Multi-target multi-mode optimization method and device, electronic equipment and storage medium

Abstract

The invention provides a multi-target multi-mode optimization method and device, electronic equipment and a storage medium, and relates to the technical field of model optimization. The method comprises the steps that sampling and numerical solution are conducted on an optimization target model, and a training set is obtained; training a neural network model based on the training set to obtain an agent model, the agent model being used for performing behavior prediction on the optimization target model; performing multi-modal hyper-parameter adjustment on a preset optimization algorithm based on the proxy model and the training set; and accessing the optimization algorithm to the optimization target model for operation to generate an optimization result. According to the method and the device, the problem of low efficiency of multi-target multi-mode optimization in related technologies is solved.

Description

Technical Field

[0001] This application relates to the field of model optimization technology, and more specifically, to a multi-objective multi-model optimization method, apparatus, electronic device, and storage medium. Background Technology

[0002] In engineering simulation design and optimization, there is a problem of optimizing black-box functions. For example, in the engineering simulation design and optimization of hollow anti-resonant optical fibers, there are a large number of partial differential equations and finite element calculations, and finally numerical calculations are performed in a geometric region. This function is often highly complex, and its internal continuity and gradient information are unknown. It is a black-box function, and the time to solve a single solution is often in minutes or hours. Its optimization is called expensive optimization.

[0003] Existing technologies face challenges in parameter optimization for such problems: traditional ergonomic methods suffer from enormous computational costs due to high-dimensional spaces, while branch-and-bound methods are limited by their small search range in the parameter space. Given the rapid development of optimization algorithms and neural networks, researchers have begun to explore these methods for parameter optimization. However, these methods still have shortcomings. For example, optimization algorithms require numerous iterations and runs to find the optimal solution, while neural networks require vast amounts of data to accurately predict the problem. Furthermore, determining the hyperparameters of neural networks and optimization algorithms is often based on prior experience, while the internal information of black-box functions is unknown, increasing the cost of hyperparameter tuning. Ultimately, optimizing hollow antiresonant optical fibers using neural networks or optimization algorithms requires a significant amount of computation.

[0004] Furthermore, regardless of whether the solution is based on a large amount of pre-given training data or a large number of iterations are given when using optimization algorithms, the data acquisition method itself already takes values ​​at equal intervals in the parameter space, and may even encrypt the data multiple times in the excellent range. Superimposing optimization algorithms on such data is very likely to result in an overly fine-scale final optimization result. The size of optical fibers is usually in the micrometer or nanometer range, and their numerical accuracy is limited by the controllable precision of the manufacturing process. Therefore, over-optimization may waste computational resources. In short, using algorithms for parameter optimization may ultimately require a considerable or even greater number of computations, with the final result being close to or slightly better than traditional optimization methods, resulting in low efficiency of existing methods for multi-objective multi-mode optimization.

[0005] As can be seen from the above, the problem of how to improve the efficiency of multi-objective and multi-mode optimization still needs to be solved. Summary of the Invention

[0006] This application provides a multi-objective, multi-mode optimization method, apparatus, electronic device, and storage medium, which can solve the problem of low efficiency in related technologies. The technical solutions are as follows:

[0007] According to one aspect of this application, a multi-objective, multi-mode optimization method is characterized by comprising:

[0008] The training set is obtained by sampling and numerically solving the target model for optimization.

[0009] The neural network model is trained based on the training set to obtain a proxy model, wherein the proxy model is used to predict the behavior of the optimization target model;

[0010] Based on the surrogate model and the training set, multimodal hyperparameters are adjusted according to a preset optimization algorithm;

[0011] The optimization algorithm is then fed into the target model for computation to generate optimization results.

[0012] According to one aspect of this application, a multi-objective, multi-mode optimization device is characterized by comprising:

[0013] The sampling module is used to sample and numerically solve the target model for optimization to obtain a training set.

[0014] The training module is used to train the neural network model based on the training set to obtain a proxy model, wherein the proxy model is used to predict the behavior of the optimization target model;

[0015] The adjustment module is used to adjust the multimodal hyperparameters based on the surrogate model and the training set for a preset optimization algorithm;

[0016] The optimization module is used to input the optimization algorithm into the optimization target model for calculation and generate optimization results.

[0017] In one exemplary embodiment, the sampling module includes:

[0018] A model building unit is used to build a corresponding geometric model for the optimization target model;

[0019] The constraint unit is used to construct constraints based on the topological consistency of the geometric model, and to solve the geometric model based on the constraints to obtain a solution model;

[0020] The sampling unit is used to sample data from the solution model to obtain training set data.

[0021] In one exemplary embodiment, the training module includes:

[0022] A function construction unit is used to obtain a neural network model and construct a scoring function for the birefringence objective function and the minimum loss objective function of the neural network model. The scoring function is used to evaluate the performance of the neural network model.

[0023] The training unit is used to train the neural network model based on the training set and the scoring function until the scoring function determines that the neural network model has been trained and a surrogate model is obtained.

[0024] In one exemplary embodiment, the training method for training the neural network model based on the training set and the scoring function is the Levin Bergogmarquard method.

[0025] In one exemplary embodiment, the adjustment module includes:

[0026] Clustering unit, used to cluster and distinguish the modalities in the proxy model based on the training set, to obtain at least one clustering interval;

[0027] The determination unit is used to determine each of the clustering intervals based on the proxy model, and to determine the target interval in each of the clustering intervals;

[0028] The hyperparameter determination unit is used to determine the hyperparameters and the actual number of evaluations of the optimization algorithm in the target interval based on the surrogate model and the preset optimization algorithm, and to determine the hyperparameters of the optimization algorithm.

