JPH08272761A - Parameter tuning method - Google Patents

Abstract

PURPOSE: To shorten the calculation time required for tuning and apply this method even when there are many parameters by finding sensitivity by the parameters for an evaluation function and tuning a parameter having high sensitivity preferentially. CONSTITUTION: The method which tunes plural parameters suitably for the specific evaluation function generates a chromosome by using the differentiation of the evaluation function. For example, the parameters which are made discrete in the chromosome arrangement of genetic algorithm are genes, whose aggregate is a chromosome. And, the sensitivity Spi regarding an (i)th element of the evaluation function Ev which is a 30 deg.-directional gain E(30) is represented as Spi = dEv / dpi , and the distribution and range of the genes are varied with this sensitivity. Parameters having high sensitivity are made in the width of variation of genes and the remaining parameters have only the low-order two bits varied at random, and the chromosome which maximizes the evaluation function are selected out of them. This process is repeated to find the optimum value of the chromosome.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a parameter tuning method for obtaining an optimum solution of multivariable parameters.

[0002]

2. Description of the Related Art Various parameter tuning methods have been proposed for a long time. In recent years, genetic algorithms (genetic algorithms, hereinafter referred to as “GA”) have been used when performing parameter tuning on a complicated evaluation function.

It is known that the genes of living organisms adapt to the environment and evolve. As a simple example, if you want to produce seeds of high yielding rice in a land with little rain, planting many seedlings of rice in such an environment, the surviving rice, that is, the mutation gene adapted to this environment. Rice plants with chromosomes, which are a set of, are crossed to promote breed improvement. GA
Is a method of engineering this process in a computer.

FIG. 6 shows a conventional GA. Here, 8
A parameter tuning method for shaping the radiation pattern of the array antenna of the element into a predetermined shape will be described in comparison with the rice variety improvement. With an 8-element array antenna as shown in FIG. 7, if the element spacing d is constant, the parameters that the designer can set are the antenna elements a _{1 to} a _{1.
It is} the amplitude and phase of the signal input to ₈ . These correspond to each gene of rice. A combination of the amplitude and phase of 8 elements corresponds to a chromosome.

In either case, a plurality of random options are prepared. For rice, grow these individuals in a light rain environment. In the case of an antenna, the radiation pattern is calculated for each combination of amplitude and phase. After that, the rice with high yield is selected from the selected rice. In the case of an antenna, a combination (excitation distribution) of amplitude phases close to a predetermined radiation pattern, where the main lobe is high and the side lobes are low, is selected here. The selected individual will have an excellent gene for the given environmental conditions. These individuals are crossed to create the next generation of chromosomes. This operation is repeated to find the optimal chromosome.

In order to perform such an operation with a computer, it is necessary to discretize the parameters to be tuned. First, the parameters are discretized assuming a 4-bit phase shifter and an attenuator. The range that the parameter should take depends on the radiation pattern to be set, but it is assumed that the phase is 0 to 360 ° and the amplitude is 0 to -16 dB. That is, the phaser has 12.5 steps per step and the attenuator has 1 dB per step. Of course, if the distribution close to the correct answer is known, the range of parameters can be narrowed by using that value as the initial value.

FIG. 8 shows an example of chromosome arrangement in a conventional GA. Each discretized parameter is a gene, and its aggregate is a chromosome. Here, the phase (binary notation) of each of the 8 elements is a gene, and the combination thereof is a chromosome. As these chromosomes, 90 chromosomes in which the upper 2 bits of the elite chromosome are preserved and only the lower 2 bits are randomly changed, and 10 mutations (all random) are prepared. When the phase of each element is P _i and the amplitude is E _xi , the evaluation function E (θ) is

[0008]

[Equation 1]

[0009] Assuming that a given radiation pattern forms a main lobe in the direction of 30 degrees, the evaluation function is
It is the gain E (30) in the 30 degree direction of (1). The selection is a method called elite preservation, and one of the combinations of the amplitude and phase having the largest evaluation function is preserved. In this way, the evaluation function is obtained for each combination of parameters corresponding to the chromosome, and the one having the maximum evaluation function is stored (selection). A new combination of parameters is created by adding a combination variation that improves the solution corresponding to the genetic information to that combination (replacement). At this time, a combination of randomly arranged parameters corresponding to mutations is mixed in at an extremely rare rate.

By repeating this series of operations, a chromosome that is a combination of parameters that maximizes the evaluation function is obtained.

[0011]

In the conventional GA, when the number of parameters to be set is large, when the number of divisions when discretizing is large, and when the evaluation function is an integral type and complicated, the combination of possible parameters is dramatically. However, depending on the performance of the computer, it may not be possible to perform calculations.

