JP2013012185A - Robust optimization apparatus, robust optimization method and computer program for the same - Google Patents

Abstract

A robust optimization apparatus capable of efficiently obtaining a design value that gives a Pareto solution with small variations is provided.
An error setting unit assigns an error factor of a set of design parameters to an orthogonal table. The characteristic value calculation unit 24 and the S / N ratio calculation unit 25 refer to the orthogonal table to which the error factors are assigned, and calculate a plurality of evaluation characteristic values and the S / N ratios for each of the design parameter sets. Then, when there is a set of design parameters in which all of the plurality of evaluation characteristic values satisfy the target value, the search range changing unit 27 satisfies all of the plurality of evaluation characteristic values and satisfies the maximum SN ratio. The search range is changed based on the set of design parameters, and the initial generation setting unit 22 is caused to generate the set of design parameters again. Therefore, design parameters can be searched in the direction in which the SN ratio increases, and a design value that gives a Pareto solution with small variations can be efficiently obtained.
[Selection] Figure 2

Description

  The present invention relates to a technique for obtaining a robust optimal solution, and in particular, in a system having a determined topology, robust optimal that can efficiently obtain a Pareto solution that satisfies a plurality of target performances in consideration of variations in design values. The present invention relates to an optimization apparatus, a robust optimization method and a computer program thereof.

  In recent years, CAE (Computer Aided Engineering) has been widely used for product development, and not only functional evaluation but also quality evaluation considering robustness has been performed. In such product development, since the relationship between objective functions is not clear in the upstream of design, it is often unclear how much a change in one objective affects other objectives. Therefore, it is very important to clarify the target relationship by obtaining the Pareto solution set. In addition, in order to increase the straightness rate in mass production, it is important to design in consideration of the characteristic variation due to the characteristic variation such as manufacturing. As a technique for designing in consideration of variation in characteristics, there is an invention disclosed in Patent Document 1 below.

  Patent Document 1 has an object to provide a robust optimization method, a robust optimization device, and a program capable of optimizing robustness while performing optimization for a plurality of functions. To do. In Patent Document 1, a robust optimization method for performing CAE calculation on a multi-objective function intended for a plurality of functions of an object, the CAE calculation is performed by assigning a predetermined error condition to the object. Characteristic value and signal-to-noise ratio are calculated, and a search for a solution of a control variable of a multi-objective function that achieves both a function based on the characteristic value and robustness based on the signal-to-noise ratio while creating each generation of the control variable And

  FIG. 8 is a flowchart for explaining the operation of the robust optimization device disclosed in Patent Document 1. First, the robust optimization device sets a control variable in the storage unit as a characteristic value optimization initial generation by an experimental design based on the reference value stored in the storage unit (S101).

  Next, the robust optimization device applies a predetermined error condition (median, error condition 1, error condition 2,..., Error condition n) to the object based on the control variable of the current generation set in the storage unit. (S102, 103).

  Next, the robust optimization device performs CAE calculation for each given error condition, and calculates the characteristic value of the object (S104). Then, the S / N ratio is calculated based on the CAE calculated characteristic value (S105). Then, it is determined whether or not the current generation has reached the planned number of generations (S106).

  If it is determined that the planned number of generations has not been reached (No at S106), the robust optimization device creates and stores the next generation control variable based on the control variable of the current generation set in the storage unit. (S107), and the process returns to S102. Then, when the processing of steps S102 to S107 is completed up to the planned number of generations (S106, Yes), a solution that satisfies a plurality of functions and robustness based on the S / N ratio is required, and the user can find a solution that matches the design requirement. Is selected (S108).

JP 2009-032104 A

Kawagishi, Kudo, “Development of Global Optimal Solution Search Method Using Orthogonal Table”, Transactions of the Japan Society of Mechanical Engineers, Vol.73, No.732, pp2335-2342, 2007 Kitayama et al., “Trade-off analysis in multi-objective optimal design”, Transactions of the Japan Society of Mechanical Engineers, volume C, 75, 754, pp 294-302, 2009

  According to the robust optimization method disclosed in Patent Document 1 described above, in searching for a Pareto solution of a multi-objective evaluation function, a solution group with a large SN ratio, that is, a solution group with a small variation is not efficiently searched. There is a problem that it takes a lot of calculation time to obtain a solution group having a large S / N ratio.