[0029] In one exemplary embodiment, the clustering unit includes:

[0030] Elbow function subunit, used to calculate the number of clusters in the surrogate model based on the elbow function;

[0031] The clustering subunit is used to cluster the training set according to the number of clusters based on the clustering algorithm, and to obtain the cluster centers and the corresponding clustering intervals of each cluster center.

[0032] In an exemplary embodiment, the determination unit includes:

[0033] The dotting subunit is used to repeatedly dot each of the clustering intervals based on the proxy model to obtain the data points corresponding to each clustering interval.

[0034] The decision function subunit is used to construct a decision function based on the number of data points, mean, and variance corresponding to each clustering interval.

[0035] The determination subunit is used to determine whether each clustering interval is a peak region based on the decision function, and to determine the clustering interval corresponding to the peak region as the target interval.

[0036] According to one aspect of this application, an electronic device includes at least one processor and at least one memory, wherein computer-readable instructions are stored on the memory; the computer-readable instructions are executed by one or more of the processors to cause the electronic device to implement the multi-objective multi-mode optimization method as described above.

[0037] According to one aspect of this application, a storage medium stores computer-readable instructions thereon, which are executed by one or more processors to implement the multi-objective, multi-mode optimization method as described above.

[0038] According to one aspect of this application, a computer program product includes computer-readable instructions stored in a storage medium, wherein one or more processors of an electronic device read the computer-readable instructions from the storage medium, load and execute the computer-readable instructions, causing the electronic device to implement the multi-objective multi-mode optimization method as described above.

[0039] The beneficial effects of the technical solution provided in this application are:

[0040] In the above technical solution, by introducing an optimization algorithm based on a surrogate model, the training set is used to train the neural network model and the optimization algorithm after sampling and numerical solution. This allows the neural network to briefly replace the internal response of the real optimization target model, and the optimization algorithm to perform multi-objective optimization on multiple modes in the optimization target model to generate optimization results. This effectively solves the problem of low efficiency in multi-objective multi-mode optimization in related technologies. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a schematic diagram based on the implementation environment involved in this application;

[0043] Figure 2 This is a flowchart illustrating a multi-objective, multi-mode optimization method according to an exemplary embodiment;

[0044] Figure 3a yes Figure 2 A flowchart of step 210 in one embodiment corresponds to the following example;

[0045] Figure 3b This is a structural diagram of a geometric model according to an exemplary embodiment;

[0046] Figure 3c This is a structural diagram of a geometric model according to an exemplary embodiment;

[0047] Figure 3d This is a structural diagram of a geometric model according to an exemplary embodiment;

[0048] Figure 4 yes Figure 2 A flowchart of step 230 in one embodiment corresponds to the following example;

[0049] Figure 5a yes Figure 2 A flowchart of step 250 in one embodiment corresponds to the following example;

[0050] Figure 5b It is an elbow diagram of a multi-objective, multi-modal optimization method in an application scenario;

[0051] Figure 5c This is a structural block diagram illustrating a multi-objective, multi-mode optimization method according to an exemplary embodiment;

[0052] Figure 6 yes Figure 5a A flowchart of step 251 in one embodiment corresponds to the following example;

[0053] Figure 7 yes Figure 5a A flowchart of step 253 in one embodiment corresponds to the previous one;

[0054] Figure 8a This is a schematic diagram illustrating the specific implementation of a multi-objective, multi-mode optimization method in an application scenario;

[0055] Figure 8b This is a birefringence and loss performance diagram of a multi-objective, multi-mode optimization method in an application scenario;

[0056] Figure 8c This is a BI, CL, HOMER performance graph of a multi-objective, multi-modal optimization method in an application scenario;

[0057] Figure 9 This is a structural block diagram of a multi-objective, multi-mode optimization device according to an exemplary embodiment;

[0058] Figure 10 This is a hardware structure diagram of a server according to an exemplary embodiment;

[0059] Figure 11 This is a structural block diagram of an electronic device according to an exemplary embodiment. Detailed Implementation

[0060] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0061] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this disclosure means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein may include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0062] As mentioned earlier, existing traditional ergonomic methods suffer from enormous computational costs due to the high-dimensional space, while branch-and-bound methods are limited by their small search range in the parameter space. Optimization problems of hollow antiresonant fibers based on neural networks or optimization algorithms require a large amount of computation. Using algorithms for parameter optimization may ultimately require a considerable number of computations, with the final results approaching or slightly outperforming traditional optimization methods, resulting in low efficiency for multi-objective, multi-mode optimization using existing methods.

[0063] As can be seen from the above, the related technologies still suffer from the drawback of low efficiency in multi-objective and multi-mode optimization.

[0064] Therefore, the multi-objective multi-mode optimization method provided in this application can effectively improve the efficiency of multi-objective multi-mode optimization. Accordingly, the multi-objective multi-mode optimization method is applicable to multi-objective multi-mode optimization devices, which can be deployed on electronic devices. These electronic devices can be computer devices configured with a von Neumann architecture, such as desktop computers, laptops, servers, etc.; they can also be electronic devices with central control functions, such as gateways; and they can also refer to portable mobile electronic devices, such as smartphones, tablets, etc.

[0065] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0066] Figure 1This is a schematic diagram of an implementation environment involved in an image processing method. It should be noted that this implementation environment is merely an example adapted to the present invention and should not be considered as providing any limitation on the scope of the invention.

[0067] The implementation environment includes a data acquisition terminal 110 and a server terminal 130.

