[0100] (9)

[0101] The following formula is used to adjust the learning factor Make adjustments:

[0102] (10)

[0103] In formulas (9) and (10), and are the adjustment amplitudes,

[0104] In this embodiment, in each iteration process, after the weight adaptive adjustment is performed, the positions and velocities of each particle are updated.

[0105] Specifically, the velocity and position updates of the particles follow the basic principles of particle swarm optimization, but are adjusted for high-dimensional and region representations. For particle i , its velocity and position update formulas in the j th dimension are respectively:

[0106] (11)

[0107] (12)

[0108] In formulas (11) and (12), is the inertia weight, and are the learning factors, and are random numbers uniformly distributed between [0, 1], is the historical optimal position of particle i in dimension j and is the global optimal position in dimension j .

[0109] In this embodiment, after the particles in the particle swarm are updated, the fitness of each particle is calculated for evaluation. To comprehensively evaluate the region where the particle is located, relevant features of the fitness value surface are introduced: the information surface measure and the gradient measure. These two indicators respectively measure the distribution diversity and the degree of change of the objective function values within the region. When evaluating the fitness of each particle, the Latin hypercube sampling method is used to sample the positions, obtaining multiple sampling points, and the function values of each of the sampling points are calculated. The information surface measure index and the gradient index are calculated based on each sampling point and the function value, and the calculated results are used as the fitness of the corresponding particle.

[0110] Specifically, for each particle, Latin hypercube sampling is performed within the defined hyper-rectangular region according to the specified number of sampling points to evaluate the quality of the region. The sampling method still uses Latin hypercube sampling, and the range in each dimension is:

[0111] (13)

[0112] In formula (13), represents the window size of the particle i in the j th dimension.

[0113] Generate N sampling points , and calculate the corresponding function values . Based on these sampling points and function values, calculate the information surface measure and gradient as the multi-objective fitness of the particle.

[0114] Furthermore, when calculating the information surface measure index in the calculation space, the information surface is defined as a triple , X represents the set of all possible solutions in the solution space, N is defined as the neighborhood relationship on X , describing the proximity, distance, or reachability between solutions, t :[[]] X × X →[0,1] represents the random information function, which is used to give the relative superiority and inferiority probability between any pair of solutions in the solution space. For any pair of solutions and , represents the probability that solution is superior to solution . Using the information function t , the information matrix can be constructed. The function t is usually assumed to be:

[0115] (14)

[0116] The information surface measure is obtained by calculating the distance between the problem information surface vector and the reference information surface vector . It is defined as follows:

[0117] (15)

[0118] In formula (15), represents the information surface vector of problem p, which is composed of the relevant terms of the information matrix M extracted from the solution space structure of the problem and is used to describe the relative solution structure of the problem; is the information surface vector of the reference surface, representing the structural information of the ideal solution space; n is the number of elements in the information vector, usually , where is the number of solutions in the solution space. The position of the global optimal point of the reference surface needs to coincide with the estimated optimal point of the problem surface. D N-dimensional sphere function exactly meets the requirements. The sphere function can be translated so that the optimal solution is located at any position in the search space, thus coinciding with the estimated optimal solution of the problem surface. Therefore, the reference function takes D N-dimensional sphere function.

[0119] When the value is large, it indicates that there is a large difference between the solution space of the problem and the ideal reference surface, which means the search path is more rugged and complex, and the optimization difficulty increases; on the contrary, when the distance is small, the solution space is relatively smooth and the search difficulty is low.

[0120] Furthermore, when calculating the gradient index in the computational space, in a multi-dimensional search space, the gradient, as a key index for evaluating the local change rate, is used to evaluate the steepness of the region and the fitness change to determine whether the region is a key region. In a multi-dimensional search space with a fitness function 𝑓, starting from the initial point x ( t ), walking with T equal step sizes, a sequence of points x ( t ), x ( t + 1), …, x ( t + T ) is obtained. During this process, the gradient norm between adjacent points can be estimated by the following formula:

[0121] (16)

[0122] In formula (16), is the Euclidean distance between points and , and through T steps of walking, T gradient estimates can be obtained.