  The present invention has been made to solve the above-described problems, and its object is to provide a robust optimization device, a robust optimization method, and a robust optimization device capable of efficiently obtaining a design value that gives a Pareto solution with small variations. To provide the computer program.

  According to one aspect of the present invention, the robust optimization device generates a plurality of design parameter sets by a probabilistic method from a design parameter search range, and assigns an error factor of the design parameter set to an orthogonal table. Means for calculating a plurality of evaluation characteristic values and their S / N ratios for each set of design parameters generated by the generating means with reference to the orthogonal table to which the error factor is assigned by the assigning means, and calculating means When there is a set of design parameters in which all of the plurality of evaluation characteristic values calculated by the above satisfy the target value, all of the plurality of evaluation characteristic values satisfy the target value and the design parameter set has the maximum SN ratio. Change means for changing the search range on the basis of and generating the design parameter set again in the generation means.

  Preferably, the changing unit further narrows the search range based on a set of design parameters in which all of the plurality of evaluation characteristic values satisfy the target value and the S / N ratio is maximum, and generates the set of design parameters in the generating unit again. Let

  Preferably, when there is no design parameter set in which all of the plurality of evaluation characteristic values calculated by the calculation means satisfy the target value, the changing means sets the design parameter set having the largest worst value among the plurality of evaluation characteristic values. Based on the above, the search range is changed, and the generating unit again generates a set of design parameters.

  Preferably, the calculating means calculates a plurality of evaluation characteristic values and SN ratios for each of the set of design parameters for each of the plurality of evaluation performances, and the changing means calculates the evaluation characteristic values calculated by the calculating means. Is generated by changing the search range based on a set of design parameters in which all of the plurality of evaluation characteristic values satisfy the target value and the SN ratio is maximum. The means again generates a set of design parameters.

  Preferably, the calculating means calculates a plurality of evaluation characteristic values and SN ratios for each of the set of design parameters for each of the plurality of evaluation performances, and the changing means calculates the evaluation characteristic values calculated by the calculating means. Is a set of design parameters in which all of the plurality of evaluation characteristic values satisfy the target value and the sum of the SN ratios of the plurality of evaluation characteristic values is maximized. Based on the above, the search range is changed, and the generating unit again generates a set of design parameters.

  Preferably, the generating means generates a plurality of design parameter sets by using a global search method in the generation of the second and subsequent design parameter sets.

  Preferably, the robust optimization device described above is an evaluation function for each of a plurality of evaluation performances, and one evaluation function based on an external instruction from among evaluation functions for evaluation using design parameters. Means for selecting a function as an objective function and selecting another as a constraint is further included. Then, the generation means generates a plurality of design parameter sets for the objective function by a probabilistic method from the design parameter search range. Further, the robust optimization device refers to the orthogonal table to which the error factor has been assigned by the assigning means, and for each of the design parameter sets generated by the generating means within the region represented by the evaluation function that is a constraint condition. Means for calculating the S / N ratio of the function, and means for changing the search range based on the set of design parameters having the maximum S / N ratio calculated for the objective function, and causing the previous generation means to regenerate the set of design parameters. Including.

  According to an aspect of the present invention, when there is a set of design parameters in which all of the plurality of evaluation characteristic values calculated by the calculation unit satisfy the target value, the changing unit sets the target for all of the plurality of evaluation characteristic values. The search range is changed based on the set of design parameters satisfying the value and having the maximum SN ratio, and the design parameter set is generated again by the generating means. Therefore, the design parameters are searched in the direction in which the SN ratio increases. Therefore, it is possible to efficiently obtain a design value that gives a Pareto solution with small variations.

  The changing means further narrows the search range based on a set of design parameters in which all of the plurality of evaluation characteristic values satisfy the target value and the SN ratio is maximum, and causes the generating means to generate the set of design parameters again. Therefore, it is possible to more efficiently obtain a design value that gives a Pareto solution with small variations.

  In addition, when there is no design parameter set in which all of the plurality of evaluation characteristic values calculated by the calculation means satisfy the target value, the changing means sets the design parameter set having the largest worst value among the plurality of evaluation characteristic values. Based on this, the search range is changed, and the generation unit again generates a set of design parameters. Therefore, the design parameter can be searched in a direction in which the evaluation characteristic value increases, and a design value that satisfies the target performance is efficiently obtained. It becomes possible.