[0068] Specifically, the acquisition terminal 110 can be considered an information acquisition device, including but not limited to electronic devices with information acquisition functions such as scanners and measuring instruments. It can also be considered a device integrating information acquisition and multi-objective multi-mode optimization, including but not limited to electronic devices such as laptops and desktop computers that combine information acquisition and multi-objective multi-mode optimization functions. For example, the acquisition terminal 110 used to acquire training set data can be a laptop computer with data acquisition capabilities; this is not a specific limitation. That is, in some embodiments, the acquisition terminal 110 can be a hollow anti-resonant fiber model used to acquire training set data.

[0069] Server 130 can also be considered a multi-objective, multi-mode optimization device, including but not limited to electronic devices with multi-objective, multi-mode optimization functions such as smartphones, desktop computers, laptops, and servers. It can also be a computer cluster composed of multiple servers, or even a cloud computing center composed of multiple servers. Server 130 is used to provide backend services, such as multi-objective, multi-mode optimization services, etc.

[0070] The server 130 and the acquisition terminal 110 establish a network communication connection in advance via wired or wireless means, and data transmission between the server 130 and the acquisition terminal 110 is realized through this network communication connection. The transmitted data includes, but is not limited to, training set data, etc.

[0071] In one application scenario, through the interaction between the acquisition terminal 110 and the server terminal 130, the acquisition terminal 110 collects training set data and uploads the training set data to the server terminal 130 to request the server terminal 130 to provide multi-objective multi-mode optimization services.

[0072] At this point, for server 130, after receiving the training set data uploaded by acquisition terminal 110, it calls the multi-objective multi-model optimization service, constructs a proxy model based on the training set data, trains it, obtains the trained proxy model and generates an optimization algorithm, and connects the optimization algorithm to the optimization target model for computation, thereby optimizing the optimization target model and solving the problem of low efficiency in multi-objective multi-model optimization in related technologies.

[0073] Please see Figure 2This application provides a multi-objective, multi-mode optimization method applicable to electronic devices, which may be... Figure 1 The server 130 shown in the implementation environment can also be a desktop computer, laptop computer, server, etc.

[0074] In the following method embodiments, for ease of description, the execution subject of each step of the method is an electronic device, but this does not constitute a specific limitation.

[0075] like Figure 2 As shown, the method may include the following steps:

[0076] Step 210: Sample and numerically solve the target model to obtain the training set.

[0077] The optimization target model is the target that needs to be optimized. For example, in the optimization process of hollow anti-resonant fiber, the optimization target model is the hollow anti-resonant fiber model.

[0078] Step 230: Train the neural network model based on the training set to obtain the surrogate model.

[0079] Among them, the surrogate model is used to predict the behavior of the target model.

[0080] By training a pre-defined neural network model using a training set, the neural network model can briefly replace and optimize the internal response of the target model, and finally obtain a surrogate model after training is completed.

[0081] In one possible implementation, the neural network model is a BP neural network.

[0082] Step 250: Adjust the multimodal hyperparameters of the preset optimization algorithm based on the surrogate model and training set.

[0083] Specifically, by using the trained surrogate model to rapidly and independently adjust the hyperparameters of the optimization algorithm for multiple modalities, the stability of the given parameters for the final result is ensured. This allows the optimization algorithm to stably move towards the global optimum with minimal computational resources and optimize resource allocation during the iteration process.

[0084] Step 270: Connect the optimization algorithm to the target model for calculation and generate optimization results.

[0085] By integrating the optimization algorithm into the target model and running it at each peak of the target model, the optimization results of each mode can be obtained. The optimization results of each optimization solution constitute a Pareto set, which contains the boundaries between multiple performance levels that cannot be compromised.

[0086] Through the above process, the optimization algorithm can be used to adjust the hyperparameters of multiple objectives and multiple modes on the neural network. The computational cost of a single operation is very low, and a large number of independent repeated experiments can be conducted to ensure the evaluation of the stability of the given parameters to the final result. This allows the hyperparameters of the optimization algorithm to be adjusted freely at a very fast speed, ensuring the accuracy and efficiency of multi-objective and multi-mode optimization.

[0087] In one exemplary embodiment, such as Figure 3a As shown, step 210 may include the following steps:

[0088] Step 211: Construct the corresponding geometric model for the target optimization model.

[0089] Among them, the geometric model is a simplified model that describes the geometric relationships in the target model for optimization.

[0090] In one possible implementation, such as Figure 3b As shown, when optimizing the target model as a hollow anti-resonant fiber, the model is simplified to an outer ring and multiple inner rings by simulating the internal components of the hollow anti-resonant fiber through a circular ring. The ratio of the outer ring to the inner ring is fixed at 0.5, and the large and small rings have the same thickness inside and outside.

[0091] Step 213: Construct constraints based on the topological consistency of the geometric model, and solve the geometric model based on the constraints to obtain the solution model.

[0092] It should be noted that, for engineering design, internal geometric components are subject to non-intersecting constraints. This is because, from a geometric modeling perspective, each independent geometric structure is typically considered a continuous, uninterrupted entity whose surface defines a closed boundary. Maintaining the continuity, manifold, and topological consistency of the geometry is crucial, as it relates to the accuracy and stability of subsequent fabrication, analysis, and simulation processes. This also means that extrema often lie on the boundaries of the feasible region controlling these geometric parameters.

[0093] For example, in the finite element analysis (FEA) used in the optimization process of hollow antiresonant optical fibers, non-manifold geometries may lead to difficulties in mesh generation, affecting the accuracy of the analysis results. To avoid destroying these properties when parameter-controlled geometric deformation, fixed ranges for its geometric parameters are generally set manually in advance. Hollow antiresonant optical fiber optimization is divided into size optimization, shape optimization, morphology optimization, and topology optimization. In the topology optimization of hollow antiresonant optical fibers, we aim to appropriately optimize displacement while changing or maintaining their basic connectivity.