[0123] Based on these gradient values, multiple indices can be defined to describe the local gradient characteristics in the search space. First, the average estimated gradient within the walk represents the average gradient magnitude between adjacent points, and its definition is:

[0124] (17)

[0125] In the calculation of formula (14), each The absolute value is used to quantify the steepness and avoid the cancellation of positive and negative slopes, so as to better evaluate the overall slope within the region. If the wandering samples cover enough search space, then can be regarded as an estimate of the gradient of adjacent points in the entire search space. Secondly, the standard deviation of the gradient relative to the mean is used to measure the degree of gradient change on the wander, and its definition is as follows:

[0126] (18)

[0127] The maximum gradient within the wander represents the maximum fitness mutation between adjacent points:

[0128] (19)

[0129] When is significantly greater than , it may indicate the existence of surface structures with obvious changes such as cliffs, steep valleys or spikes. When and are both high, it indicates that the ruggedness of the landscape is large and the fitness changes violently.

[0130] To ensure that the calculation of the gradient is not affected by the range of fitness values or the domain of the function, the fitness difference and the distance between points can be normalized. The normalized gradient estimation formula is:

[0131] (20)

[0132] In formula (20), and are the maximum and minimum fitness values during the wander process respectively, and are the boundaries of the i -dimensional search space. This normalization process can eliminate the interference of the fitness value range and the spatial scale on the gradient calculation, making the gradient values in different regions comparable.

[0133] In other embodiments, in addition to using the above information surface measure and gradient index, other indexes such as the number of extreme points can be introduced. By measuring the distribution characteristics of extreme points in the function space, these new indexes can enrich the fitness evaluation function, thus more comprehensively reflecting the optimization effect of particles and improving the reliability and applicability of the optimization results.

[0134] Furthermore, according to the preset mutation probability, mutate the positions of some of the updated particles, while keeping the positions of the other part of the particles unchanged.

[0135] In this embodiment, the particles update their individual optimal positions according to the fitness function. The global optimal position is selected from a set of non-dominated solutions maintained by the external archive, and the solutions in the external archive are updated to store the current set of non-dominated solutions.

[0136] In step S140, to save the non-dominated solution set, an external archive mechanism is introduced. In each iteration, new non-dominated solutions are added to the archive, and the solutions dominated by the new solutions are removed. To prevent the archive from becoming too large, a maximum capacity of the archive is set. When the archive capacity exceeds this value, the solutions in the archive are sorted according to the crowding distance, and the solutions with smaller crowding distances are removed to maintain the diversity of the solutions.

[0137] In this embodiment, when solving the Pareto optimization solution based on all the individual optimal positions and the global optimal position optimized according to historical iterations: according to the fitness, the particles corresponding to all the individual optimal positions and the global optimal position are non-dominated sorted, and the particles are divided into different front levels. The crowding distance of each solution in the objective function is calculated, the solutions in the first front are sorted in descending order according to the crowding distance, and through the elite selection strategy, the elite solutions are selected from the sorted solution set, and the solution with the largest crowding distance is selected as the optimal Pareto front solution.

[0138] Specifically, in the external archive, to solve the Pareto optimization solution, first, according to all the individual optimal positions and the global optimal position optimized in historical iterations, the corresponding particles are non-dominated sorted, and the particles are divided into different front levels. Then, the crowding distance of each solution in the objective space is calculated, and selection is made according to the non-dominated sorting level and the crowding distance, and finally the Pareto optimization solution is obtained. Among them, non-dominated sorting is used to stratify the particles and identify their optimization priorities. The crowding distance calculation is used to evaluate the sparsity of the solutions and maintain the diversity. The particles are finally sorted in the order of priority of levels and secondary priority of crowding distance, the external archive is updated, and the redundant solutions are removed.

