Agent model assisted multi-target amplifier size optimization algorithm

Abstract

The invention provides a multi-objective amplifier size optimization algorithm assisted by an agent model, and relates to the technical field of analog circuit optimization design, and the algorithm comprises the following steps: defining an objective function, and generating a weight vector and an initial population; target values of the individuals are calculated, and an LGBM proxy model is constructed according to the individuals and the target values; constructing a neighbor set for the weight vectors, randomly selecting two weight vectors from the neighbor set, and taking individuals corresponding to the two weight vectors as parent individuals to generate new individuals; a target value of a new individual is obtained through prediction or calculation of an LGBM agent model; calculating an aggregation function value of the individual based on the target value in combination with an aggregation function, and updating the population and the external population under the current iteration round according to the aggregation function value; and carrying out algorithm iteration, updating the agent model and the weight vector in iteration until the maximum number of iterations is reached, and outputting an external population. According to the method, efficient and low-cost optimization of the size of the multi-target amplifier is realized, the precision of the proxy model is improved, and Pareto frontier convergence is accelerated.

Description

Technical Field

[0001] The present invention relates to the technical field of analog circuit optimization design, and in particular to a multi-objective amplifier size optimization algorithm assisted by an agent model. Background Art

[0002] As a core module in electronic systems, amplifier performance (such as gain, power consumption, and stability) directly determines the system's signal processing capabilities, playing a crucial role in fields such as communications and medical equipment. The core of amplifier design lies in finding the optimal balance between conflicting performance objectives (high gain, low power consumption, and high stability) by adjusting parameters such as transistor aspect ratios and compensation capacitors.

[0003] Traditional amplifier design relies heavily on high-precision circuit simulation (such as SPICE and Spectre) to verify performance. However, such simulations are computationally extremely complex, with a single simulation taking minutes to hours. This results in high costs (computational and time costs) of repeatedly adjusting parameters during the design process, severely restricting design efficiency.

[0004] To address this issue, surrogate model-based optimization methods have gradually become a research hotspot. These methods replace high-cost simulations with low-computational-cost surrogate models (such as regression models) to rapidly predict amplifier performance, thereby reducing reliance on simulation. However, existing surrogate model-based amplifier design methods still have significant limitations: First, multi-objective optimization capabilities are insufficient: Most methods are only applicable to single-objective optimization scenarios, or simplify multi-objective problems into single-objective ones by introducing performance metrics (FoM). While this simplification reduces computational complexity, it fails to effectively capture the inherent conflicts between objectives such as gain, power consumption, and stability. Consequently, the optimization solution set fails to cover the full range of multi-objective trade-offs and fails to provide diverse optimal solutions for practical designs. Second, surrogate models suffer from limited predictive accuracy: Traditional surrogate models (such as basic regression models) have imperfect update mechanisms and rely solely on initial simulation data for training, failing to fully utilize historical design solutions generated during the optimization process (such as population iteration data) and accumulated size optimization databases. Due to the strong nonlinear and non-stationary coupling between amplifier parameters and performance (such as the nonlinear effect of transistor size changes on gain), statically trained surrogate models are prone to prediction bias, making them ineffective in accurately supporting automated design. Finally, the direction of population evolution is insufficiently guided: In existing methods, the weight vectors guiding the population's search direction are often fixed or simply adjusted in a few iterations. This fails to adapt to the requirements of different stages of the optimization process (such as the need to explore multiple directions in the early stages and converge to a high-quality region in the later stages). This results in ineffective search of the population in non-optimal sub-directions, a large number of iterations, and difficulty in quickly approaching the Pareto frontier of the multi-objective optimal solution, further increasing the design cycle.

[0005] How to solve the above technical problems is the subject faced by the present invention. Summary of the Invention

[0006] In order to address the deficiencies of the prior art, the present invention provides a proxy model-assisted multi-objective amplifier size optimization algorithm that achieves efficient and low-cost optimization of multi-objective amplifier sizes, improves the accuracy of the proxy model, and accelerates the convergence of the Pareto front.

[0007] The technical solution adopted by the present invention to solve the technical problem is: the present invention provides a multi-objective amplifier size optimization algorithm assisted by a proxy model, comprising the following steps: S1. Build an external population and size optimization database, define the objective function of the amplifier size optimization problem, generate N weight vectors according to the objective function, and generate an initial population based on the weight vectors; The initial population includes N individuals, each of which corresponds to a weight vector; S2. Calculate the target value of the individual in the initial population, build the LGBM proxy model based on the individual and target values, and define the prediction error threshold of the LGBM proxy model ; Prediction error threshold of LGBM surrogate model According to experience, the value is 0.945.

[0008] S3. Construct a neighbor set for the weight vector, randomly select two weight vectors from the neighbor set, and use the individuals corresponding to the two weight vectors as parent individuals to generate a new individual; S4. Predict the target value of the new individual through the LGBM agent model and calculate the prediction error , if the prediction error Less than the prediction error threshold , the LGBM proxy model is used to predict the target value of the new individual, otherwise the target value of the new individual is obtained by calculation; The prediction error calculation formula is as follows:

[0009] is the true value of the i-th sample (the target value calculated by circuit simulation), is the predicted value of the i-th sample (the target value predicted by the LGBM surrogate model), is the average of all true values, , n is the number of samples.

[0010] It should be noted that when obtaining the target value of a new individual, it is necessary to determine whether to use the LGBM proxy model to predict the target value or to calculate the target value through a circuit simulator based on the prediction error of the LGBM proxy model. When the prediction error is less than the prediction error threshold, it means that the target value predicted by the model is within a reasonable range. At this time, the proxy model is used to predict the target value of the new individual; when the prediction error is greater than the prediction error threshold, it means that the target value predicted by the model does not meet the requirements. At this time, the target value of the new individual is calculated through a circuit simulator.