[0094] Specifically, by using restricted path topology optimization, the main parameters of the geometric model are defined as variables. The constraints on each variable are calculated while maintaining the topological consistency of the geometric model. This allows the axial / radial geometric structures to expand / shrink simultaneously with the radial / axial geometric structures, and enables reasonable adaptive adjustment of the spatial positions of multiple geometric structures to achieve the best results while ensuring continuity, manifold, and topological consistency remain unchanged. For example, ... Figure 3c As shown in the figure, C1, C2, C3, C4, and C5 are the centers of the annulus, and the intersection situation during the parameter optimization process is as follows. Figure 3b As shown in the left figure, the main parameters in the geometric model, such as the distance between the circle centers and the radius, are defined as variables x1(t1), x2(t2), x3(r1), x4(r2), and x5(R). Simultaneously, each circle center is located in polar coordinates, with center coordinates set as pi(ρi, θi). After solving, the position of each circle center is reconsidered, and the constraint limit is that the circles are tangent, equivalent to the distance between any two adjacent circle centers being greater than the sum of their radii. In other words, the geometric model is constrained by four inequalities:

[0095] |p1-p2|>r1+r2|p2-p3|>2r2,|p3-p4|>r1+r2|p1-p5|>2r1.

[0096] In one possible implementation, the constraint is a missing corner constraint. For example... Figure 3d As shown,

[0097] Define 2*φ1 and 2*φ2 as the central angles corresponding to the large and small annexes respectively. Due to the axial symmetry of the geometric structure, if the upper half of the circle is tangent to all the semicircles, the existence of the missing angle is equivalent to dividing it equally so that the annexes do not intersect.

[0098] At this point, the polar coordinates of C4 are fixed at P4 = (ρ4, θ4) = (R-r1, Π). If there are still empty angles after considering the angles occupied by these parts, these empty angles can eventually be divided into four parts and placed on the boundaries where each pair of annexes may be tangent. Figure 3d (The red * position in the text).

[0099] Constraints are set based on the size of the missing angle, transforming the optimization process into an optimization problem under mixed integer nonlinear inequality constraints. The origin o is defined as the center of the cladding circle. The intersection point of the axis corresponding to 0° and C1 is A. The center of C1 is B. A tangent line is drawn from the center to C2, intersecting C2 at D. The center of C2 is C. The intersection point of C2 and C3 is E. The tangent line is drawn from the center to C3, with the point of tangency at F. The center of C4 is G. I is the intersection point of the 180° axis and the outer circle. Since the actual radius controllable accuracy is limited by the manufacturing difficulty, and too many solutions would lead to too many combination problems and unnecessary computational increases, the radius values ​​of the two sizes of the outer ring are rounded within the constraints of the nonlinear equation, i.e., r1, r2 ∈ N*, φ1 = ∠BOA, φ2 = ∠COD, ∠BOA = arcsin(r1 / R-r1), ∠COD = arcsin(r2 / R-r2). The calculation process for the angle α is shown below:

[0100]

[0101] Based on the calculation process of the angle α, the constraint relationship between r1, r2, and x3, x4 is ultimately set to alpla greater than or equal to 0.

[0102] Step 215: Solve the geometric model based on the constraints to obtain the solution model.

[0103] After obtaining the constraints, the solutions for different combinations of the geometric model are obtained according to the constraint formula.

[0104] In one possible implementation, the geometric model parameter radius r1 is set to 8, 9, and 10, and the parameter radius r2 is set to 15, 16, and 17. The values ​​of parameter α in the constraint conditions under different combinations can be obtained, as shown in the table below:

[0105]

[0106] Table 1: Magnitude of alpha under different combinations of radii

[0107] Specifically, by selecting three sets of solutions 10-15, 9-16, and 8-17 on the diagonal, three solution models, model1, model2, and model3, are generated.

[0108] Step 217: Sample data from the solution model to obtain training set data.

[0109] In this process, since some parameters of the geometric model are affected by nonlinear inequality constraints, after solving within a given region, the resulting solution model is used to calculate data, and training set data is generated based on the obtained data.

[0110] In one possible implementation, 700 data points were calculated to generate the training set data for three solution models.

[0111] Through the above process, optimization is achieved by considering the reduction of processing complexity and minimizing the impact on performance through a geometric model, thereby improving optimization efficiency. Given the geometric characteristics of the model and the constraints on some parameters, it is proven that the constraints belong to a mixed nonlinear inequality constraint, and optimization is performed within the feasible region. Parameters with good performance within the interval are considered in the optimization process, making the solution domain more complete. Simultaneously, the model is simple, transferable, and can adapt its spatial position to changes in geometric parameters. It can reasonably and adaptively adjust the spatial positions of multiple geometric shapes to achieve the best results, thus greatly improving optimization accuracy and efficiency.

[0112] In one exemplary embodiment, such as Figure 4 As shown, step 230 may include the following steps:

[0113] Step 231: Obtain the neural network model and construct a scoring function for the birefringence objective function and the minimum loss objective function of the neural network model.

[0114] The scoring function is used to evaluate the performance of the neural network model.

[0115] Specifically, the birefringence performance and minimum loss performance of the neural network model are quantified by the birefringence objective function and the minimum loss objective function, and different performances are comprehensively considered by the scoring function, so that multiple performances can be optimized simultaneously.