  In addition, since the calculation means calculates a plurality of evaluation characteristic values and SN ratios for each of the set of design parameters for each of the plurality of evaluation performances, the pareto has a small variation even when there are a plurality of evaluation performances. It is possible to efficiently obtain a design value that gives a solution.

  In addition, since the generation means generates a plurality of design parameter sets using the global search method in the generation of the second and subsequent design parameter sets, the design value that gives a Pareto solution with a small amount of calculation and little variation is efficiently used. Can be obtained.

  Further, a multi-objective problem using a plurality of evaluation functions is selected by selecting one evaluation function as an objective function and the other as a constraint condition, and replacing it with a single-objective optimization problem using an objective function with a constraint condition. Thereby, it is possible to efficiently obtain a design value that gives a Pareto solution with a small amount of calculation and little variation.

It is a block diagram which shows the structural example of the robust optimization apparatus in embodiment of this invention. It is a block diagram which shows the functional structure of the robust optimization apparatus in embodiment of this invention. It is a flowchart for demonstrating the process sequence of the robust optimization apparatus in embodiment of this invention. It is a figure which shows an example of the ranking of a characteristic value. It is a figure which shows another example of the ranking of a characteristic value. It is a figure which shows an example of the ranking of the characteristic F2 in case there are two or more evaluation functions. It is the figure which made the worst value and SN ratio of the evaluation characteristic value computed by the robust optimization apparatus in this Embodiment into the graph. 10 is a flowchart for explaining the operation of the robust optimization device disclosed in Patent Document 1;

  The robust optimization device according to the embodiment of the present invention considers variations due to internal disturbances such as manufacturing tolerances and element variations and disturbances such as temperature in a system with large nonlinearity and interaction, and satisfies a plurality of target performances. Efficiently finding a Pareto solution group that also improves robustness. More specifically, the robust optimization device is an evaluation function for each of a plurality of performances to be evaluated of a design target (circuit or the like), and an evaluation function (a plurality of types of evaluations) for evaluating using design parameters. Function) as a target function, or a single-objective optimization function using one evaluation function selected from a plurality of types of evaluation functions. In the first embodiment, the former multi-objective optimization will be described, and in the second embodiment, the latter single-objective optimization will be described. The evaluation function is expressed by a combination of design parameters (design factors).

(Embodiment 1)
FIG. 1 is a block diagram illustrating a configuration example of a robust optimization device according to an embodiment of the present invention. The robust optimization device is realized by a general computer, and includes a computer main body 1, a display device 2, an FD drive 3 in which an FD (Flexible Disk) 4 is mounted, a keyboard 5, a mouse 6, and a CD-ROM (Compact Disc-Read). CD-ROM device 7 on which only memory (8) is mounted, and network communication device 9. The robust optimization program is supplied by a recording medium such as FD4 or CD-ROM8. As the program is executed by the computer main body 1, robust optimization is performed. The program may be supplied to the computer main body 1 from another computer via a communication line.

  The computer main body 1 includes a CPU 10, a ROM (Read Only Memory) 11, a RAM (Random Access Memory) 12, and a hard disk 13. The CPU 10 performs processing while inputting / outputting data to / from the display device 2, FD drive 3, keyboard 5, mouse 6, CD-ROM device 7, network communication device 9, ROM 11, RAM 12 or hard disk 13. The program recorded on the FD 4 or the CD-ROM 8 is stored in the hard disk 13 by the CPU 10 via the FD drive 3 or the CD-ROM device 7. The CPU 10 performs robust optimization by loading a program from the hard disk 13 to the RAM 12 and executing it appropriately.

  FIG. 2 is a block diagram showing a functional configuration of the robust optimization device according to the embodiment of the present invention. This robust optimization device includes an objective function determination unit 20, a calculation condition input unit 21, an initial generation setting unit 22, an error setting unit 23, a characteristic value calculation unit 24, an SN ratio calculation unit 25, and a ranking unit. 26, a search range changing unit 27, and a Pareto solution group extracting unit 28.

  The objective function determination unit 20 determines whether to perform multi-objective optimization or single-objective optimization for optimization based on an instruction according to a user operation from the keyboard 5 or the mouse 6.