For example, (a) 8 parameters are discretized into 4 bits, that is, 16 values, and 1024 is used to obtain an evaluation function.
If it is necessary to calculate the number of times, (b) 8 parameters are discretized into 8 bits, that is, 64 values, and 2048 is used to obtain the evaluation function.
The case where calculation is required once is explained. Comparing the calculation time of the evaluation function with 1000 chromosomes in these two cases, the number of possible parameter combinations in case (a) is 16 ⁸ ≈ 4.3 × 10 ⁹ and the number of calculations is 1024. × 1000 times. In the case of (b), the number of possible combinations of parameters is 256 ⁸ ≈ 1.8 × 10 ¹⁹ and the number of calculations is 2048 × 1000. Of course, not all of this calculation is done, but the probability of finding the optimal value is
It will be 10 ^-10 . Furthermore, the calculation time per generation is also quadrupled.

It is an object of the present invention to provide a parameter tuning method which can significantly reduce the calculation time required for tuning and can be applied even when there are many parameters.

[0014]

According to the parameter tuning method of the present invention, the sensitivity for each parameter with respect to the evaluation function is obtained, and the parameter having high sensitivity is preferentially tuned.

[0015]

According to the present invention, the number of times of convergence is greatly shortened by preferentially tuning a highly sensitive parameter,
The calculation time required for tuning can be greatly reduced. This is especially effective when there are many parameters to be tuned.

[0016]

EXAMPLE The AG in the parameter tuning method of the present invention is almost the same as in the prior art. The feature of the present invention resides in a method for generating a chromosome. That is, the feature is that the chromosome is generated by using the differentiation of the evaluation function. Hereinafter, the case where the maximum directivity is provided in the direction of 30 degrees will be described as in the case of the description of the related art.

The evaluation function Ev is a gain E (30) in the direction of 30 degrees.
Is. The sensitivity of this evaluation function Ev for each element is obtained, and the variable range of each element is weighted. For example, when there is an excitation distribution as shown in FIG. 8, how much the evaluation function changes with each increment of each parameter is calculated. The sensitivity S _Pi of the evaluation function for the i-th element is S _Pi = ∂Ev / ∂P _i (2). The parameter tuning of the present invention is characterized by using this sensitivity to improve the convergence.

(First Embodiment) FIG. 1 shows a first embodiment of the parameter tuning method of the present invention. In the conventional arrangement example of chromosomes shown in FIG. 8, 90 chromosomes out of 100 chromosomes randomly give only the lower 2 bits of the gene, but in this example, the sensitivity given by equation (2) is used. Vary gene allocation and range. The phase of each element is changed from 0 to 360 degrees in steps of 22.5 degrees. Given the phase array shown in FIG. 8, the change in the evaluation function when the phase of each element changes in steps of 22.5 degrees is obtained. This is the formula
It is the sensitivity given by (2). The eight sensitivities are compared. For example, _assume that the sensitivity S _P3 of the third element is particularly large. In this case, as in the example of chromosome arrangement shown in FIG. 2, all 16 chromosomes that the phase P ₃ of the element a ₃ can take, that is, all the chromosomes from 22.5 degrees to 360 degrees are candidates.

As described above, in the case of high sensitivity, the range of gene change is increased. For the rest, only the lower 2 bits are changed randomly as in the conventional example. From these, select the chromosome that maximizes the evaluation function. Thereafter, the same alternation / selection as in the conventional example is repeated to find the optimum value of the chromosome. In the present embodiment, the chromosomes can be secured preferentially from the one having the highest sensitivity, so that the calculation time can be greatly shortened.

(Second Embodiment) FIG. 3 shows a second embodiment of the parameter tuning method of the present invention. In this embodiment,
It is characterized by using the multivariable successive approximation method for taking the sensitivity. Regarding the multivariable successive approximation method, refer to the literature (eg, Genichi Taguchi, “Experimental Design Method (above)”, Maruzen, pp.331-338, 19).
88). The multivariable successive approximation method is
When the sensitivity of (2) is calculated, variables other than those that are partially differentiated are used as constraint conditions, and average conditions based on the orthogonal table are assumed. Assuming a 4-bit phase shifter as in the first embodiment, there are 16 possible values for the parameters. Such a value is called a level. In this case, a 16-level model is used, and an unrealistically large orthogonal table must be used. Therefore, a method of gradually narrowing the parameter range is used. That is, the parameter range is gradually narrowed in the three-level model.