[0116] In one possible implementation, f is the birefringence objective function, and g is the minimum loss objective function. The training objective is to obtain the minimum g while obtaining the maximum f. Therefore, based on the weighted sum method, the score function F = w1f - w2g is defined. Considering the difference in magnitude and value between the two, w1 = 10000 and w2 = -0.8 are finally determined.

[0117] Step 233: Train the neural network model based on the training set and the scoring function until the scoring function determines that the neural network model has been trained and the surrogate model is obtained.

[0118] The parameters of the neural network are continuously adjusted using data from the training set. The effectiveness of the neural network model training is then determined by the scoring function until the performance of the neural network model finally converges.

[0119] In one possible implementation, the neural network model is a BP neural network with 64 intermediate nodes.

[0120] In one exemplary embodiment, the training method for training the neural network model based on the training set and the scoring function is the Levin Bergogmarquard method.

[0121] Through the above process, a surrogate model that can replace the target optimization model is obtained. This surrogate model can then be used to perform multi-objective and multi-modal simulations during the optimization process, thereby improving optimization efficiency.

[0122] In one exemplary embodiment, such as Figure 5a As shown, step 250 may include the following steps:

[0123] Step 251: Cluster and distinguish the modalities in the proxy model based on the training set to obtain at least one clustering interval.

[0124] In one exemplary embodiment, such as Figure 6 As shown, step 251 may include the following steps:

[0125] Step 2511: Calculate the number of clusters in the surrogate model based on the elbow function.

[0126] It should be noted that when calculating different numbers of clusters for the surrogate model using the elbow function, the cohesion value under each cluster represents the sum of the distances from each point within the cluster to its centroid, thus reflecting the tightness of the clustering. Figure 5b As shown in the figure, Inertia is the cohesion value and Cluster Number is the number of clusters. Since more clusters mean less distance accumulation, the cohesion value will decrease as the number of clusters increases. However, after a certain point, adding more clusters will cause the rate of decrease in cohesion value to slow down significantly. This point is called the "elbow" and is usually considered a candidate for the optimal number of clusters. The optimal number of clusters is determined by the elbow.

[0127] In one possible implementation, the Inertia cohesion value is calculated using the following formula:

[0128] [text{Inertia}=sum_{i=1}^{k}\sum_{x in C_i}||x-mu_i||^2].

[0129] Where k is the number of clusters, C_i is the set of points in the i-th cluster, mu_i is the center of the i-th cluster, x is a point in C_i, and ||x-\mu_i||^2 is the square of the Euclidean distance from point x to its cluster center mu_i.

[0130] Step 2513: Based on the clustering algorithm, the training set is clustered according to the number of clusters to obtain the cluster centers and the corresponding cluster intervals of each cluster center.

[0131] It should be noted that, therefore, after determining the optimal number of clusters through the elbow function, the training set is clustered using a clustering algorithm to determine the cluster centers and corresponding cluster intervals. Within the cluster intervals, it is possible to determine whether each region is where the peak is located.

[0132] One possible implementation is to use the K-MEANS algorithm for clustering.

[0133] The above process prevents clustering algorithms from causing further error accumulation on neural networks, thus improving optimization efficiency.

[0134] Step 253: Determine the target interval in each clustering interval based on the surrogate model.

[0135] In one exemplary embodiment, such as Figure 7 As shown, step 253 may include the following steps:

[0136] Step 2531: Based on the surrogate model, repeatedly mark points for each cluster interval to obtain the data points corresponding to each cluster interval.

[0137] By repeatedly marking points, the mean will increase to varying degrees and converge as the number of points increases, based on the law of large numbers. At the same time, the increased number of points increases the point density within the hypercube, making the results more stable and obtaining more accurate optimization results.

[0138] Step 2533: Construct a decision function based on the number of data points, mean, and variance corresponding to each cluster interval.

[0139] In one possible implementation, after calculating the F-mean and F-mean squared error of the data points, the values ​​of the calculated quantity, mean, and variance are subjected to min-max normalization to obtain the normalized variables.

[0140] The decision function formula is f = -normalized number + normalized avg - normalizedSD, where number is the number of calculations, avg is the mean, and SD is the variance.

[0141] Step 2535: Determine whether each clustering interval is a peak region based on the decision function, and determine the clustering interval corresponding to the peak region as the target interval.

[0142] Since the optimization process is a multi-objective conflicting decision problem, it is necessary to obtain the largest possible average value and the smallest possible mean square error with the least possible computational resources. Therefore, by calculating the maximum value of each cluster interval through the decision function, it is determined whether each cluster interval is a peak region. At the same time, based on the calculation of the decision function, it is determined how much computational resources are needed to stably obtain the peak value of each model. Finally, the maximum value of the decision function is given as the decision standard to determine the target interval.

[0143] Through the above process, based on the sampled values, the elbow function is used to determine the number of clusters and the number of peaks. Based on the number of peaks given by the elbow function, the clustering algorithm is used to find the cluster centers and the parameter range of the clusters. This allows the optimization algorithm to run in the hypercube where peaks exist for multimodal and multi-objective applications, further reducing the waste of computing power. At the same time, it can achieve the best optimization results with the least amount of computing resources, thus improving optimization efficiency.

[0144] Step 255: Based on the surrogate model and the preset optimization algorithm, determine the hyperparameters of the optimization algorithm and the number of actual evaluations in the target interval, and determine the hyperparameters of the optimization algorithm.