  The calculation condition input unit 21 inputs design parameters and error factors to be considered, the range of design parameters to be searched, and the level of error factors. These calculation conditions are input by the user using the keyboard 5 and mouse 6 shown in FIG. The error factor level is desirably a value of ± 3δ or more, and is a discontinuous value.

  The initial generation setting unit 22 generates a set of a plurality of design values stochastically from the design parameter search range input by the calculation condition input unit 21, and sets these as the initial generation. The generation of the set of design values is performed by a known stochastic method such as the Monte Carlo method.

  The error setting unit 23 assigns these error factors to the orthogonal table according to the level and type of the error factor input by the calculation condition input unit 21. This level shall be at least 2 levels.

  The characteristic value calculation unit 24 refers to the orthogonal table to which the error factor is assigned, and calculates a plurality of characteristic values (changes in characteristic values) corresponding to the orthogonal table by performing CAE calculation. In the first embodiment, a plurality of types of evaluation functions (objective functions) are used. Therefore, characteristic values corresponding to each of a plurality of types of evaluation functions are calculated. Hereinafter, the characteristic value indicated by the evaluation function is also referred to as an evaluation characteristic value.

  The SN ratio calculation unit 25 calculates an average μ and a variance δ of a plurality of characteristic values calculated by the characteristic value calculation unit 24, and calculates an SN ratio η by the following equation.

η = 10 log (μ / δ) ² (1)
The ranking unit 26 extracts the worst value from a plurality of characteristic values corresponding to one design value calculated by the characteristic value calculation unit 24, and ranks each design value based on the vector with the SN ratio. To do. Here, an average value may be used as the characteristic value.

  The search range changing unit 27 narrows the design parameter search range when a design value that satisfies the target performance is obtained. As a method for narrowing the search range, a value half the previous value is used. The global optimum solution search method disclosed in Non-Patent Document 1 is used. In Non-Patent Document 1, the ratio between the previous optimal value and the current optimal value is multiplied by a certain constant.

  When the SN ratio of the characteristic value satisfies a predetermined value, the Pareto solution group extraction unit 28 extracts the Pareto solution group and displays the relationship between the plurality of Pareto solution groups and the evaluation characteristics on the display device 2.

  FIG. 3 is a flowchart for explaining the processing procedure of the robust optimization device according to the embodiment of the present invention. Here, the objective function determination unit 20 determines that multi-objective optimization is to be executed. First, the calculation condition input unit 21 inputs a design parameter, an error factor to be considered, a design parameter search range, and an error factor level (S11).

  Next, the initial generation setting unit 22 generates a set of a plurality of design values by a probabilistic method from the design parameter search range input by the calculation condition input unit 21 and sets it as a plurality of initial generations (S12). ). This set of design values may be generated each time a characteristic value is calculated, or a plurality of sets of design values may be generated at a time and stored in the RAM 12 or the like.

  Next, the error setting unit 23 assigns these error factors to the orthogonal table according to the level and type of error factors (S13). As a result, an error can be given to the design parameter, and the design parameter can be varied.

  The characteristic value calculation unit 24 refers to the orthogonal table to which the error factor is assigned by the error setting unit 23, and calculates a plurality of characteristic values by CAE calculation (S14). Then, the SN ratio calculation unit 25 calculates the SN ratio from the plurality of characteristic values calculated by the characteristic value calculation unit 24 (S15). An SN ratio corresponding to each of a plurality of types of objective functions is calculated.

  Further, the total value (SN = SN1 + SN2... + SNn) of the SN ratios of a plurality of types (n) of objective functions may be calculated, and the calculated value may be used as a new SN ratio.

  The characteristic value calculated by the characteristic value calculation unit 24 and the SN ratio calculated by the SN ratio calculation unit 25 are stored in the storage unit 29 together with the design value (S16). The storage unit 29 is provided in the RAM 12 or the hard disk 13.

  Next, the ranking unit 26 extracts the worst value of the characteristic value from the characteristic values calculated by the characteristic value calculating unit 24, and performs ranking based on the SN ratio of the characteristic value (S17). Then, it is determined whether or not the performance is satisfied based on the worst value of the characteristic value (S18). Here, an average value may be used as the characteristic value.