As shown in Table 1, the initial level is 0 at the first level of the phases P _{1 to} P ₈ in each element, 8 at the second level (180 degrees), and 16 at the third level (360 degrees). Is assigned to the orthogonal table L36 shown in Table 2. The circled numbers in the table represent each level.

[0022]

[Table 1]

[0023]

[Table 2]

The phase of each element is assumed at the level indicated by each column of the orthogonal table. For example, since the first row is all at the first level, it is assumed that the phase of all elements is 0 degree. Since the second line is all at the second level, it is assumed to be 180 degrees. The evaluation function is obtained with such combinations of levels for all 36 rows. Next, the phase P ₁ of the element a ₁ is the first level 1,
The sum of the evaluation functions of lines 4, 7, 10, 13, 16, 19, 19, 22, 25, 28, 31, 34 is the value of the first level of the element a ₁ . The sum of the evaluation functions is similarly obtained for the second level and the third level.
Table 3 shows the results of performing this operation for each element. The underlined level is the optimum level (minimum value).

[0025]

[Table 3]

By this operation, the level at which the reciprocal of the expression (1) of the evaluation function is minimized is selected, and in the next operation, as shown in Table 4, this level is set as the second level and the parameter width is 1/2. 90 degrees

[0027]

[Table 4]

By repeating this operation four times, the approximate solution of the optimum value can be obtained with an accuracy of 22.5 degrees. When the orthogonal table L36 of Table 2 is used, an approximate solution can be reached by calculating the evaluation function only 36 × 4 times. Using this method, G
It is possible to obtain an approximate solution without using A. However, if the initial level values are too far apart, there is a high risk of falling to a local minimum, and it is difficult to find an optimal solution.

Therefore, the phase combination obtained by the successive approximation method must be included in the phase combination of the initial values of GA. FIG. 4 shows an example of arrangement of chromosomes in this example. Also, the optimum solution selected by the first generation is added to the candidates for the combination of phases by using the optimum solution selected by the first generation as the second level. In order to verify the effects of the above steps, the more complicated main lobe,
Simulations were performed using the case of making a beam with low side lobes. FIG. 5 shows the result of attempting optimization by the method of the present embodiment using the amplitude and phase of 8 elements as parameters. The evaluation function is the ratio of the main lobe gain and the maximum side lobe gain. The horizontal axis of FIG. 5 is the generation, and the calculation time can be equivalently considered. The vertical axis is the evaluation function. White circles are the results of normal GA, and black circles are the results of the method of this example. In the 28th, 36th, and 38th generations, the combination of amplitude and phase obtained by the multivariable successive approximation method, which is a feature of the method of this embodiment, is used, and it can be seen that the evaluation function is rapidly improved. Further, it can be seen that the same evaluation function value is obtained by the method of the present embodiment, but the number of times of convergence is about 1/3. Further, if there are many parameters to be tuned, a larger effect is expected.

As described above, by combining the GA and the multi-variable successive approximation method, it is possible not only to set parameters with high sensitivity preferentially but also to prevent the local minimum from falling, and also to reduce the calculation time. It can be greatly shortened.

[0031]

As described above, the parameter tuning can be performed at high speed by using the present invention. Although the example of determining the excitation distribution of the array antenna is shown in the description of the embodiment, the present invention can be applied to any parameter tuning. For example, the resistance of an electric circuit,
The present invention can be applied to the problem of obtaining optimum values of capacitance and inductance, and all problems to which GA can be applied, such as personnel allocation and determination of interpolation curve.

[Brief description of drawings]

FIG. 1 is a flowchart showing a first embodiment of a parameter tuning method of the present invention.

FIG. 2 is a diagram showing an example of chromosome arrangement in the first embodiment.

FIG. 3 is a flowchart showing a second embodiment of the parameter tuning method of the present invention.

FIG. 4 is a diagram showing an example of chromosome arrangement in the second embodiment.

FIG. 5 is a diagram showing a state of convergence in the second embodiment.

FIG. 6 is a flowchart showing a conventional GA.

FIG. 7 is a diagram showing an arrangement of an 8-element array antenna.

FIG. 8 is a diagram showing an example of chromosome arrangement in a conventional GA.

Claims (1)

[Claims] 1. A parameter tuning method for optimally tuning a plurality of parameters with respect to a predetermined evaluation function, having a combination of a plurality of discretized parameters, calculating an evaluation function for each parameter, and determining the sensitivity thereof. The characteristic is that the parameter to be tuned is selected from the sensitivity, the range in which the parameter is changed is varied, the optimum value is calculated from the combination of multiple parameters, and the above process is repeated to find the optimum parameter combination. Parameter tuning method.