Black box parameter optimization method fusing multiple coordinate system forms

Abstract

The invention discloses a black box parameter optimization method fusing multiple coordinate system forms. The method comprises the following steps: S1, initializing a plurality of populations; wherein the populations are expressed in different coordinate system forms; each individual in each population is a candidate solution of the black box parameter to be optimized; s2, performing independent updating and fitness calculation on the populations in different coordinate system forms by using a JADE solver; s3, determining a dominant coordinate system form and a dominant population based on the fitness of all individuals; s4, updating the dominant population in the dominant coordinate system form by using a JADE solver; s5, judging whether a termination condition is met or not; if yes, outputting an optimal solution in the current dominant population as an optimized black box parameter; and if not, performing coordinate system conversion on the current dominant population to obtain populations of the current dominant population in all coordinate system forms, and returning to S2. According to the method, the collaborative optimization potential among different coordinate system forms when the same black box parameter is optimized can be effectively mined, and the optimization efficiency and robustness are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of parameter optimization, and more particularly to a black-box parameter optimization method that integrates multiple coordinate system forms. Background Art

[0002] In complex black-box parameter optimization problems, such as actual scenarios like aircraft airfoil parameter optimization, model parameter optimization in machine learning, and cutting angle optimization of semiconductor circular wafers, the following characteristics often exist: 1) The objective function is expressed as a black-box model that cannot be analytically expressed; 2) There are non-linear coupling relationships between parameters; 3) The search space has multi-modal and high-dimensional characteristics. Traditional optimization algorithms usually adopt a single coordinate system form, that is, the Cartesian coordinate system encoding search scheme, resulting in the search process being easily affected by the initial population distribution and difficult to break through the local optimal trap. For example, in aircraft airfoil parameter optimization, when fixedly using the Cartesian coordinate system for parameter encoding, it may not be able to effectively capture the geometric characteristics of airfoil parameter combinations with rotational symmetry characteristics, resulting in low search efficiency.

[0003] In the prior art, some research attempts to improve the algorithm performance by introducing an external archive mechanism (such as the JADE algorithm) or improving the crossover and mutation strategies, but essentially it is still limited to the optimization framework of a single coordinate system form. Although some scholars have recently proposed a multi-task optimization framework, it is mainly aimed at the parallel solution of multiple independent problems and fails to effectively explore the collaborative optimization potential between different coordinate system forms of the same problem. For example, in the cutting angle optimization of semiconductor circular wafers, using the polar coordinate system can more intuitively process the cutting angle parameters of semiconductor circular wafers, but the existing methods lack a mechanism to dynamically fuse the search information of the two coordinate system forms of polar coordinates and Cartesian coordinates, resulting in the inability to fully utilize the complementary advantages of different coordinate system forms.

[0004] Therefore, how to provide a black-box parameter optimization method that integrates multiple coordinate system forms, which can effectively explore the collaborative optimization potential between different coordinate system forms when optimizing the same black-box parameter, so as to improve the optimization efficiency and robustness is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a black-box parameter optimization method that integrates multiple coordinate system forms.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A black-box parameter optimization method that integrates multiple coordinate system forms, comprising the following steps:

[0008] S1: Initialize several populations; among them, each population is represented in a different coordinate system form; each individual in each population is a candidate solution for the black-box parameters to be optimized; the black-box parameters are aircraft airfoil parameters, model parameters in machine learning, or cutting angles of semiconductor circular wafers;

[0009] S2: Use the JADE solver to independently update and calculate the fitness of each population in different coordinate system forms respectively;

[0010] S3: Determine the dominant coordinate system form and the dominant population based on the fitness of all individuals;

[0011] S4: Use the JADE solver to update the dominant population in the dominant coordinate system form;

[0012] S5: Determine whether the termination condition is reached; if so, output the optimal solution in the current dominant population as the optimized black-box parameters; if not, perform coordinate system transformation on the current dominant population to obtain the populations of the current dominant population in all coordinate system forms, and return to S2.

[0013] Preferably, S2 specifically includes:

[0014] S21: Use the JADE solver to independently update each population in different coordinate system forms for t1 rounds to obtain updated populations in different coordinate system forms;

[0015] S22: Calculate the fitness of each individual in each updated population in S21.