[0139] Furthermore, to handle the multi-objective optimization problem (maximization objective), a non-dominated sorting method based on Pareto optimality is adopted. For particle p and particle q , if the following conditions are met, it is said that particle p dominates particle q : for all objective functions m , there is ; there is at least one objective function m , such that . In fact, the multi-objective optimization problem is to solve the multi-objectives for the two proposed indicators, namely objective 1: maximizing the information surface measure, and 2: maximizing the gradient.

[0140] Based on the above definitions, non-dominated sorting is performed on all particles, dividing them into different front levels. Then, the crowding distance of the particles in each front level is calculated to evaluate the sparsity of the particles in the objective space and is used to maintain the diversity of the solutions. For the particles in a certain front, the crowding distance is calculated including: for each objective function m , the particles are sorted in ascending order according to the fitness value. For the sorted particles, the crowding distances of the first and the last particles are set to infinity, that is:

[0141] (21)

[0142] For the intermediate particles, the crowding distance is calculated as:

[0143] (22)

[0144] In formula (22), and respectively represent the objective functions of the nearest particles on both sides of the m th particle on the objective function i , and respectively represent the maximum and minimum values of all particles on the objective function m .

[0145] The total crowding distance of each particle is the sum of its distances on all objective functions:

[0146] (23)

[0147] Then elitist selection is performed. Specifically, first, the particles are sorted according to the non-dominated sorting levels. If the number of Pareto-optimal solutions in the external archive exceeds the preset capacity limit, further screening is required. For the particles at the same level, they are sorted in descending order according to the crowding distance. The particles with a large crowding distance are distributed in the sparse region and are preferentially retained; the particles with a small crowding distance are distributed in the dense region and are preferentially removed. Starting from the particles with the lowest priority, they are removed until the capacity of the Pareto-optimal solutions in the external archive meets the requirements.

[0148] In this embodiment, during each iteration process, when updating the velocity of the particles, the selection of the global optimal position is crucial for the performance of the algorithm. In this algorithm, an elitist strategy is adopted, and the solution with a larger crowding distance is selected from the first front (non-dominated solution set) of the external archive as the global optimal position, which helps to maintain the diversity of the solutions and avoid premature convergence.

[0149] In this embodiment, to prevent the particle swarm from falling into a local optimum and increase the diversity of the population, a periodic restart strategy is introduced. During the iterative optimization of the particle swarm, according to the periodic restart strategy, at a preset period, a part of the particles in the current particle swarm are selected with a preset probability to re-initialize their positions and velocities.

[0150] In step S150, according to requirements, the particles in the preset positions before sorting can be selected from the external archive as the final key regions for output. And in each key region, specific numerical values of each dimension parameter are selected to generate a device design scheme.

[0151] As Figure 2 shown, it is a schematic diagram of the steps of the particle swarm optimization process.

[0152] In the above key region recognition method based on multi-objective optimization, by adopting an improved particle swarm optimization algorithm, the key regions in the surrogate model can be effectively searched. After obtaining the design parameters and their ranges of the target device, and the surrogate model obtained from the target device, an initial population is generated by randomly initializing the initial positions and velocities of each particle. During the initialization process, if the initial position of a particle does not meet the quantitative constraints, a repair strategy is applied to adjust it to the feasible region. Subsequently, the algorithm updates the weights of the particles through an adaptation strategy, and in each round of iteration, adjusts their positions and velocities according to the fitness calculation including the penalty function to ensure that the generated solutions meet all constraint conditions while optimizing the objectives.

[0153] During the optimization process, the algorithm determines whether to perform position mutation on a particle according to the mutation probability. If the mutation condition is not met, the current position remains unchanged. After each iteration ends, the individual best solution and the global best solution of the particle are updated, and the custody information of these solutions is saved in the external archive, ensuring the stability and accuracy of the results. In addition, to further improve the exploration ability of the algorithm, a non-dominated sorting and elite selection strategy is introduced in the flowchart, and the Pareto solution set is updated by the feasibility priority method, so that the algorithm shows better solution set quality in multi-objective optimization problems.