  FIG. 4 is a diagram illustrating an example of ranking of characteristic values. FIG. 4 is for the characteristic F1, and a graph is created with the vector of the worst value of the characteristic value and the SN ratio. In FIG. 4, the characteristic values (1) to (3) satisfy the target performance. In this case, the design value corresponding to the characteristic value (3) having the maximum SN ratio is set as the initial value of the next generation.

  FIG. 5 is a diagram illustrating another example of ranking of characteristic values. In FIG. 5, all the characteristic values including the characteristic values (1) to (3) do not satisfy the target performance. In this case, the design value corresponding to the characteristic value (1) having the highest performance is set as the next generation initial value.

  FIG. 6 is a diagram illustrating an example of the ranking of the characteristic F2 when there are a plurality of evaluation functions. For example, when the variation of the characteristic F1 is made as small as possible and the characteristic value only needs to satisfy the target performance even if the SN ratio of the characteristic F2 is small, that is, the priority order for increasing the SN ratio of the characteristic F1 is If it is higher than the priority order for increasing the SN ratio of F2, among the characteristic values including the characteristic values (1) to (3) satisfying the target performance of F2 from the graph shown in FIG. The design value corresponding to the characteristic value having the maximum S / N ratio is set as the next generation initial value. The priority is determined by the user based on experience. The user operates the keyboard 5 or mouse 6 to input the priority order.

  When the characteristic value does not satisfy the target performance (S18, No), the ranking unit 26 sets the design value that maximizes the performance among the design values stored in the storage unit 29 as the initial value of the next generation. The design parameter search range is set according to (S22). Then, a set of a plurality of design values is generated from the search range by a probabilistic method, and the processes after step S13 are performed as the next-generation design values.

  When the characteristic value satisfies the target performance (S18, Yes), the ranking unit 26 selects the design value that maximizes the SN ratio from the design values stored in the storage unit 29 as the next generation initial value. (S19). Then, it is determined whether or not the SN ratio satisfies a predetermined SN ratio (S20).

  If the predetermined SN ratio is not satisfied (S20, No), the search range changing unit 27 sets the search range to be narrow (S23). As a method for narrowing the search range, the global optimum solution search method disclosed in Non-Patent Document 1 is used. Then, a set of a plurality of design values is generated from the search range by a probabilistic method, and the processes after step S13 are performed as the next-generation design values.

  If the predetermined SN ratio is satisfied (S20, Yes), the Pareto solution group extraction unit 28 extracts the Pareto solution group that satisfies the target performance and satisfies the SN ratio, and displays it in the display device 2. The graph is displayed and the process ends. The Pareto optimal solution may be determined by an interactive method while the designer looks at the graph, or a trade-off analysis algorithm described in Non-Patent Document 2 may be used.

  If the processes in steps S11 to S20 and S23 shown in FIG. 3 have been performed up to the scheduled generation, the process proceeds to step S21.

As the above characteristic value, it may be calculated from the calculated value of the target function using the following expression, or the constraint condition may be described using another calculating expression such as an exponential function. In the following expression, 10 ^** indicates a power of 10.

Characteristic value = 10 ^** ((calculated value−target performance) / 10) (2)
FIG. 7 is a graph showing the worst value of the evaluation characteristic value and the S / N ratio calculated by the robust optimization device according to the present embodiment. In FIG. 7, the S / N ratio indicating the variation in the characteristic value is on the horizontal axis, the worst value of the evaluation characteristic value is on the vertical axis, and the target performance is 1.0. As can be seen from FIG. 7, the evaluation characteristic value satisfies the target performance as the generation progresses, and converges in a direction in which the variation becomes smaller (the SN ratio becomes larger).

  In addition, after a rough search of the design parameter range in the first initial generation, the search for the second and subsequent design parameters is performed using a global optimization method such as SA (Simulated Annealing) or GA (Genetic Algorithm). It may be.

  The design value may be a lumped constant having a jump value such as a resistance element. In this case, it is assumed that an element is selected with a uniform probability from among the skipped values.

(Embodiment 2)
In the above-described first embodiment, multi-objective optimization has been described, but in the second embodiment, a case will be described in which the objective function determining unit 20 determines to perform single-objective optimization.