[0011] S5. Calculate the aggregate function value of the individual based on the target value combined with the aggregate function, update the population and external population in the current iteration round according to the aggregate function value, and store the new individual and the target value of the new individual in the size optimization database; S6. Set the maximum number of iterations. When the number of iterations does not reach the maximum value, execute S3-S5 in a loop, and update the LGBM proxy model and weight vector during the iteration. When the number of iterations reaches the maximum value, the algorithm ends and outputs the external population.

[0012] It should be noted that the core concept of LGBM is to gradually minimize the loss function by iteratively fitting the residual or negative gradient of the current model, ultimately forming a powerful additive model. A histogram algorithm is used to segment continuous data into k discrete values, constructing a k-width histogram, effectively reducing memory consumption. The Gradient Boosting Decision Tree (GBDT) is then trained using a leaf-split strategy, which prioritizes splitting leaf nodes with the highest gain, improving the model's predictive accuracy.

[0013] Preferably, the external population is an empty array at the beginning of the iteration, and the storage limit is set to , non-dominated individuals are stored in the iteration; the size optimization database is an empty database at the beginning of the iteration, and the new individual and the target value of the new individual are stored as a piece of data in the iteration, and a data label is added. The data label includes the iteration round when the data is stored, the number of times the data is accumulated for training the LGBM proxy model, and whether the target value is predicted by the LGBM proxy model; the generation of N weight vectors adopts the Das and Dennis's method, and the generation of the initial population adopts the Latin hypercube sampling method.

[0014] Preferably, the target values of the individuals in the initial population and the target values of the new individuals obtained by calculation are both calculated using a circuit simulator Spectre.

[0015] Preferably, the constructing of the neighbor set includes: calculating the Euclidean distance between all weight vectors, and selecting k weight vectors with the closest distance to each weight vector to construct the neighbor set; The generating of new individuals includes performing uniform crossover and Gaussian mutation on the parent individuals.

[0016] Preferably, the step of calculating the aggregate function value of the individual based on the target value in combination with the aggregate function, and updating the population and the external population in the current iteration round according to the aggregate function value includes: Based on the target value of the new individual and the target values of the individuals corresponding to the k weight vectors of the neighbor set, the aggregation function value of the new individual and the aggregation function value of the individuals corresponding to the k weight vectors of the neighbor set are calculated according to the pre-defined aggregation function; The aggregation function formula is as follows:

[0017] Where, For individuals, is the number of objective functions, For the j The objective function, For the j The reference point of the objective function, For the j The weight vector of the objective function, For the j The weight of the objective function.

[0018] Compare the aggregation function value of the new individual with the aggregation function values of the individuals corresponding to the k weight vectors of the neighbor set. If the aggregation function value of the new individual is smaller than the aggregation function value of the individuals corresponding to the k weight vectors of the neighbor set, then replace the individuals whose aggregation function value is larger than the aggregation function value of the new individual among the individuals corresponding to the k weight vectors of the neighbor set with the new individual to obtain the updated population. If the external population does not reach the storage limit , the new individual is directly added to the external population. Otherwise, the dominance relationship between the new individual target value and the target values of all individuals in the external population is compared. If the dominance level of the new individual target value is high, the new individual is used to replace the individual with the lowest dominance level in the external population to obtain the updated external population.

[0019] Preferably, updating the LGBM proxy model and weight vector in the iteration includes: In each iteration, all individuals and target values of the population in the previous iteration are collected to form a temporary data set , for the temporary dataset Perform deduplication processing to obtain a streamlined data set ; Based on the data labels in the size optimization database and in combination with a predefined data selection formula, data is filtered from the size optimization database as an additional sample set; the predefined data selection formula is specifically expressed as follows:

[0020] Where, is the probability of data selection, is the iteration round when data is stored, The number of times the data is used to train the LGBM proxy model; It should be noted that the formula prioritizes data with fewer training times to reduce the risk of overfitting; assigning higher weights to recent data allows the model to quickly adapt to changes in the design space. This not only optimizes data utilization efficiency, but also significantly improves the model's ability to predict amplifier performance, providing a solid foundation for automated design.

[0021] The dataset will be streamlined and additional sample sets to obtain the model update dataset, and divide the model update dataset into training set, validation set and test set; Use the training set to incrementally train the LGBM proxy model, use the validation set to adjust the LGBM model hyperparameters, and evaluate the LGBM proxy model performance on the test set; From the size optimization database, select based on the data label using the maximum and minimum fill principle The target values of the items are obtained by using the data predicted by the LGBM proxy model. The circuit simulator Spectre is used to calculate the target values of the items, and the calculated target values are used to replace the target values predicted by the LGBM proxy model stored in the size optimization database. The maximum and minimum filling principle includes: taking individuals in the data obtained by predicting the target value in the size optimization database through the LGBM agent model as candidate individuals , the individuals in the data whose target values are not predicted by the LGBM proxy model are regarded as sampled individuals , calculate each candidate individual With the sampled individuals The distance between , and determine With all The minimum distance ; Among all candidate individuals In, based on Select the next sampling individual, where is the next sampling individual, and C is the set of candidate individuals.

[0022] It should be noted that if there are multiple candidate individuals with the same maximum and minimum distances, one of these points will be randomly selected as the next sampling individual.

[0023] The maximum-minimum fill criterion is a method used in surrogate-assisted optimization algorithms to select data points for real-world evaluation. This criterion selects individuals for real-world evaluation by calculating the distance between candidate individuals and already sampled individuals, ensuring a uniform distribution of sampled individuals in the search space and preventing excessive clustering of sample points in specific areas. By performing real-world evaluations on individuals and replacing the target values predicted by the LGBM surrogate model in the size optimization database with the target values obtained from the real-world evaluations, we avoid model drift caused by the LGBM surrogate model predicting all the data used to train the model, which in turn leads to reduced algorithm diversity and convergence.