[0154] As the number of iterations increases, the algorithm adopts a periodic restart strategy to prevent the algorithm from falling into a local optimum and ensure the diversity of the solution set. After reaching the set number of iterations, the Pareto optimal solutions are extracted from the external archive, and finally the global optimization result is output.

[0155] This method characterizes regions by proposing a new particle coding method, enabling it to adaptively adjust. Meanwhile, by introducing a multi-dimensional fitness evaluation mechanism, it conducts multi-objective fitness evaluation by integrating two dimensions, namely the information surface measure and the gradient, comprehensively reflecting the optimization effect and enhancing the diversity and comprehensiveness of the optimization results. In this method, a dynamic parameter adjustment strategy is designed to dynamically adjust the values of the inertia weight, cognitive factor, and social factor according to the iteration process, balancing the global search and local search capabilities and enhancing the convergence speed and search range of the algorithm. Combining the archive management and elite strategy of non-dominated sorting and crowding degree calculation to maintain a high-quality and diverse non-dominated solution set, improving the overall performance of the optimization algorithm. Introducing diversity and exploratory evaluation indicators, dynamically evaluating and maintaining population diversity by calculating the variance, coverage radius, and uniform distribution indicators of the population, preventing the particle swarm from prematurely converging to a local optimal solution, ensuring comprehensive coverage of the search space and the continuous exploration ability of the optimization process. Finally, adding in-depth analysis to the fitness evaluation, using the local minimum search algorithm to count the number of extreme points in the optimization region, further evaluating the diversity and complexity of the optimization objectives, and providing a deeper analysis basis for the fitness evaluation. Through these improvements, this method can effectively solve the shortcomings in the existing technology and improve the application effect of the multi-objective optimization algorithm in complex problems.

[0156] It should be understood that although Figure 1 the steps in the flowchart of Figure 1 are shown in sequence according to the arrows, these steps do not necessarily execute in the order indicated by the arrows. Unless otherwise clearly stated in this article, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover,

[0157] In one embodiment, as Figure 3 shown, a key region recognition device based on multi-objective optimization is provided, including: a surrogate model obtaining module 200, a design parameter obtaining module 210, an initial particle swarm construction module 220, an iterative optimization module 230, a Pareto optimal solution solving module 240, and a key region recognition completion module 250, where:

[0158] The surrogate model obtaining module 200 is configured to obtain a digital model corresponding to a target device to be designed and obtain a corresponding surrogate model according to the digital model;

[0159] A design parameter acquisition module 210 is configured to acquire design parameters related to the target device. The design parameters include parameters in multiple dimensions and the numerical ranges of the respective parameters.

[0160] An initial particle swarm construction module 220 is configured to randomly generate the initial positions and velocities of particles and construct an initial particle swarm according to the surrogate model, the design parameters, and the parameters related to the preset particle swarm optimization algorithm. Each particle corresponds to a parameter design area to be optimized.

[0161] An iterative optimization module 230 is configured to perform multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of the particles according to the current states, individual optimal positions, and global optimal positions of the particles, evaluate the fitness of each updated particle by using a multi-dimensional fitness evaluation mechanism, mutate the updated particles under a preset mutation probability, and update the individual optimal positions and global optimal positions of the particles.

[0162] A Pareto optimal solution solving module 240 is configured to save the individual optimal positions and global optimal positions of the updated particles to an external archive. In the external archive, solve the Pareto optimal solution according to all the individual optimal positions and global optimal positions after historical iterative optimizations, and save the solution result to the external archive.

[0163] A critical area identification completion module 250 is configured to, until the number of iterative optimizations meets the preset number of iterations, obtain the Pareto optimal solution from the external archive, obtain a preset number of optimal particles according to the Pareto optimal solution, and the parameter design area corresponding to the optimal particles is the critical area, thereby realizing the identification of the critical area.