[0145] In one possible implementation, such as Figure 5c As shown, training data is first obtained by sampling and numerically solving the surrogate model. The number of clusters and cluster centers are calculated using a clustering function. Within multiple given clustering intervals after clustering, the cluster number and cluster range are calculated. The solution volume and hyperparameters are determined using the surrogate model to guide the determination of the target interval. Based on the neural network and the predicted optimization algorithm, the expected number of real evaluations and the hyperparameters of the optimization algorithm are determined within the interval. Finally, the pre-defined optimization algorithm is integrated into the real model for computation.

[0146] Through the above process, by introducing an optimization algorithm based on a surrogate model, the optimization algorithm can be used for multi-objective and multi-modal optimization, thereby achieving accurate generation of the optimization algorithm and improving the accuracy and efficiency of multi-objective optimization.

[0147] Figure 8aThis is a schematic diagram illustrating the specific implementation of a multi-objective, multi-mode optimization method in an application scenario. In this scenario, a neural network is constructed as a surrogate model for a hollow anti-resonant fiber (HC-ARF) model. Nonlinear inequality constraints are applied, and three solution models, Model-1, Model-2, and Model-3, are obtained. A total of 700 data points are used to train the neural network for these three models. After comparing various neural network training methods, the BP neural network with the highest accuracy is selected as the surrogate model. Next, the two objective functions of loss and birefringence are transformed into a scoring function F using a weighted sum method. Subsequently, the number of clusters for each model is calculated using the elbow function, and the K-MEANS algorithm is used for clustering to obtain the variable interval for each cluster.

[0148] Among these, all three solution models reached a turning point at 3 to 4 clusters, while the sampling of the entire space was only 700 points, with less than 250 samples per model, which is relatively sparse. Furthermore, considering that using clustering algorithms on neural networks would further amplify errors, a 3-cluster clustering approach based on the KMEANS clustering algorithm was ultimately chosen. The final clustering result is as follows:

[0149] In model1, C1 has t1∈[0.95, 1.45], t2∈[0.95, 1.45], R∈[24, 60], C2 has t1∈[0.2, 0.7], t2∈[0.2, 0.7], R∈[44, 60], and C3 has t1∈[0.2, 0.7], t2∈[0.2, 0.7], R∈[20, 40].

[0150] Model2, C1 has t1∈[0.95, 1.45], t2∈[0.95, 1.45], R∈[44, 60], C2 has t1∈[0.2, 0.7], t2∈[0.2, 0.7], R∈[20, 60], and C3 has t1∈[0.2, 0.7], t2∈[0.2, 0.7], R∈[24, 40].

[0151] Model3, C1 is t1∈[0.95, 1.45], t2∈[0.95, 1.45], R∈[24, 60], C2 is t1∈[0.2, 0.7], t2∈[0.2, 0.7], R∈[20, 40], C3 is t1∈[0.2, 0.7], t2∈[0.2, 0.7], R∈[44, 60].

[0152] Repeatedly plotting points in each interval of each model to determine whether each region is the location of a peak. After calculation, the clustering intervals of the three models have two peaks in the given full space.

[0153] After determining the peak values, a total of six peak regions were obtained for the three models. Based on the neural network's judgment, the total number of calculations and the number of points per calculation were determined for each region. In regions C1 and C2, n points were used per calculation, and the experiment was repeated independently 50 times. The maximum value of F generated in these 50 trials was used to calculate the mean and standard deviation. The number of points increased from 100 to 500. If the total computational resources were limited, the number of segmentations started from 3; if the computational resources were abundant, the number of segmentations started from 4.

[0154] The mean and root mean square error of the F-values ​​and the decision function f obtained by the three models for different numbers of dots in the C1C2 region and different number of splits under the optimal number of dots are model1-c1(a), model1-c2(b), model2-c1(d), model2-c2(e), model3-c1(f), and model3-c2(g).

[0155] Based on the value of the decision function, the final decision is...

[0156] In model 1, the decision number on C1 is 400 (5 * 80), and the decision number on C2 is 400 (8 * 50).

[0157] In model 2, the decision number on C1 is 300 (4 * 75), and the decision number on C2 is 400 (5 * 80).

[0158] In model 3, the decision number in C1 is 500 (7*71), and the decision number in C2 is 300 (4*75).

[0159] Calculations are performed using COMSOL WITH MATLAB in the hollow anti-resonant fiber model (HC-ARF).

[0160] The overall algorithm flow is as follows:

[0161] For model1-c1:

[0162] 1. i = 1, Ci is the parameter space that satisfies the constraints.

[0163] 2. Given a dotting pattern (n1, n2, ..., nN), where ni is the number of dots per dot, N-1 is the number of divisions, and ∑ni = number, i is 1...N.

[0164] 3. Use Latin hypercube sampling to assign values ​​to the parameter vector X1(x1..x5).....Xni(x1..x5) within Ci.

[0165] 4. Assign the parameter vector to the HC-ARF model in COMSOL to calculate f, g, F.

[0166] 5. Remove unreasonable f and g data.

[0167] 6. Randomly select m hyperplanes to bisect the space, such that the difference in the amount of data in the two sides of the space is less than or equal to ni / 10.

[0168] 7. i = i + 1.

[0169] 8. Find the segmentation method of MAX|left max-right max|, and denote the side with the maximum value as Ci.

[0170] 9. Repeat step 3 until i = N.