[0024] When the number of iterations is less than 40% of the maximum number of iterations, the weight vector is not updated; When 40% of the maximum number of iterations ≤ the number of iterations < 70% of the maximum number of iterations, after updating the population in each round of iteration, the target values of the individuals in the updated population are normalized to obtain the target values of the individuals after the maximum-minimum normalization. Based on the target values of the individuals after the maximum-minimum normalization, the diversity index is calculated. ,like ,in, 、 、 Represent the diversity indicators of the current iteration, the previous generation of the current iteration, and the two generations before the current iteration, respectively. , is the optimal constant obtained through experiments, then cluster the updated population individuals into T classes, calculate the density of each class and sort them in descending order, and obtain the density descending order of T classes; according to the pre-defined quantity calculation formula, calculate the number num of weight vectors that need to be adjusted, combined with the density descending order of T classes, delete num weight vectors in T classes, and add num weight vectors; The formula for calculating the diversity index is as follows:

[0025] In the formula, S represents the external population output by the algorithm in the current iteration, |S| represents the number of solutions in the external population, The calculation is The mean

[0026] and All middle and The target value in the kth dimension, For solution The minimum Manhattan distance to all other solutions in the solution set S.

[0027] When 70% of the maximum number of iterations < the number of iterations ≤ the maximum number of iterations, calculate the convergence index ,like ,in, 、 、 They represent the convergence indexes of the current iteration, the previous generation of the current iteration, and the two generations before the current iteration, respectively. , is the optimal constant obtained through experiments, then cluster the updated population individuals into T classes, calculate the density of each class and sort them in ascending order, and obtain the density ascending order of T classes; according to the pre-defined quantity calculation formula, calculate the number num of weight vectors that need to be adjusted, combined with the density ascending order of T classes, delete num weight vectors in T classes, and add num weight vectors; The formula for calculating the convergence index is as follows:

[0028] S is the external population output by the algorithm in the current iteration, is an individual in the population, Z is the reference point of the population, that is, the maximum value in each dimension, for arrive The hyperrectangular region between It is the Lebesgue measure, which is used to calculate the volume of a multidimensional space set.

[0029] The predefined quantity calculation formula is specifically expressed as follows:

[0030] Where, is the current iteration number, is the number of individuals in the updated population.

[0031] The density calculation formula is as follows:

[0032] Where, is the class after the j-th clustering, is the centroid of the class after the j-th clustering, for The samples in is the number of samples in the class after the jth clustering, is the Euclidean distance. The numerator of the formula is the size of a class (number of samples), and the denominator is the sum of the distances from all samples to the centroid of the class (the smaller the distance, the more compact the cluster). Therefore, the greater the density, the tighter the cluster.

[0033] It should be noted that in the early stages of iteration (<40%), the population is dispersed and the knowledge of the target space is limited. If the weight vector is adjusted too early, the search direction may converge to the local optimum too early. By fixing the weight vector and maintaining the diversity of the initial sampling, the algorithm can ensure that the potential multi-objective trade-off directions are fully covered, providing rich basic data for subsequent stages.

[0034] In the middle of the iteration (40%-70%), the algorithm has initially converged to some high-quality areas, but may ignore some "niche" but valuable trade-off directions (such as "medium gain-medium power consumption"). By deleting the weight vectors of the high-density class and adding the weight vectors of the low-density class, the algorithm guides the population to evolve in directions that have not been fully explored, avoids falling into local optimality, and expands the coverage of the Pareto frontier.

[0035] In the later stages of iteration (70%-100%), the algorithm has identified most high-quality areas and the focus shifts to refined convergence, focusing on the most promising sub-directions. Weight vectors for low-density categories are deleted, and weight vectors for high-density categories are added. This concentrates resources to accelerate convergence, reduce redundant searches, and quickly approach the theoretical optimal solution.

[0036] Preferably, the clustering of the updated population individuals adopts an angle-based vector clustering method, including: By initialization uniformly distributed 2D vectors Division Classes, the calculation method is:

[0037] where t=1,2,…, ; The value of depends on the specific experiment.

[0038] Create a loop that randomly selects two objective functions from the objective functions of the amplifier size optimization problem. For each two-dimensional vector ,in accordance with An individual is selected from the updated population and assigned to the tth class until all individuals in the updated population are clustered and the cycle ends.

[0039] It should be noted that in the multi-objective optimization of automated amplifier design, the complex coupling of design parameters requires algorithms that can efficiently coordinate population distributions to rapidly approach the Pareto frontier. Traditional partition-based clustering methods directly divide the population by objective value, resulting in individuals with similar objectives being grouped into the same cluster. This leads to cluster polarization: solutions with excellent convergence are concentrated in a few clusters, while solutions with poor performance are dispersed elsewhere, severely limiting the algorithm's ability to explore the multi-dimensional amplifier design space. Therefore, an angle-based vector clustering method is employed. By using the angle similarity criterion, the solutions within each cluster are highly consistent in their multi-objective trade-off characteristics.

[0040] Preferably, the deleting num weight vectors in class T and adding num weight vectors includes: When 40% of the maximum number of iterations ≤ the number of iterations < 70% of the maximum number of iterations, sort in descending order of T class and record it as , ,..., ,right Add a new weight vector, if Only one individual , then find the individual The nearest num individuals ,k=1,2,...,num; and The centroid of the corresponding weight vector is inserted as the new weight vector; if it contains multiple individuals, two individuals are randomly selected and the centroid of the weight vector corresponding to the two individuals is inserted as the new weight vector until num weight vectors are inserted; Delete the weight vector if The number of individuals e≥num, then from Randomly select num individuals and delete the weight vectors corresponding to num individuals; if If the number of individuals e < num, then delete the weight vectors corresponding to e individuals, update num = num-e, and continue to traverse the next category until num weight vectors are deleted; When 70% of the maximum number of iterations < the number of iterations ≤ the maximum number of iterations, sort in ascending order of T class and record it as , ,..., ,right Add a new weight vector, from Randomly select two individuals from the , and insert the centroid of the weight vectors corresponding to the two individuals as the new weight vector, until num weight vectors are inserted; Delete the weight vector if The number of individuals e≥num, then from Randomly select num individuals and delete the weight vectors corresponding to num individuals; if If the number of individuals e<num, delete the weight vectors corresponding to e individuals, update num=num-e, and continue to traverse the next category until num weight vectors are deleted.