[0164] For the specific limitations on the critical area identification device based on multi-objective optimization, reference can be made to the limitations on the critical area identification method based on multi-objective optimization in the foregoing text, which will not be elaborated herein. Each module in the above critical area identification device based on multi-objective optimization can be implemented in whole or in part by software, hardware, and their combination. The above modules can be embedded in the processor in the computer device in the form of hardware or be independent of the processor, or can be stored in the memory in the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0165] In one embodiment, a computer device is provided. The computer device can be a terminal, and its internal structure diagram can be as Figure 4As shown in the figure. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it realizes a key area recognition method based on multi-objective optimization. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer covering the display screen, or a button, a trackball, or a touchpad provided on the outer shell of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0166] Those skilled in the art can understand that Figure 4 the structure shown in the figure is only a block diagram of some structures related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0167] In one embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory. When the processor executes the computer program, the following steps are implemented:

[0168] Obtain a digital model corresponding to the target device to be designed, and obtain a corresponding surrogate model according to the digital model;

[0169] Obtain design parameters related to the target device. The design parameters include parameters in multiple dimensions and the value ranges of each parameter;

[0170] According to the surrogate model, design parameters, and parameters related to the preset particle swarm optimization algorithm, randomly generate the initial positions and velocities of particles, and construct an initial particle swarm. Among them, each particle corresponds to a parameter design area to be optimized;

[0171] Perform multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of each particle according to the current state, individual optimal position, and global optimal position of each particle. Use a multi-dimensional fitness evaluation mechanism to evaluate the fitness of each updated particle, and mutate the updated particles under a preset mutation probability, and update the individual optimal positions and global optimal positions of each particle;

[0172] Save the individual optimal positions and the global optimal position of each updated particle to an external archive. In the external archive, solve the Pareto optimization solution based on all the individual optimal positions and the global optimal position optimized in each historical iteration, and save the solution result to the external archive;

[0173] Until the number of iterative optimizations meets the preset number of iterations, obtain the Pareto optimization solution from the external archive, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design area corresponding to the optimal particles is the key area, and the identification of the key area is realized.

[0174] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0175] Obtain the digital model corresponding to the target device to be designed, and obtain the corresponding surrogate model according to the digital model;

[0176] Obtain the design parameters related to the target device. The design parameters include parameters in multiple dimensions and the numerical range of each parameter;

[0177] According to the surrogate model, the design parameters, and the preset parameters related to the particle swarm optimization algorithm, randomly generate the initial positions and velocities of the particles, and construct an initial particle swarm. Among them, each particle corresponds to a parameter design area to be optimized;

[0178] Perform multiple iterative optimizations on the initial particle swarm. In each iteration process, update the positions and velocities of the particles according to the current states, individual optimal positions, and global optimal positions of the particles, evaluate the fitness of each updated particle using a multi-dimensional fitness evaluation mechanism, and mutate the updated particles with a preset mutation probability, and update the individual optimal positions and the global optimal position of each particle;

[0179] Save the individual optimal positions and the global optimal position of each updated particle to an external archive. In the external archive, solve the Pareto optimization solution based on all the individual optimal positions and the global optimal position optimized in each historical iteration, and save the solution result to the external archive;

[0180] Until the number of iterative optimizations meets the preset number of iterations, obtain the Pareto optimization solution from the external archive, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design area corresponding to the optimal particles is the key area, and the identification of the key area is realized.

[0181] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0182] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0183] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the method of the present application should be subject to the appended claims.