[0171] In this application scenario, six models with different modalities were obtained. Parallel computing was used to process all six models simultaneously, reducing the time required for serial computation to 1 / 6. After iterating the algorithm on the six models, a clear Pareto boundary was observed, proving the effectiveness of this paper in solving a multi-objective optimization problem. The birefringence and loss performance obtained after different rounds of computation on the six models are as follows: Figure 8b As shown, after iterating the six model access algorithms, a clear Pareto boundary is evident, proving the effectiveness of this paper in solving a multi-objective optimization problem. The performance of the five optimal models in their operating bands at BI, CL, and HOMER is as follows: Figure 8c As shown, the operating wavelengths for Model 1 are 1.475-1.9, Model 2 is 1.5-2.1, Model 3 is 1.425-1.975, Model 4 is 1.475-1.9, and Model 5 is 1.35-2.775. The highest scores and corresponding parameters for the five models are as follows:

[0172] MODEL1-C1

[0173] 0.683543505 0.434292362 15 1044.06444531 2.09061E-05 0.0240514320.189819848MODEL1-C2

[0174] 1.428354518 1.372696687 16945.22847796 3.34398E-05 0.0562107260.289428972MODEL2-C1

[0175] 0.6332845 0.578980943 16 9 24.02953262 0.000117563 0.3639677630.884460436MODEL2-C2

[0176] 1.365774751 1.403265184 178 30.560344299.30559E-05 0.3297769790.666737529MODEL3-C1

[0177] 0.627310845 0.591362741 17 8 44.44124951 3.86E-05 0.1030329980.303857606

[0178] In the structure proposed in this paper, the lowest loss can reach 3.54*10-3 (model 1), the highest birefringence can reach 1.25*10-4 (model 4), the HOMER can reach 50 (model 4), and the bandwidth can reach 1.425um (model 5). As can be seen from the table, the innovations compared to other optimizations of HC-ARF are that a multimodal model under mixed nonlinear constraints is solved with less computational resources. Furthermore, it has lower fabrication difficulty, providing diverse options for fabrication and users.

[0179] Please see Figure 9 This application provides a multi-objective multi-mode optimization device 900, including but not limited to: a sampling module 910, a training module 930, an adjustment module 950, and an optimization module 970.

[0180] The sampling module 910 is used to sample and numerically solve the target model to obtain the training set.

[0181] Training module 930 is used to train a neural network model based on a training set to obtain a proxy model, wherein the proxy model is used to predict the behavior of the target model.

[0182] The adjustment module 950 is used to adjust the multimodal hyperparameters based on the surrogate model and training set for a preset optimization algorithm.

[0183] The optimization module 970 is used to input the optimization algorithm into the optimization target model for calculation and generate optimization results.

[0184] It should be noted that the multi-objective multi-mode optimization device provided in the above embodiments is only illustrated by the division of the above functional modules when performing multi-objective multi-mode optimization. In actual applications, the above functions can be assigned to different functional modules as needed. That is, the internal structure of the multi-objective multi-mode optimization device will be divided into different functional modules to complete all or part of the functions described above.

[0185] Furthermore, the embodiments of the multi-objective multi-mode optimization device and the multi-objective multi-mode optimization method provided in the above embodiments belong to the same concept. The specific way in which each module performs its operation has been described in detail in the method embodiments, and will not be repeated here.

[0186] Figure 10 A schematic diagram of the structure of a server is shown according to an exemplary embodiment. This server is suitable for... Figure 1 The server 130 in the implementation environment is shown.

[0187] It should be noted that this server is merely an example adapted to this application and should not be construed as providing any limitation on the scope of use of this application. Nor should this server be interpreted as requiring or depending on any specific feature. Figure 10 One or more components of the exemplary server 2000 shown.

[0188] The hardware architecture of Server 2000 can vary significantly due to differences in configuration or performance, such as... Figure 10 As shown, server 2000 includes: power supply 210, interface 230, at least one memory 250, at least one central processing unit (CPU) 270, and at least one GPU processor 290.

[0189] Specifically, power supply 210 is used to provide operating voltage for the various hardware devices on server 2000.

[0190] Interface 230 includes at least one wired or wireless network interface 231 for interacting with external devices. For example, to perform... Figure 1 The diagram illustrates the interaction between terminal 100 and server 200 in the implementation environment.

[0191] Of course, in other examples adapted in this application, interface 230 may further include at least one serial-to-parallel conversion interface 233, at least one input / output interface 235, and at least one USB interface 237, etc. Figure 10 As shown, this does not constitute a specific limitation.

[0192] The memory 250 serves as a carrier for resource storage and can be a read-only memory, random access memory, disk, or optical disk, etc. The resources stored on it include the operating system 251, application programs 253, and data 255, etc., and the storage method can be temporary storage or permanent storage.

[0193] The operating system 251 is used to manage and control the various hardware devices and application programs 253 on the server 2000, so as to enable the central processing unit 270 to perform calculations and processing on the massive data 255 in the memory 250. It can be Windows Server™, Mac OS X™, Unix™, Linux™, FreeBSD™, etc.

[0194] Application 253 is a computer-readable instruction based on operating system 251 that performs at least one specific task, and may include at least one module ( Figure 10 (Not shown), each module may contain computer-readable instructions for server 2000. For example, the multi-objective multi-mode optimization device can be considered as application 253 deployed on server 2000.

[0195] Data 255 can be photos, images, etc. stored on a disk, or recommendation information, etc., stored in memory 250.

[0196] The central processing unit 270 may include one or more processors and is configured to communicate with the memory 250 via at least one communication bus to read computer-readable instructions stored in the memory 250, thereby enabling the computation and processing of massive amounts of data 255 in the memory 250. For example, a multi-objective, multi-mode optimization method can be implemented by the central processing unit 270 reading a series of computer-readable instructions stored in the memory 250.

[0197] The GPU processor 290 has multiple parallel processing cores. Through these processing cores and an optimized memory architecture, the GPU processor 290 processes and operates on massive amounts of data 255 in memory 250 in parallel, thereby training the neural network to complete a multi-objective, multi-mode optimization method.