[0016] Preferably, the dominant coordinate system form is determined based on the following formula;

[0017]

[0018]

[0019] where, F dominant represents the dominant coordinate system form; δ NP represents the screening function; form represents the coordinate system form; represents the m-th individual of the populations in different coordinate system forms; represents the fitness of; NP represents the number of individuals included in the population.

[0020] Preferably, the dominant population is obtained based on the following steps:

[0021] S31: Sort all individuals according to their fitness; among them, all individuals are the individuals in each updated population in S22;

[0022] S32: Screen the top NP individuals before screening to obtain the dominant population;

[0023] S33: Convert the top NP individuals screened into the form of the dominant coordinate system to obtain the dominant population in the form of the dominant coordinate system.

[0024] Preferably, S4 specifically includes:

[0025] S41: Initialize the external archive of the dominant population;

[0026] S42: Use the JADE solver including the external archive of the dominant population to update the dominant population in the form of the dominant coordinate system for t2 rounds to obtain the updated dominant population in the form of the dominant coordinate system.

[0027] Preferably, S41 specifically includes the following steps:

[0028] S411: Obtain the proportion of the updated populations in different coordinate system forms in S21 in the dominant population;

[0029] S412: Perform boundary processing on the proportion obtained in S411;

[0030] S413: Calculate the reverse selection ratio of the updated populations in different coordinate system forms based on the proportion after boundary processing;

[0031] S414: Select individuals from the updated populations in different coordinate system forms according to their corresponding reverse selection ratios and inject them into the external archive of the dominant population.

[0032] Preferably, S412 specifically includes the following steps:

[0033] Compare the proportion obtained in S411 with 0.05. If the proportion obtained in S411 is greater than 0.05, the proportion after boundary processing is the proportion obtained in S411; if the proportion obtained in S411 is less than or equal to 0.05, the proportion after boundary processing is 0.05.

[0034] Preferably, calculate the reverse selection ratio of the updated populations in different coordinate system forms based on the following formula

[0035]

[0036] where M represents the number of coordinate systems in different forms; p i represents the proportion after boundary processing; W i represents the reverse selection ratio of the updated populations in different coordinate system forms.

[0037] Preferably, the termination condition in S5 is that the number of times of repeating S3 - S4 reaches t3 or the fitness of the optimal solution in the current dominant population reaches the preset fitness range.

[0038] Preferably, the coordinate system forms include Cartesian coordinate system form, polar coordinate system form, and PCA transformation coordinate system form.

[0039] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a black-box parameter optimization method that integrates multiple coordinate system forms, which can effectively explore the collaborative optimization potential between different coordinate system forms when optimizing the same black-box parameter, thereby improving the optimization efficiency and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to the provided drawings.

[0041] Figure 1 It is a flowchart of a black-box parameter optimization method that integrates multiple coordinate system forms provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0043] As Figure 1 shown, the embodiments of the present invention disclose a black-box parameter optimization method that integrates multiple coordinate system forms, including the following steps:

[0044] S1: Initialize several populations; wherein, each population is represented in a different coordinate system form; each individual in each population is a candidate solution for the black-box parameter to be optimized; the black-box parameter is an aircraft airfoil parameter, a model parameter in machine learning, or a cutting angle of a semiconductor circular wafer;

[0045] Further, the coordinate system forms include Cartesian coordinate system form, polar coordinate system form, and PCA transformation coordinate system form. Specifically: The present invention initializes 3 populations, each population includes NP individuals, one population is represented in Cartesian coordinate system form, one population is represented in polar coordinate system form, and one population is represented in PCA transformation coordinate system form.

[0046] S2: Use the JADE solver to independently update and calculate the fitness of each population in different coordinate system forms;

[0047] Furthermore, S2 specifically includes:

[0048] S21: Use the JADE solver to independently update each population in different coordinate system forms for t1 rounds to obtain updated populations in different coordinate system forms;

[0049] Specifically:

[0050] Use the JADE solver to independently update the population in Cartesian coordinate system form for t1 rounds to obtain the updated population in Cartesian coordinate system form;

[0051] Use the JADE solver to independently update the population in polar coordinate system form for t1 rounds to obtain the updated population in polar coordinate system form;

[0052] Use the JADE solver to independently update the population in PCA transformed coordinate system form for t1 rounds to obtain the updated population in PCA transformed coordinate system form.