[0041] It should be noted that if there are z classes with the same density and the same maximum or minimum value, z ≥ 2, then one class is randomly selected from the z classes to delete or add the weight vector.

[0042] The beneficial effects of the present invention are: achieving efficient and low-cost optimization of multi-objective amplifier size, improving the accuracy of the proxy model, and accelerating the convergence of the Pareto front. The proxy model is used to predict the target value, reducing the computational cost and time cost of circuit simulation, combining the multi-objective optimization algorithm and the weight vector to guide the evolution direction of the population, and solving the problem that the proxy-based methods in the prior art are limited to a single target or simplifying multiple targets through the FoM. During the algorithm iteration, the LGBM proxy model is updated using the historical design scheme and the size optimization database, effectively improving the prediction accuracy of the LGBM proxy model. At the same time, for different iteration stages, the weight vector is updated according to different strategies to ensure that the population searches in the optimal sub-direction, accelerate the approach to the optimal Pareto front, and reduce the number of population iterations. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A diagram showing the steps for implementing the method of the present invention.

[0044] Figure 2 This is a circuit schematic diagram of a two-stage operational amplifier according to embodiment 2 of the present invention.

[0045] Figure 3 This is a circuit schematic diagram of a folded cascode operational amplifier according to embodiment 2 of the present invention. DETAILED DESCRIPTION

[0046] In order to clearly illustrate the technical features of this solution, the solution is described below through specific implementation methods.

[0047] Example 1: See also Figure 1 As shown, this embodiment is a multi-objective amplifier size optimization algorithm assisted by a proxy model, comprising the following steps: Step S1: construct an external population and size optimization database, define the objective function of the amplifier size optimization problem, generate N weight vectors according to the objective function, and generate an initial population based on the weight vectors; the initial population includes N individuals, each individual corresponds to a weight vector.

[0048] The external population is an empty array at the beginning of the iteration, and the storage limit is set to , non-dominated individuals are stored in the iteration; the size optimization database is an empty database at the beginning of the iteration. During the iteration, the new individual and the target value of the new individual are stored as a data item and a data label is added. The data label includes the iteration round when the data is stored, the number of times the data is used to train the LGBM proxy model, and whether the target value is predicted by the LGBM proxy model; the Das and Dennis's method is used to generate N weight vectors, and the Latin hypercube sampling method is used to generate the initial population.

[0049] Step S2: Calculate the target value of the individuals in the initial population, build the LGBM proxy model based on the individuals and the target value, and define the prediction error threshold of the LGBM proxy model. .

[0050] Prediction error threshold of LGBM surrogate model According to experience, the value is 0.945.

[0051] The target values of individuals in the initial population are calculated using the circuit simulator Spectre.

[0052] Step S3: construct a neighbor set for the weight vector, randomly select two weight vectors from the neighbor set, and use the individuals corresponding to the two weight vectors as parent individuals to generate new individuals.

[0053] Constructing a neighbor set includes: calculating the Euclidean distance between all weight vectors, and selecting the k weight vectors with the closest distance to each weight vector to construct a neighbor set; Generating new individuals involves performing uniform crossover and Gaussian mutation on parent individuals.

[0054] Step S4: Predict the target value of the new individual through the LGBM proxy model and calculate the prediction error , if the prediction error Greater than the prediction error threshold , the target value of the new individual is obtained by calculation, otherwise the LGBM proxy model is used to predict the target value of the new individual.

[0055] The prediction error calculation formula is as follows:

[0056] is the true value of the i-th sample (the target value calculated by circuit simulation), is the predicted value of the i-th sample (the target value predicted by the LGBM surrogate model), is the average of all true values, , n is the number of samples.

[0057] The target value of the new individual is obtained by calculation using the circuit simulator Spectre.

[0058] It should be noted that when obtaining the target value of a new individual, it is necessary to determine whether to use the LGBM proxy model to predict the target value or to calculate the target value through a circuit simulator based on the prediction error of the LGBM proxy model. When the prediction error is less than the prediction error threshold, it means that the target value predicted by the model is within a reasonable range. At this time, the proxy model is used to predict the target value of the new individual; when the prediction error is greater than the prediction error threshold, it means that the target value predicted by the model does not meet the requirements. At this time, the target value of the new individual is calculated through a circuit simulator.

[0059] Step S5: Calculate the aggregate function value of the individual based on the target value combined with the aggregate function, update the population and external population in the current iteration round according to the aggregate function value, and store the new individual and the target value of the new individual in the size optimization database.

[0060] Based on the target value of the new individual and the target values of the individuals corresponding to the k weight vectors of the neighbor set, the aggregation function value of the new individual and the aggregation function value of the individuals corresponding to the k weight vectors of the neighbor set are calculated according to the pre-defined aggregation function; The aggregate function formula is as follows:

[0061] Where, For individuals, is the number of objective functions, For the j The objective function, For the j The reference point of the objective function, For the j The weight vector of the objective function, For the j The weight of the objective function.

[0062] Compare the aggregation function value of the new individual with the aggregation function values of the individuals corresponding to the k weight vectors of the neighbor set. If the aggregation function value of the new individual is smaller than the aggregation function value of the individuals corresponding to the k weight vectors of the neighbor set, then replace the individuals whose aggregation function value is larger than the aggregation function value of the new individual among the individuals corresponding to the k weight vectors of the neighbor set with the new individual to obtain the updated population. If the external population does not reach the storage limit , the new individual is directly added to the external population. Otherwise, the dominance relationship between the new individual target value and the target values of all individuals in the external population is compared. If the dominance level of the new individual target value is high, the new individual is used to replace the individual with the lowest dominance level in the external population to obtain the updated external population.

[0063] Step S6: Set the maximum number of iterations. When the number of iterations does not reach the maximum value, execute S3-S5 in a loop, and update the LGBM proxy model and weight vector during the iteration. When the number of iterations reaches the maximum value, the algorithm ends and outputs the external population.