Claims

1. A key area identification method based on multi-objective optimization, characterized in that: The method comprises: Obtaining a digital model corresponding to the target device to be designed, and obtaining a corresponding proxy model based on the digital model; Acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; According to the proxy model, the design parameters and the preset particle swarm optimization algorithm related parameters, the initial position and speed of the particles are randomly generated to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; The initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. An algorithm improvement strategy is used to adaptively adjust the inertia weight and learning factor when updating the position and speed of each particle. A multi-dimensional fitness evaluation mechanism is used to evaluate the fitness of each updated particle, and the updated particles are mutated under a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. The updated individual optimal position and the global optimal position of each particle are saved in an external archive, in which a Pareto optimal solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved in the external archive; Until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, so as to realize the identification of the key region.

2. The key area identification method based on multi-objective optimization according to claim 1 is characterized in that: When constructing the initial particle swarm: Define the sampling space of particles according to the numerical range of design parameters in each dimension; The Latin hypercube sampling method is used to generate multi-dimensional uniformly distributed initial positions in the particle sampling space; According to the preset particle swarm optimization algorithm related parameters, a preset number of initial particles are randomly generated in the particle sampling space; The velocity of each initial particle is randomly initialized to obtain the initial particle group.

3. The key area identification method based on multi-objective optimization according to claim 2 is characterized in that: After the initial particle group is generated, it is determined whether the initial position of each initial particle satisfies the quantitative constraint, and a repair strategy is adopted to adjust the position of the initial particle that does not satisfy the quantitative constraint to a position that satisfies the quantitative constraint.

4. The key area identification method based on multi-objective optimization according to claim 3 is characterized in that: The multi-dimensional fitness evaluation mechanism includes information surface measurement indicators and gradient indicators; When evaluating the fitness of each particle, a Latin hypercube sampling method is used to perform sampling in the area represented by the particle to obtain a plurality of sampling points, and a function value of each sampling point is calculated; According to the sampling points and function values, the information surface measurement index and the gradient index are calculated, and the calculated results are used as the fitness of the corresponding particles.

5. The key area identification method based on multi-objective optimization according to any one of claims 1 to 4, characterized in that: In the process of iterative optimization of the particle swarm, according to the periodic restart strategy, some particles are selected from the current particle swarm with a preset probability to reinitialize the position and speed at a preset period.

6. The key area identification method based on multi-objective optimization according to claim 5 is characterized in that: When solving the Pareto optimization solution based on all individual optimal positions and the global optimal position after historical iterative optimization: According to the fitness, all particles corresponding to the individual optimal positions and the global optimal position are non-dominated and sorted, and the particles are divided into different frontier levels; Calculate the crowding distance of each solution in the objective function, and sort the solutions in the first frontier in descending order according to the crowding distance; Through the elite selection strategy, the elite solution is selected from the sorted solution set, and the solution with the largest congestion distance is selected from the elite solution as the optimal Pareto front solution.

7. A key area identification device based on multi-objective optimization, characterized in that: The device comprises: The proxy model obtaining module is used to obtain the digital model corresponding to the target device to be designed, and obtain the corresponding proxy model according to the digital model; A design parameter acquisition module, used to acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; An initial particle swarm construction module is used to randomly generate initial positions and velocities of particles according to the proxy model, design parameters and preset particle swarm optimization algorithm related parameters, and construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; An iterative optimization module is used to perform multiple iterative optimizations on the initial particle swarm. In each iterative process, the position and velocity of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. An algorithm improvement strategy is used to adaptively adjust the inertia weight and learning factor when updating the position and velocity of each particle. A multi-dimensional fitness evaluation mechanism is used to evaluate the fitness of each updated particle, and the updated particles are mutated under a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. A Pareto optimization solution solving module is used to save the individual optimal position and the global optimal position of each particle after update to an external archive, in which the Pareto optimization solution is solved according to all the individual optimal positions and the global optimal positions after each historical iteration optimization, and the solution result is saved to the external archive; The key area identification completion module is used to obtain a Pareto optimization solution from the external archive until the number of iterative optimizations meets a preset number of iterations, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design area corresponding to the optimal particle is the key area, so as to realize the identification of the key area.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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