  The configuration and processing procedure of the robust optimization apparatus of the second embodiment are basically the same as the configuration of FIG. 2 and the procedure of FIG. 3 of the first embodiment, but the calculation of the SN ratio η is performed. This is different from the first embodiment. Therefore, in the second embodiment, the SN ratio calculation unit 25 has an SN ratio calculation unit 25a as one function, and the SN ratio calculation unit 25a (see FIG. 2) calculates the SN ratio η.

  In the flowchart of FIG. 3, the SN ratio η is calculated by the SN ratio calculation unit 25a (step S15a) instead of the SN ratio calculation by the SN ratio calculation unit 25 (step S15).

  In the second embodiment, the objective function determination unit 20 selects, as an objective function, one evaluation function that exhibits a characteristic for which variation is desired to be reduced, from among a plurality of evaluation functions, in accordance with a user operation. The user can select one evaluation function from experience. For example, a plurality of types of evaluation functions are displayed on the display device 2, and the user can select a desired evaluation function by operating the keyboard 6 or the mouse 5. In the single-objective optimization, a design value is obtained for a single-objective function that is one objective function selected from the multi-objective functions.

  When one evaluation function is selected, the other evaluation functions are used as constraints. In this case, the multi-objective problem is replaced with a single-objective optimization problem. An error factor is given as an orthogonal table to satisfy a constraint condition determined from the specifications, and a search is performed so that the SN ratio of the single objective function is as large as possible.

  In the second embodiment, it is assumed that an evaluation function of the following expression (3) using design parameters is defined for a plurality of evaluation performances of a circuit to be designed.

  The objective function determination unit 20 generates a plurality of types of evaluation functions (fi (x, M), i is the type of the evaluation function) represented by Expression (3) and displays it on the display device 2. One evaluation function having a large SN ratio, that is, a characteristic for which variation is desired to be reduced is selected as an objective function f1 from among a plurality of displayed evaluation functions. When other evaluation functions other than this are treated as m inequality constraints that are m kinds of design specifications (that is, combinations of n design factors xj), the single-objective optimization of the SN ratio η is as follows. Formula (4) can be formulated.

In Equation (4), R ^m represents a search area based on m constraints. X indicates an area (executable area) that satisfies all the constraint conditions. The S / N ratio calculation unit 25a calculates the S / N ratio η of the objective function f1 so as to be optimized, that is, maximized in the executable region X according to the equation (4).

  Also in the second embodiment, a graph showing the SN ratio η and performance (that is, the value of the objective function f1) is created for the selected objective function f1 as shown in FIG. 7, and the performance satisfies the design specifications from the graph. A design value (design parameter value) having as large an SN ratio η as possible is calculated.

  The processing of the second embodiment will be described with reference to the flowchart of FIG. The objective function determination unit 20 determines in advance that single-objective optimization is to be performed, and the user operates the keyboard 6 or the mouse 5 to select one evaluation function from among a plurality of evaluation functions as the objective function f1. Assume that the other is selected as the above constraint.

  First, as in the first embodiment, the calculation condition input unit 21 inputs design parameters that determine the characteristics of the circuit to be designed, error factors to be considered, design parameter search ranges, and error factor levels ( S11).

  Next, as in the first embodiment, the initial generation setting unit 22 sets a plurality of design values for the objective function f1 by a probabilistic method from the design parameter search range input by the calculation condition input unit 21. Are set as a plurality of initial generations (S12).

  Next, as in the first embodiment, the error setting unit 23 assigns these error factors to the orthogonal table according to the level and type of error factors (S13).

  Similarly to the first embodiment, the characteristic value calculation unit 24 refers to the orthogonal table to which the error factor has been assigned by the error setting unit 23, and performs a plurality of characteristic values (changes in characteristic values) for the objective function f1 by CAE calculation. ) Is calculated (S14).

  Then, the SN ratio calculation unit 25a determines whether the plurality of characteristic values calculated by the characteristic value calculation unit 24 satisfy the constraint condition of the objective function f1 of the above equation (4) within the executable region X, The value of the objective function f1 is optimized within the executable region X. Thereby, the optimum value (that is, the maximum value) of the SN ratio η of the objective function f1 can be calculated (S15a).