[0053] It should be noted that: the value of t1 should be as small as possible to make the cost of maintaining multiple populations controllable. The specific value of t1 should be combined with the dimension size n of the black box parameters to be optimized, and it is recommended to be set to or n;

[0054] S22: Calculate the fitness of each individual in each updated population in S21.

[0055] Specifically:

[0056] Calculate the fitness of each individual in the updated population in Cartesian coordinate system form;

[0057] Calculate the fitness of each individual in the updated population in polar coordinate system form;

[0058] Calculate the fitness of each individual in the updated population in PCA transformed coordinate system form.

[0059] S3: Determine the dominant coordinate system form and the dominant population based on the fitness of all individuals;

[0060] Furthermore, determine the dominant coordinate system form based on the following formula;

[0061]

[0062] where, F dominant represents the dominant coordinate system form; δ NPrepresents a screening function; form represents the form of the coordinate system (i.e., Cartesian coordinate system, polar coordinate system, and PCA transformation coordinate system); represents the m-th individual of the population in different coordinate system forms; represents the fitness of; NP represents the number of individuals included in the population.

[0063] Further, the dominant population is obtained based on the following steps:

[0064] S31: Sort the fitness of all individuals; where all individuals are the individuals in each updated population in S22;

[0065] Specifically: Overall sort the fitness of each individual in the updated population in Cartesian coordinate system form, the fitness of each individual in the updated population in polar coordinate system form, and the fitness of each individual in the updated population in PCA transformation coordinate system form;

[0066] S32: Select the top NP individuals to obtain the dominant population;

[0067] S33: Convert the selected top NP individuals into the dominant coordinate system form to obtain the dominant population in the dominant coordinate system form.

[0068] It can be understood that: The dominant coordinate system form may be the Cartesian coordinate system, the polar coordinate system, and the PCA transformation coordinate system; Therefore, S33 will involve the mutual conversion of the Cartesian coordinate system, the polar coordinate system, and the PCA transformation coordinate system:

[0069] Assume:

[0070] an individual of the population in Cartesian coordinate system form n represents the dimension of the individual, that is, the dimension of the black box parameter to be optimized.

[0071] an individual of the population in polar coordinate system form where, when n = 2, θ1 ∈ [0, 2π]; when n > 2 and j = 1, …, n - 2, θ j ∈ [-π, π]; when n > 2 and j = n - 1, θ j ∈ [0, 2π];

[0072] an individual of the population in PCA transformation coordinate system form

[0073] 1) The conversion from polar coordinate system form to Cartesian coordinate system form adopts the following formula:

[0074]

[0075] x n = ρcosθ1 (3);

[0076] It should be noted that: if n = 2, then formulas (1) and (3) are used for conversion;

[0077] if n > 2, then formulas (1), (2) and (3) are used for conversion.

[0078] 2) The conversion from Cartesian coordinate system form to polar coordinate system form uses the following formula:

[0079]

[0080] 3) The conversion from Cartesian coordinate system form to PCA transformation coordinate system form uses the following formula:

[0081]

[0082] C = UΛU T (8);

[0083] where represents the m-th individual of the population in Cartesian coordinate system form; C is the covariance matrix of; Λ is the diagonal matrix formed by arranging the eigenvalues of the covariance matrix C in descending order; U is the matrix formed by arranging the eigenvectors of the covariance matrix C in the order of eigenvalues.

[0084] 4) The conversion from PCA transformation coordinate system form to Cartesian coordinate system form uses the following formula

[0085]

[0086] 5) The polar coordinate system form and the PCA transformation coordinate system form can use the Cartesian coordinate system form as an intermediate form and then be converted to each other.

[0087] It can be understood that: when the population is updated or initialized, the following boundary constraint conditions need to be satisfied:

[0088] The boundary constraint of the Cartesian coordinate system is [lowerbound i , upperbound i n ∈ [R, R] n ; lowerbound i , upperbound i represent the upper and lower boundaries of the i-th dimension of the individual;

[0089] The boundary constraint ρBound of ρ in the polar coordinate system is:

[0090]

[0091] ​When n = 2, θ1 ∈ [0, 2π]; when n > 2 and j = 1, …, n - 2, θ j ∈ [-π, π]; when n > 2 and j = n - 1, there is θ j ∈ [0, 2π];

[0092] It should be noted that: ρBound set in the present invention is based on the first dimension in the individual. Therefore, after the conversions of formula (1), formula (2) and formula (3) are completed, it is necessary to multiply by the scaling factors corresponding to the respective dimensions; among them, the scaling factor of the i-th dimension After the conversions of formula (4) and formula (5) are completed, it is necessary to divide by the scaling factors corresponding to the respective dimensions.