[0064] Update the LGBM surrogate model in iterations: In each iteration, all individuals and target values of the population in the previous iteration are collected to form a temporary data set , for the temporary dataset Perform deduplication processing to obtain a streamlined data set ; Based on the data labels in the size optimization database and the predefined data selection formula, data is filtered from the size optimization database as an additional sample set. The predefined data selection formula is specifically expressed as follows:

[0065] Where, is the probability of data selection, is the iteration round when data is stored, The number of times the data is used to train the LGBM proxy model; It should be noted that the formula prioritizes data with fewer training times to reduce the risk of overfitting; assigning higher weights to recent data allows the model to quickly adapt to changes in the design space. This not only optimizes data utilization efficiency, but also significantly improves the model's ability to predict amplifier performance, providing a solid foundation for automated design.

[0066] The dataset will be streamlined and additional sample sets to obtain the model update dataset, and divide the model update dataset into training set, validation set and test set; Use the training set to incrementally train the LGBM proxy model, use the validation set to adjust the LGBM model hyperparameters, and evaluate the LGBM proxy model performance on the test set; From the size optimization database, select based on the data label using the maximum and minimum fill principle The target values of the items are obtained by using the data predicted by the LGBM proxy model. The circuit simulator Spectre is used to calculate the target values of the items, and the calculated target values are used to replace the target values predicted by the LGBM proxy model stored in the size optimization database. The maximum and minimum filling principle includes: taking the individuals in the data obtained by predicting the target value in the size optimization database through the LGBM proxy model as candidate individuals , the individuals in the data whose target values are not predicted by the LGBM proxy model are regarded as sampled individuals , calculate each candidate individual With the sampled individuals The distance between , and determine With all The minimum distance ; Among all candidate individuals In, based on Select the next sampling individual, where is the next sampling individual, and C is the set of candidate individuals.

[0067] It should be noted that if there are multiple candidate individuals with the same maximum and minimum distances, one of these points will be randomly selected as the next sampling individual.

[0068] The maximum-minimum fill criterion is a method used in surrogate-assisted optimization algorithms to select data points for real-world evaluation. This criterion selects individuals for real-world evaluation by calculating the distance between candidate individuals and already sampled individuals, ensuring a uniform distribution of sampled individuals in the search space and preventing excessive clustering of sample points in specific areas. By performing real-world evaluations on individuals and replacing the target values predicted by the LGBM surrogate model in the size optimization database with the target values obtained from the real-world evaluations, we avoid model drift caused by the LGBM surrogate model predicting all the data used to train the model, which in turn leads to reduced algorithm diversity and convergence.

[0069] Update the weight vector in iterations: When the number of iterations is less than 40% of the maximum number of iterations, the weight vector is not updated; When 40% of the maximum number of iterations ≤ the number of iterations < 70% of the maximum number of iterations, after updating the population in each round of iteration, the target values of the individuals in the updated population are normalized to obtain the target values of the individuals after the maximum-minimum normalization. Based on the target values of the individuals after the maximum-minimum normalization, the diversity index is calculated. ,like ,in, 、 、 Represent the diversity indicators of the current iteration, the previous generation of the current iteration, and the two generations before the current iteration, respectively. Then cluster the updated population individuals into T categories, calculate the density of each category and arrange the T categories in descending order, recorded as , ,..., ,right Add a new weight vector, if Only one individual , then find the individual The nearest num individuals ,k=1,2,...,num; and The centroid of the corresponding weight vector is inserted as the new weight vector; if it contains multiple individuals, two individuals are randomly selected and the centroid of the weight vector corresponding to the two individuals is inserted as the new weight vector until num weight vectors are inserted; Delete the weight vector if The number of individuals e≥num, then from Randomly select num individuals and delete the weight vectors corresponding to num individuals; if If the number of individuals e<num, delete the weight vectors corresponding to e individuals, update num=num-e, and continue to traverse the next category until num weight vectors are deleted.

[0070] The formula for calculating the diversity index is as follows:

[0071] In the formula, S represents the external population output by the algorithm in the current iteration, |S| represents the number of solutions in the external population, The calculation is The mean

[0072] and All middle and The target value in the kth dimension, For solution The minimum Manhattan distance to all other solutions in the solution set S.

[0073] When 70% of the maximum number of iterations < the number of iterations ≤ the maximum number of iterations, calculate the convergence index ,like ,in, 、 、 They represent the convergence indexes of the current iteration, the previous generation of the current iteration, and the two generations before the current iteration, respectively. , then cluster the updated population individuals into T categories, calculate the density of each category and arrange the T categories in ascending order, recorded as , ,..., ,right Add a new weight vector, from Randomly select two individuals from the , and insert the centroid of the weight vectors corresponding to the two individuals as the new weight vector, until num weight vectors are inserted; Delete the weight vector if The number of individuals e≥num, then from Randomly select num individuals and delete the weight vectors corresponding to num individuals; if If the number of individuals e<num, delete the weight vectors corresponding to e individuals, update num=num-e, and continue to traverse the next category until num weight vectors are deleted.

[0074] It should be noted that if there are z classes with the same density and the same maximum or minimum value, z ≥ 2, then one class is randomly selected from the z classes to delete or add the weight vector.

[0075] The formula for calculating the convergence index is as follows:

[0076] S represents the external population output by the algorithm in the current iteration, is an individual in the population, Z is the reference point of the population, that is, the maximum value in each dimension, for arrive The hyperrectangular region between It is the Lebesgue measure, which is used to calculate the volume of a multidimensional space set.

[0077] The predefined quantity calculation formula is specifically expressed as follows:

[0078] Where, is the current iteration number, is the number of individuals in the updated population.

[0079] The density calculation formula is as follows:

[0080] Where, is the class after the j-th clustering, is the centroid of the class after the j-th clustering, for The samples in is the number of samples in the class after the j-th clustering, is the Euclidean distance. The numerator of the formula is the size of a class (number of samples), and the denominator is the sum of the distances from all samples to the centroid of the class (the smaller the distance, the more compact the cluster). Therefore, the greater the density, the tighter the cluster.