  The characteristic value calculated by the characteristic value calculation unit 24 and the SN ratio η calculated by the SN ratio calculation unit 25a are stored in the storage unit 29 together with the design value (S16).

  Next, the ranking unit 26 extracts the worst value of the characteristic value from the characteristic values calculated by the characteristic value calculation unit 24 as in the first embodiment, and ranks the design value based on the SN ratio η. (S17). Then, it is determined whether or not the performance is satisfied based on the worst value of the characteristic value (S18). The ranking of the characteristic values is shown in FIG. 4 or FIG. 5, for example.

  When the characteristic value does not satisfy the target performance (No in S18), the ranking unit 26 generates the next design value that maximizes the performance from the design values stored in the storage unit 29, as in the first embodiment. The design parameter search range is set according to the initial value (S22). Then, a set of a plurality of design values is generated from the search range by a probabilistic method, and the processing after step S13 is performed as a next-generation design value for the objective function f1.

  When the characteristic value satisfies the target performance (S18, Yes), the ranking unit 26 determines that the SN ratio η is the largest among the design values stored in the storage unit 29, as in the first embodiment. This design value is set as an initial value for the next generation (S19). Then, it is determined whether or not the SN ratio η satisfies a predetermined SN ratio (S20).

  When the predetermined SN ratio is not satisfied (S20, No), the search range changing unit 27 sets the search range to be narrow as in the first embodiment (S23). Then, a set of a plurality of design values is generated from the search range by a probabilistic method, and the processing after step S13 is performed as a next-generation design value for the objective function f1.

  If the predetermined SN ratio is satisfied (S20, Yes), the Pareto solution group extraction unit 28 extracts the Pareto solution group that satisfies the target performance and satisfies the SN ratio, and displays it in the display device 2. The graph is displayed and the process ends.

  Also in the second embodiment, when the processes in steps S11 to S20 and S23 shown in FIG. 3 are performed up to the scheduled generation, the process proceeds to step S21.

  As described above, according to the robust optimization devices in the first and second embodiments, an error factor is assigned to an orthogonal table, and design parameters are determined in consideration of the worst values of variations such as manufacturing variations and environmental changes. As a result, it became possible to design products with high yield and high quality performance.

  In addition, when the characteristic value satisfies the target performance, the design parameter is searched in the direction in which the S / N ratio increases, so that it is possible to efficiently obtain a design value that gives a Pareto solution with small variations. became.

  Further, when the characteristic value does not satisfy the target performance, the design parameter is searched in the direction in which the characteristic value increases, so that it is possible to efficiently obtain the design value that satisfies the target performance.

  In addition, the coarse search of the design parameter range in the first initial generation and then the search of the design parameter for the second and subsequent times are performed using the global optimization method, so the pareto with less calculation and less variation. The design value that gives the solution can be obtained efficiently.

  Preferably, a set of generated design values having characteristics satisfying the target performance and having the maximum S / N ratio is selected, but the length of the microstrip line determined by the design constraints, for example, the area of the substrate A Pareto solution (a set of design values) may be thinned out by program processing or user operation based on manufacturing constraints such as sheath width. Thereby, a more practical solution can be obtained.

  Alternatively, the solution may be searched by setting the finally obtained design value as the center value and expanding the search range around it. As a result, a larger number of design parameter sets near the Pareto front can be searched.

  The embodiment disclosed this time should be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

  DESCRIPTION OF SYMBOLS 1 Computer main body, 2 Display apparatus, 3 FD drive, 4 FD, 5 Keyboard, 6 Mouse, 7 CD-ROM apparatus, 8 CD-ROM, 9 Network communication apparatus, 10 CPU, 11 ROM, 12 RAM, 13 Hard disk, 21 Calculation condition input unit, 22 Initial generation setting unit, 23 Error setting unit, 24 Characteristic value calculation unit, 25, 251 SN ratio calculation unit, 26 Ranking unit, 27 Search range change unit, 28 Pareto solution group extraction unit, 29 Storage unit .