[0093] It should be noted that: the present invention selects the individuals with the top NP / 2 fitness rankings for learning the parameters (U and C) of PCA transformation.

[0094] S4: Use the JADE solver to update the dominant population in the form of the dominant coordinate system;

[0095] Further, S4 specifically includes:

[0096] S41: Initialize the external archive of the dominant population;

[0097] Further, S41 specifically includes the following steps:

[0098] S411: Obtain the proportion of the updated populations in different coordinate system forms in S21 in the dominant population;

[0099] S412: Perform boundary processing on the proportion obtained in S411;

[0100] Further, S412 specifically includes the following steps:

[0101] Compare the proportion obtained in S411 with 0.05. If the proportion obtained in S411 is greater than 0.05, the proportion after boundary processing is the proportion obtained in S411; if the proportion obtained in S411 is less than or equal to 0.05, the proportion after boundary processing is 0.05.

[0102] S413: Calculate the reverse selection ratio of the updated populations in different coordinate system forms based on the proportion after boundary processing;

[0103] Further, calculate the reverse selection ratio of the updated populations in different coordinate system forms based on the following formula

[0104]

[0105] where M represents the number of coordinate system forms of different types (M = 3 in the embodiment of the present invention); p iIndicates the proportion after boundary processing; W i Indicates the reverse selection ratio of the updated population in different coordinate system forms.

[0106] S414: Select individuals from the updated population in different coordinate system forms according to their corresponding reverse selection ratios and inject them into the external archive of the dominant population.

[0107] S42: Use the JADE solver including the external archive of the dominant population to update the dominant population in the dominant coordinate system form for t2 rounds to obtain the updated dominant population in the dominant coordinate system form.

[0108] It can be understood that: t2 should be significantly greater than t1 so that computing resources can be reasonably and efficiently allocated. The setting of t2 can be in a proportional relationship with t1, such as t2 = k * t1, where it is recommended that k takes 4 - 8.

[0109] S5: Determine whether the termination condition is reached; if so, output the optimal solution in the updated dominant population as the optimized black box parameter; if not, perform coordinate system transformation on the current dominant population to obtain the populations of the current dominant population in all coordinate system forms, and return to S2.

[0110] Specifically:

[0111] 1) If the termination condition is not reached and it is assumed that the dominant coordinate system form is the Cartesian coordinate system form;

[0112] Then convert the updated dominant population in the Cartesian coordinate system form into an equivalent updated dominant population in the polar coordinate system form and an equivalent updated dominant population in the PCA transformation coordinate system form, and use the updated dominant population in the Cartesian coordinate system form, the equivalent updated dominant population in the polar coordinate form, and the equivalent updated dominant population in the PCA transformation coordinate system form as the populations in each different coordinate system form in S2, and repeat S2 - S3.

[0113] 2) If the termination condition is not reached and it is assumed that the dominant coordinate system form is the polar coordinate system form; then convert the updated dominant population in the polar coordinate system form into an equivalent updated dominant population in the Cartesian coordinate system form and an equivalent updated dominant population in the PCA transformation coordinate system form, and use the updated dominant population in the polar coordinate form, the equivalent updated dominant population in the Cartesian coordinate system form, and the updated dominant population in the PCA transformation coordinate system form as the populations in each different coordinate system form in S2, and repeat S2 - S3.

[0114] 3) If the termination condition is not met and it is assumed that the form of the dominant coordinate system is the form of the PCA transformation coordinate system; then the updated dominant population in the form of the PCA transformation coordinate system is converted into an updated dominant population in the equivalent Cartesian coordinate system form and an updated dominant population in the equivalent polar coordinate system form, and the updated dominant population in the form of the PCA transformation coordinate system, the updated dominant population in the equivalent Cartesian coordinate system form, and the updated dominant population in the equivalent polar coordinate form are used as the populations in each different coordinate system form in S2, and S2 - S3 are repeatedly executed.