[0198] Furthermore, this application can also be implemented through hardware circuits or a combination of hardware circuits and software. Therefore, the implementation of this application is not limited to any specific hardware circuit, software, or combination thereof.

[0199] Please see Figure 11 This application provides an electronic device 4000, which may include: a desktop computer, a laptop computer, a server, etc.

[0200] exist Figure 11In this context, the electronic device 4000 includes at least one processor 4001 and at least one memory 4003.

[0201] The data interaction between the processor 4001 and the memory 4003 can be achieved through at least one communication bus 4002. This communication bus 4002 may include a path for transmitting data between the processor 4001 and the memory 4003. The communication bus 4002 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The communication bus 4002 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 11 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0202] Optionally, the electronic device 4000 may further include a transceiver 4004, which can be used for data interaction between the electronic device and other electronic devices, such as sending and / or receiving data. It should be noted that in practical applications, the transceiver 4004 is not limited to one type, and the structure of the electronic device 4000 does not constitute a limitation on the embodiments of this application.

[0203] Processor 4001 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 4001 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0204] The memory 4003 may be a ROM (Read Only Memory) or other type of static storage device capable of storing static information and instructions, RAM (Random Access Memory) or other type of dynamic storage device capable of storing information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program instructions or code in the form of instructions or data structures and accessible by the electronic device 4000, but not limited thereto.

[0205] The memory 4003 stores computer-readable instructions, and the processor 4001 can read the computer-readable instructions stored in the memory 4003 through the communication bus 4002.

[0206] The computer-readable instructions are executed by one or more processors 4001 to implement the multi-objective, multi-mode optimization methods in the above embodiments.

[0207] Furthermore, this application provides a storage medium storing computer-readable instructions that are executed by one or more processors to implement the above-described multi-objective multi-mode optimization method.

[0208] This application provides a computer program product including computer-readable instructions stored in a storage medium. One or more processors of an electronic device read the computer-readable instructions from the storage medium, load and execute the computer-readable instructions, thereby enabling the electronic device to implement the above-mentioned multi-objective multi-mode optimization method.

[0209] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0210] The above are only some embodiments of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A multi-objective multi-modal optimization method, characterized in that, The method comprises the following steps: sampling and numerically solving the optimization target model to obtain a training set; training a neural network model based on the training set to obtain a proxy model, wherein the proxy model is used for behavior prediction of the optimization target model; performing multi-modal hyperparameter adjustment on a preset optimization algorithm based on the proxy model and the training set; connecting the optimization algorithm to the optimization target model for operation to generate an optimization result.

2. The method of claim 1, wherein, The sampling and numerical solving of the optimization target model to obtain the training set comprises the following steps: constructing a corresponding geometric model for the optimization target model; constructing a constraint condition based on the topological consistency of the geometric model; solving the geometric model based on the constraint condition to obtain a solution model; sampling data from the solution model to obtain training set data.

3. The method of claim 1, wherein, The training of the neural network model based on the training set to obtain the proxy model comprises the following steps: obtaining a neural network model and constructing a score function for the birefringence objective function and the minimum loss objective function of the neural network model, wherein the score function is used to evaluate the performance of the neural network model; training the neural network model based on the training set and the score function until the score function determines that the training of the neural network model is completed, and obtaining the proxy model.

4. The method of claim 3, wherein, The training method based on the training set and the score function for training the neural network model is the Levenberg-Marquardt method.

5. The method of claim 1, wherein, The multi-modal hyperparameter adjustment on the preset optimization algorithm based on the proxy model and the training set comprises the following steps: clustering and distinguishing the modes in the proxy model based on the training set to obtain at least one clustering interval; determining a target interval in each of the clustering intervals based on the proxy model; determining the hyperparameters of the optimization algorithm in the target interval based on the proxy model and the preset optimization algorithm, and determining the hyperparameters of the optimization algorithm.

6. The method of claim 5, wherein, The clustering and distinguishing of the modes in the proxy model based on the training set to obtain at least one clustering interval comprises the following steps: calculating the number of clusters in the proxy model based on an elbow function; clustering the training set based on a clustering algorithm according to the number of clusters to obtain cluster centers and clustering intervals corresponding to each cluster center.

7. The method of claim 5, wherein, The determination of a target interval in each of the clustering intervals based on the proxy model comprises the following steps: repeatedly dotting each of the clustering intervals based on the proxy model to obtain data points corresponding to each clustering interval; constructing a decision function based on the number of calculations, the mean, and the variance of the data points corresponding to each clustering interval; determining whether each of the clustering intervals is a peak region based on the decision function, and determining the clustering interval corresponding to the peak region as the target interval.

8. A multi-objective multi-modal optimization apparatus, characterized by, The method comprises the following steps: a sampling module for sampling and numerically solving an optimization target model to obtain a training set; a training module for training a neural network model based on the training set to obtain a proxy model, wherein the proxy model is used for behavior prediction of the optimization target model; An adjusting module is configured to perform multi-modal hyperparameter adjustment on a preset optimization algorithm based on the proxy model and the training set; An optimization module is configured to connect the optimization algorithm to the optimization target model to perform calculation and generate an optimization result.

9. An electronic device, comprising: Comprise: At least one processor and at least one memory, The memory has computer readable instructions stored thereon; The computer readable instructions are executed by one or more processors to enable the electronic device to implement the device control method of any one of claims 1 to 7.

10. A storage medium having stored thereon computer readable instructions, characterized in that, The computer readable instructions are executed by one or more processors to implement the multi-target multi-modal optimization method of any one of claims 1 to 7.

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