Claims (9)

A generating means for generating a plurality of sets of design parameters by a probabilistic method from a design parameter search range;
An assigning means for assigning error factors of a set of design parameters to an orthogonal table;
A calculation means for calculating a plurality of evaluation characteristic values and an S / N ratio thereof for each of the set of design parameters generated by the generation means with reference to the orthogonal table to which the error factor is assigned by the assignment means;
When there is a set of design parameters in which all of the plurality of evaluation characteristic values calculated by the calculating means satisfy the target value, all of the plurality of evaluation characteristic values satisfy the target value and the design parameter has the maximum SN ratio. And a change means for changing the search range based on the set and causing the generation means to generate the set of design parameters again.   The changing means further narrows the search range based on a set of design parameters in which all of the plurality of evaluation characteristic values satisfy the target value and the SN ratio is maximum, and causes the generating means to generate the set of design parameters again. The robust optimization device according to claim 1.   When there is no set of design parameters in which all of the plurality of evaluation characteristic values calculated by the calculation unit satisfy the target value, the changing unit sets the design parameter set having the largest worst value of the plurality of evaluation characteristic values. The robust optimization device according to claim 1 or 2, wherein a search range is changed based on the design parameter set and the generation unit is caused to generate a set of design parameters again. The calculation means calculates, for each of a plurality of evaluation performances, a plurality of evaluation characteristic values and an SN ratio for each of the set of design parameters,
The changing means has a design parameter set in which all of the evaluation characteristic values calculated by the calculation means satisfy the target value, and all of the plurality of evaluation characteristic values satisfy the target value and have the highest priority. 4. The robust optimization device according to claim 1, wherein a search range is changed based on a set of design parameters having a maximum S / N ratio with high evaluation performance, and the generation unit is again generated with the set of design parameters. . The calculation means calculates, for each of a plurality of evaluation performances, a plurality of evaluation characteristic values and an SN ratio for each of the set of design parameters,
The changing means has a plurality of evaluation characteristic values satisfying the target value when there is a set of design parameters in which all of the evaluation characteristic values calculated by the calculating means satisfy the target value, and a plurality of evaluation characteristics The robust optimum according to any one of claims 1 to 3, wherein a search range is changed based on a set of design parameters that maximizes a total SN ratio of characteristic values, and the generating means is caused to generate the set of design parameters again. Device.   The robust optimization apparatus according to claim 1, wherein the generation unit generates a plurality of design parameter sets using a global search method in the generation of the second and subsequent design parameter sets. An evaluation function for each of a plurality of evaluation performances, and one evaluation function is selected as an objective function based on an external instruction from evaluation functions for evaluation using design parameters, and the others are constrained Further comprising means for selecting as a condition;
The generating means generates a plurality of design parameter sets for the objective function by a probabilistic method from the design parameter search range,
With reference to the orthogonal table to which the error factor is assigned by the assigning means, the SN ratio of the objective function is determined for each set of design parameters generated by the generating means within the region represented by the evaluation function that is a constraint condition. Means for calculating;
7. The method according to claim 1, further comprising means for changing a search range based on a set of design parameters having a maximum signal-to-noise ratio calculated with respect to an objective function, and causing the generating means to generate the set of design parameters again. Robust optimization device according to crab. A robust optimization method that allows a computer to find a Pareto solution group,
Causing the computer to generate a plurality of sets of design parameters by a probabilistic method from a design parameter search range;
Causing the computer to assign an error factor for a set of design parameters to an orthogonal table;
Causing the computer to calculate a plurality of evaluation characteristic values and S / N ratios for each of the generated set of design parameters with reference to the orthogonal table to which an error factor is assigned;
When there is a set of design parameters in which all of the plurality of calculated evaluation characteristic values satisfy the target value, all of the plurality of evaluation characteristic values satisfy the target value and the set of design parameters has the maximum SN ratio. And a step of changing the search range based on and generating a set of design parameters again. A computer program that causes a computer to seek a Pareto solution group,
Causing the computer to generate a plurality of sets of design parameters by a probabilistic method from a design parameter search range;
Causing the computer to assign an error factor for a set of design parameters to an orthogonal table;
Causing the computer to calculate a plurality of evaluation characteristic values and S / N ratios for each of the generated set of design parameters with reference to the orthogonal table to which an error factor is assigned;
When there is a set of design parameters in which all of the plurality of calculated evaluation characteristic values satisfy the target value, all of the plurality of evaluation characteristic values satisfy the target value and the set of design parameters has the maximum SN ratio. And a step of changing the search range on the basis of and generating a set of design parameters again.

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