[0115] Further, the termination condition in S5 is that the number of times of repeatedly executing S3 - S4 reaches t3 or the fitness of the optimal solution in the current dominant population reaches the preset fitness range.

[0116] The various embodiments in this specification are described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the description in the method part.

[0117] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A black-box parameter optimization method integrating various coordinate system forms, characterized in that It includes the following steps: S1: Initialize several populations; where each population is represented in a different coordinate system form; each individual in each population is a candidate solution for the black-box parameters to be optimized; the black-box parameters are aircraft airfoil parameters, model parameters in machine learning, or cutting angles of semiconductor circular wafers; S2: Use the JADE solver to independently update and calculate the fitness of each population in different coordinate system forms respectively; S3: Determine the dominant coordinate system form and the dominant population based on the fitness of all individuals; S4: Use the JADE solver to update the dominant population in the dominant coordinate system form; S5: Judge whether the termination condition is reached; if so, output the optimal solution in the current dominant population as the optimized black-box parameters; if not, perform coordinate system transformation on the current dominant population to obtain the populations of the current dominant population in all coordinate system forms, and return to S2.

2. The black box parameter optimization method integrating various coordinate system forms according to claim 1, characterized in that S2 specifically includes: S21: Use the JADE solver to independently update each population in different coordinate system forms for t1 rounds to obtain updated populations in different coordinate system forms; S22: Calculate the fitness of each individual in each updated population in S21.

3. A black box parameter optimization method integrating multiple coordinate system forms according to claim 2, characterized in that Determine the dominant coordinate system form based on the following formula; Among them, F dominant represents the form of the dominant coordinate system; δ NP represents the screening function; form represents the form of the coordinate system; represents the m-th individual of the population in different coordinate system forms; represents the fitness of; NP represents the number of individuals included in the population.

4. A black box parameter optimization method integrating multiple coordinate system forms according to claim 3, characterized in that The dominant population is obtained based on the following steps: S31: Sort the fitness of all individuals; where all individuals are the individuals in each updated population in S22; S32: Select the top NP individuals to obtain the dominant population; S33: Convert the selected top NP individuals to the dominant coordinate system form to obtain the dominant population in the dominant coordinate system form.

5. A black box parameter optimization method integrating various coordinate system forms according to claim 4, characterized in that S4 specifically includes: S41: Initialize the external archive of the dominant population; S42: Use the JADE solver including the external archive of the dominant population to update the dominant population in the dominant coordinate system form for t2 rounds to obtain the updated dominant population in the dominant coordinate system form.

6. A black box parameter optimization method integrating multiple coordinate system forms according to claim 5, characterized in that S41 specifically includes the following steps: S411: Obtain the proportion of the updated populations in different coordinate system forms in S21 in the dominant population; S412: Perform boundary processing on the proportion obtained in S411; S413: Calculate the reverse selection proportion of the updated populations in different coordinate system forms based on the proportion after boundary processing; S414: Select individuals from the updated populations in different coordinate system forms according to their corresponding reverse selection proportions and inject them into the external archive of the dominant population.

7. A black box parameter optimization method integrating multiple coordinate system forms according to claim 6, characterized in that, S412 specifically includes the following steps: Compare the proportion obtained in S411 with 0.

05. If the proportion obtained in S411 is greater than 0.05, the proportion after boundary processing is the proportion obtained in S411; if the proportion obtained in S411 is less than or equal to 0.05, the proportion after boundary processing is 0.

05.

8. A black box parameter optimization method integrating various coordinate system forms according to claim 6, characterized in that, Calculate the reverse selection proportion of the updated populations in different coordinate system forms based on the following formula Among them, M represents the number of different forms of coordinate systems; p i represents the proportion after boundary processing; W i represents the reverse selection ratio of the updated population in different coordinate system forms.

9. A black box parameter optimization method integrating multiple coordinate system forms according to claim 1, characterized in that The termination condition in S5 is that the number of times of repeating S3 - S4 reaches t3 or the fitness of the optimal solution in the current dominant population reaches the preset fitness range.

10. A black box parameter optimization method integrating various coordinate system forms according to claim 1, characterized in that The coordinate system forms include Cartesian coordinate system form, polar coordinate system form, and PCA transformation coordinate system form.

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