[0081] It should be noted that in the early stages of iteration (<40%), the population is dispersed and the knowledge of the target space is limited. If the weight vector is adjusted too early, the search direction may converge to the local optimum too early. By fixing the weight vector and maintaining the diversity of the initial sampling, the algorithm can ensure that the potential multi-objective trade-off directions are fully covered, providing rich basic data for subsequent stages.

[0082] In the middle of the iteration (40%-70%), the algorithm has initially converged to some high-quality areas, but may ignore some "niche" but valuable trade-off directions (such as "medium gain-medium power consumption"). By deleting the weight vectors of the high-density class and adding the weight vectors of the low-density class, the algorithm guides the population to evolve in directions that have not been fully explored, avoids falling into local optimality, and expands the coverage of the Pareto frontier.

[0083] In the later stages of iteration (70%-100%), the algorithm has identified most high-quality areas and the focus shifts to refined convergence, focusing on the most promising sub-directions. Weight vectors for low-density categories are deleted, and weight vectors for high-density categories are added. This concentrates resources to accelerate convergence, reduce redundant searches, and quickly approach the theoretical optimal solution.

[0084] The updated population individuals are clustered using an angle-based vector clustering method, including: By initialization uniformly distributed 2D vectors Division Classes, the calculation method is:

[0085] where t=1,2,…, ; The value of depends on the specific experiment.

[0086] Create a loop that randomly selects two objective functions from the objective functions of the amplifier size optimization problem. For each two-dimensional vector ,in accordance with An individual is selected from the updated population and assigned to the tth class until all individuals in the updated population are clustered and the cycle ends.

[0087] It should be noted that in the multi-objective optimization of automated amplifier design, the complex coupling of design parameters requires algorithms that can efficiently coordinate population distributions to rapidly approach the Pareto frontier. Traditional partition-based clustering methods directly divide the population by objective value, resulting in individuals with similar objectives being grouped into the same cluster. This leads to cluster polarization: solutions with excellent convergence are concentrated in a few clusters, while solutions with poor performance are dispersed elsewhere, severely limiting the algorithm's ability to explore the multi-dimensional amplifier design space. Therefore, an angle-based vector clustering method is employed. By using the angle similarity criterion, the solutions within each cluster are highly consistent in their multi-objective trade-off characteristics.

[0088] Example 2: To verify the effectiveness of the proposed method, this example used two classic analog circuits, a two-stage operational amplifier (TSOA) and a folded cascode operational amplifier (FCOA), as experimental cases. Both circuits were implemented using ICSPROUT 55nm process technology. Six advanced algorithms were selected as benchmarks for comparison: LDS-AF, SSDE, PC-SAEA, MO-L2SMEA, MCEA-D, and ADSAPSO. These algorithms are surrogate model optimization algorithms for analog circuit problems. A comprehensive evaluation of each algorithm's optimization capabilities and efficiency was conducted by analyzing the best performance metrics, average HV metrics, and runtime achieved during circuit optimization. The "+", "=", and "-" symbols indicate that the proposed algorithm has significant advantages, comparable performance, or significant disadvantages compared to the original algorithm, respectively.

[0089] In this embodiment, the proxy model prediction error threshold =0.945, decay rate is 0.01, update threshold and The comparison algorithms all adopt the optimal parameter configuration recommended in the original literature. The upper limit of the number of true evaluations for all algorithms is set to 1000 times.

[0090] The circuit diagram of the secondary operational amplifier is as follows Figure 2As shown in Figure 1, the circuit consists of three parts: a bias circuit, an input-stage amplifier circuit, and an output-stage amplifier circuit. The bias circuit, consisting of M8-M13 and resistor RB, is a cascode Widlar current source. M8 and M9 have the same width-to-length ratio. Compared to M13, M12 has resistor RB added to its source, forming a micro-current source that generates current. The symmetrical M11 and M12 form a cascode structure, minimizing current errors caused by channel length modulation. While providing bias current, they also provide a bias voltage for the gate of M14. The input-stage amplifier circuit consists of M1-M5. M1 and M2 form a PMOS differential input pair, with differential inputs VN and VP, respectively. VN is the inverting input, and VP is the non-inverting input. Compared to single-ended inputs, this effectively suppresses common-mode signal interference. M3 and M4 current mirrors act as active loads. M5 provides a constant bias current for the first stage, with its drain connected to the power supply voltage VDD. The output stage amplifier circuit is composed of M6 and M7. M6 is a common source amplifier, and M7 provides a constant bias current for it and serves as the second stage output load. The output terminal of the circuit is connected to the drain of M6, and an external load capacitor is connected. The phase compensation circuit is composed of M14 and Cc. M14 works in the linear region and is equivalent to a resistor. Together with the capacitor Cc, it is connected between the second-stage input and output to form an RC Miller compensation.

[0091] In the Two-Stage Operational Amplifier (TSOA) problem, the decision variable dimension is 18, and the target space dimension is 3. The three optimization objectives for this circuit design problem are maximizing gain, common-mode rejection ratio (CMRR), and power supply rejection ratio (PSRR). In industrial applications, a circuit design is considered qualified if all three objectives exceed 70dB.

[0092] In this embodiment, the weights corresponding to Gain, CMRR, and PSRR are W = {0.5, 0.3, 0.2}. The hypervolume (HV) metric is used to evaluate the performance of these surrogate model-based optimization algorithms on TSOA. The specific values are shown in Table 1 below: Table 1 Average performance and HV of 7 surrogate model-based optimization algorithms on TSOA problem

[0093] As shown in the TSOA data column in Table 1, the S-MOEA / D algorithm achieved the best maximum performance metric for this circuit optimization. Furthermore, analysis based on the average HV (hypervolume) metric showed that S-MOEA / D had the best convergence performance. In terms of algorithm runtime, none of the seven compared algorithms demonstrated a significant improvement in optimization speed, due to the time-consuming nature of actual circuit evaluation in analog circuit optimization.

[0094] The circuit diagram of the folded cascode operational amplifier is as follows: Figure 3 As shown, the circuit primarily consists of a differential input stage, an intermediate amplifier stage, and an output driver stage. The differential input stage comprises a pair of PMOS transistors M1 and M2, which receive the differential signal (VIN+, VIN-). Tail current source M0 provides a constant bias current, achieving high common-mode rejection ratio (CMRR) and low-noise amplification. The intermediate amplifier stage utilizes a cascode structure formed by M5, M6, and M7 to increase voltage gain. A current mirror formed by M3 and M4 stabilizes the operating point. VB4 provides the bias voltage for M3 and M4, ensuring the current mirror operates in the proper saturation region, thus stabilizing current and gain. The output stage utilizes a Class-AB complementary structure formed by M8 (PMOS) and M9 and M10 (NMOS), reducing output impedance and enhancing current drive capability to ensure signal swing. Bias voltages VB1 and VB2 and the power supplies (VDD, VSS) provide the quiescent operating point for each stage. Node VB3 may be connected to a Miller compensation capacitor to optimize frequency response. VOUT is used for output performance testing. The circuit is a typical high-performance operational amplifier architecture that takes into account high gain, low power consumption and stability through multi-stage collaborative design.

[0095] In the Folded-Cascode Operational Amplifier (FCOA) problem, the decision variable dimension is 14, and the target space dimension is 2. The two optimization objectives for this circuit design problem are maximizing gain and phase margin (PM). In industrial applications, a circuit design is considered feasible if its gain exceeds 55dB and its phase margin is greater than 45 degrees.

[0096] In this embodiment, the weights corresponding to Gain and PM are W = {0.75, 0.25}. The hypervolume (HV) metric is used to evaluate the performance of these surrogate model-based optimization algorithms on FCOA. The specific values are shown in Table 2 below: Table 2 Average performance and HV of seven surrogate model-based optimization algorithms on the FCOA problem

[0097] As shown in the FCOA data column in Table 2, the S-MOEA / D algorithm also achieved the best maximum performance index and the best convergence performance in optimizing this circuit. In terms of algorithm runtime, similar to the TSOA problem, none of the compared algorithms showed a significant advantage.

[0098] This paper proposes an automatic analog circuit amplifier design method (S-MOEA / D) based on a lightweight gradient boosting decision tree, aiming to achieve amplifier parameter optimization. The method includes a low-cost SrM online update strategy and an adaptive weight vector strategy based on population distribution. In the online update strategy, by utilizing the historical information of the population and the information of the public database, the model's ability to characterize analog circuit information is significantly improved, thereby improving the prediction accuracy. The weight vector update strategy ensures that the population searches in the optimal sub-direction, accelerating the population's approach to the Pareto front. In comparative experiments, compared with six other state-of-the-art SAEAs, S-MOEA / D demonstrated strong competitiveness in low-dimensional problems. The results of the analog circuit case further verified that S-MOEA / D has superior optimization capabilities in analog circuit optimization.

[0099] Technical features not described in the present invention can be achieved through or by adopting existing technologies and will not be described in detail here. Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A multi-objective amplifier size optimization algorithm assisted by a proxy model, characterized in that: The following steps are involved: S1. Build an external population and size optimization database, define the objective function of the amplifier size optimization problem, generate N weight vectors according to the objective function, and generate an initial population based on the weight vectors; The initial population includes N individuals, each of which corresponds to a weight vector; S2. Calculate the target value of the individual in the initial population, build the LGBM proxy model based on the individual and target values, and define the prediction error threshold of the LGBM proxy model ; S3. Construct a neighbor set for the weight vector, randomly select two weight vectors from the neighbor set, and use the individuals corresponding to the two weight vectors as parent individuals to generate a new individual; S4. Predict the target value of the new individual through the LGBM agent model and calculate the prediction error , if the prediction error Less than the prediction error threshold , the LGBM proxy model is used to predict the target value of the new individual, otherwise the target value of the new individual is obtained by calculation; S5. Calculate the aggregate function value of the individual based on the target value combined with the aggregate function, update the population and external population in the current iteration round according to the aggregate function value, and store the new individual and the target value of the new individual in the size optimization database; S6. Set the maximum number of iterations. When the number of iterations does not reach the maximum value, execute S3-S5 in a loop, and update the LGBM proxy model and weight vector during the iteration. When the number of iterations reaches the maximum value, the algorithm ends and outputs the external population.

2. The proxy model-assisted multi-objective amplifier size optimization algorithm according to claim 1, characterized in that: The external population is an empty array at the beginning of the iteration, and the storage limit is set to , store non-dominated individuals in the iteration; The size optimization database is an empty database at the beginning of the iteration. During the iteration, the new individual and the target value of the new individual are stored as a piece of data, and a data label is added. The data label includes the iteration round when the data is stored, the number of times the data is accumulated for training the LGBM proxy model, and whether the target value is predicted by the LGBM proxy model; the generation of N weight vectors adopts the Das and Dennis's method, and the generation of the initial population adopts the Latin hypercube sampling method.

3. The proxy model-assisted multi-objective amplifier size optimization algorithm according to claim 2, characterized in that: The target values of the individuals in the initial population and the target values of the new individuals obtained by calculation are both calculated using the circuit simulator Spectre.

4. The proxy model-assisted multi-objective amplifier size optimization algorithm according to claim 3, characterized in that: The constructing of the neighbor set includes: calculating the Euclidean distance between all weight vectors, and selecting the k weight vectors with the closest distance to each weight vector to construct the neighbor set; The generating of new individuals includes performing uniform crossover and Gaussian mutation on parent individuals.

5. The proxy model-assisted multi-objective amplifier size optimization algorithm according to claim 4, characterized in that: The step of calculating the aggregate function value of the individual based on the target value combined with the aggregate function, and updating the population and the external population in the current iteration round according to the aggregate function value includes: Based on the target value of the new individual and the target values of the individuals corresponding to the k weight vectors of the neighbor set, the aggregation function value of the new individual and the aggregation function value of the individuals corresponding to the k weight vectors of the neighbor set are calculated according to the pre-defined aggregation function; The aggregation function formula is as follows: ； Where, For individuals, is the number of objective functions, For the j The objective function, For the j The reference point of the objective function, For the j The weight vector of the objective function, For the j The weight of the objective function; Compare the aggregation function value of the new individual with the aggregation function values of the individuals corresponding to the k weight vectors of the neighbor set. If the aggregation function value of the new individual is smaller than the aggregation function value of the individuals corresponding to the k weight vectors of the neighbor set, then replace the individuals whose aggregation function value is larger than the aggregation function value of the new individual among the individuals corresponding to the k weight vectors of the neighbor set with the new individual to obtain the updated population. If the external population does not reach the storage limit , the new individual is directly added to the external population. Otherwise, the dominance relationship between the new individual target value and the target values of all individuals in the external population is compared. If the dominance level of the new individual target value is high, the new individual is used to replace the individual with the lowest dominance level in the external population to obtain the updated external population.

6. The proxy model-assisted multi-objective amplifier size optimization algorithm according to claim 5, characterized in that: Updating the LGBM agent model and weight vector in iterations includes: In each iteration, all individuals and target values of the population in the previous iteration are collected to form a temporary data set , for the temporary dataset Perform deduplication processing to obtain a streamlined data set ; Based on the data labels in the size optimization database and in combination with a predefined data selection formula, data is filtered from the size optimization database as an additional sample set; the predefined data selection formula is specifically expressed as follows: ； Where, is the probability of data selection, is the iteration round when data is stored, The number of times the data is used to train the LGBM proxy model; The dataset will be streamlined and additional sample sets to obtain the model update dataset, and divide the model update dataset into training set, validation set and test set; Use the training set to incrementally train the LGBM proxy model, use the validation set to adjust the LGBM model hyperparameters, and evaluate the LGBM proxy model performance on the test set; From the size optimization database, select based on the data label using the maximum and minimum fill principle The target values of the items are obtained by using the data predicted by the LGBM proxy model. The circuit simulator Spectre is used to calculate the target values of the items, and the calculated target values are used to replace the target values predicted by the LGBM proxy model stored in the size optimization database. The maximum and minimum filling principle includes: taking individuals in the data obtained by predicting the target value in the size optimization database through the LGBM agent model as candidate individuals , the individuals in the data whose target values are not predicted by the LGBM proxy model are regarded as sampled individuals , calculate each candidate individual With the sampled individuals The distance between , and determine With all The minimum distance ; Among all candidate individuals In, based on Select the next sampling individual, where is the next sampling individual, and C is the candidate individual set; When the number of iterations is less than 40% of the maximum number of iterations, the weight vector is not updated; When 40% of the maximum number of iterations ≤ the number of iterations < 70% of the maximum number of iterations, after updating the population in each round of iteration, the target values of the individuals in the updated population are normalized to obtain the target values of the individuals after the maximum-minimum normalization. Based on the target values of the individuals after the maximum-minimum normalization, the diversity index is calculated. ,like ,in, 、 、 Represent the diversity indicators of the current iteration, the previous generation of the current iteration, and the two generations before the current iteration, respectively. If is a constant, the updated population individuals are clustered into T classes, the density of each class is calculated and sorted in descending order, and the density of the T classes is sorted in descending order. According to the predefined quantity calculation formula, the number num of weight vectors that need to be adjusted is calculated. Combined with the density of the T classes in descending order, num weight vectors are deleted from the T class and num weight vectors are added. When 70% of the maximum number of iterations < the number of iterations ≤ the maximum number of iterations, calculate the convergence index ,like ,in, 、 、 They represent the convergence indexes of the current iteration, the previous generation of the current iteration, and the two generations before the current iteration, respectively. If is a constant, the individuals in the updated population are clustered into T classes, the density of each class is calculated and sorted in ascending order, and the density of the T classes is sorted in ascending order. According to the predefined quantity calculation formula, the number num of weight vectors that need to be adjusted is calculated. Combined with the density sorting of the T classes in ascending order, num weight vectors are deleted from the T class and num weight vectors are added. The predefined quantity calculation formula is specifically expressed as follows: ； Where, is the current iteration number, is the number of individuals in the updated population.

7. The proxy model-assisted multi-objective amplifier size optimization algorithm according to claim 6, characterized in that: The updated population individuals are clustered using an angle-based vector clustering method, including: By initialization uniformly distributed 2D vectors Division Classes, the calculation method is: ； where t=1,2,…, ; Create a loop that randomly selects two objective functions from the objective functions of the amplifier size optimization problem. For each two-dimensional vector ,in accordance with An individual is selected from the updated population and assigned to the tth class until all individuals in the updated population are clustered and the cycle ends.

8. The proxy model-assisted multi-objective amplifier size optimization algorithm according to claim 7, characterized in that: The deleting num weight vectors in class T and adding num weight vectors includes: When 40% of the maximum number of iterations ≤ the number of iterations < 70% of the maximum number of iterations, sort in descending order of T class and record it as , ,..., ,right Add a new weight vector, if Only one individual , then find the individual The nearest num individuals ,k=1,2,...,num; and The centroid of the corresponding weight vector is inserted as the new weight vector; if it contains multiple individuals, two individuals are randomly selected and the centroid of the weight vector corresponding to the two individuals is inserted as the new weight vector until num weight vectors are inserted; Delete the weight vector if The number of individuals e≥num, then from Randomly select num individuals and delete the weight vectors corresponding to num individuals; if If the number of individuals e < num, then delete the weight vectors corresponding to e individuals, update num = num-e, and continue to traverse the next category until num weight vectors are deleted; When 70% of the maximum number of iterations < the number of iterations ≤ the maximum number of iterations, sort in ascending order of T class and record it as , ,..., ,right Add a new weight vector, from Randomly select two individuals from the , and insert the centroid of the weight vectors corresponding to the two individuals as the new weight vector, until num weight vectors are inserted; Delete the weight vector if The number of individuals e≥num, then from Randomly select num individuals and delete the weight vectors corresponding to num individuals; if If the number of individuals e<num, delete the weight vectors corresponding to e individuals, update num=num-e, and continue to traverse the next category until num weight vectors are deleted.

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