Optimization device, optimization method, and computer program

Abstract

To realize optimization by minimizing an objective function for determining the shape of a structure, even when the boundary condition is not defined clearly.SOLUTION: An optimization device comprises: an acquisition unit that acquires an objective function for evaluating calculation targets to be optimized and constraint conditions to be satisfied by the objective function; a calculation unit that calculates solutions of calculation conditions that minimize the objective function in a calculation area determined by the calculation targets and that gives a shape of a boundary condition in a differential equation; an evaluation unit that calculates the objective function using the solutions of the calculation conditions, and evaluates whether or not design variables obtained from the calculation values of the objective function satisfy the constraint conditions; and an optimization unit that repeats the calculation by the calculation unit and the evaluation by the evaluation unit until the calculation values of the objective function converge to below a preset threshold.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an optimization device, an optimization method, and a computer program.

Background Art

[0002] In the design of a structure, a method of optimizing the shape of the structure under design-defined constraint conditions is known (see, for example, Patent Document 1). In the region shape optimization method described in Patent Document 1, in order for the objective function for evaluating the shape of the structure to obtain a stable and convergent solution, the object or the target region is regarded as a linear elastic body, and the shape gradient function of each point on the boundary of the region is calculated.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the technique described in Patent Document 1, in order to converge the objective function, as design requirements, boundary conditions such as Dirichlet conditions that define fixed parts of the structure and Neumann conditions that define forces applied to the structure and heat transfer from the outside are required to be clearly defined in advance. In other words, when the boundary conditions are not defined in advance or when the fixed conditions or weighting conditions are unclear, it may not be possible to obtain the solution necessary to determine the shape of the structure, and there is a risk that the shape of the structure cannot be optimized.

[0005] The present invention has been made to solve the above-described problems, and aims to minimize an objective function for determining the shape of a structure even when the boundary conditions are not clearly defined.

Means for Solving the Problems

[0006] The present invention has been made to solve the above-described problems and can be realized in the following forms.

[0007] (1) According to one aspect of the present invention, an optimization device is provided. The optimization device includes: an acquisition unit that acquires an objective function for evaluating a calculation target to be optimized and constraint conditions that the objective function should satisfy; a calculation unit that calculates a solution of the calculation conditions for minimizing the objective function in a calculation region determined by the calculation target, the calculation conditions giving the shape of boundary conditions in a differential equation; an evaluation unit that calculates the objective function using the solution of the calculation conditions and evaluates whether a design variable obtained from the calculated value of the objective function satisfies the constraint conditions; and an optimization unit that repeats the calculation by the calculation unit and the evaluation by the evaluation unit until the calculated value of the objective function converges to less than a preset threshold value.

[0008] According to this configuration, as numerical values necessary for calculating the objective function, instead of default values, the solution of the differential equation calculated by the calculation unit is given. Until the objective function converges to less than the threshold value, the calculation unit calculates while changing the solution of the differential equation, so that the objective function is automatically given the solutions of a plurality of different differential equations. As a result, for example, in the automatic search for the optimal fixed part during the design of a structure and the automatic search for the optimal joint part between structures, conditions such as physical characteristics that were conventionally given in advance by a designer or the like are automatically searched by the optimization device of this configuration.

[0009] (2) In the optimization device of the above aspect, the optimization unit may obtain a ratio between the calculated value of the objective function and a design variable obtained from the objective function, and repeat the calculation by the calculation unit and the evaluation by the evaluation unit until the obtained ratio converges to less than the preset threshold value. According to this configuration, each time the calculation of the objective function is repeated, the solution given to the objective function calculated by the calculation unit is different. Therefore, the convergence condition is determined using, as an index, the sensitivity obtained from both the solution calculated by the calculation unit and the calculated value of the objective function, so that the calculated value of the objective function converges with a small number of calculation repetitions.

[0010] (3) In the optimization device of the above aspect, the design domain may be expressed by a mathematical formula, and the parameters included in the mathematical formula may be used as part of the design variables. According to this configuration, the relevance between the solution of the differential equation calculated by the calculation unit and the parameters is high, and the calculation target can be optimized more preferably.

[0011] (4) In the optimization device of the above aspect, the calculation conditions may be default values and default displacements that give the Dirichlet condition and the Neumann condition. According to this configuration, since the calculation conditions expressed by the differential equation are the Dirichlet condition and the Neumann condition, the solution of the differential equation can be calculated easily.

[0012] Note that the present invention can be realized in various aspects. For example, it can be realized in the form of an optimization device, an evaluation device, a system including these devices, an optimization system, an optimization method, a computer program for executing these devices and methods, a server device for distributing this computer program, a non-transitory storage medium storing the computer program, and the like.

Brief Description of the Drawings

[0013]

Figure 1

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Mode for Carrying Out the Invention

[0014] <Embodiment> 1. Schematic configuration of the optimization device: FIG. 1 is a schematic block diagram of an optimization device 100 as an embodiment of the present invention. The optimization device 100 of the present embodiment acquires a CAD (computer-aided design) model or geometry as a calculation target, and optimizes the shape of the CAD model by evaluating an objective function under preset constraint conditions. In the present embodiment, instead of specific numerical values input as known boundary conditions when calculating the objective function, calculation conditions represented by differential equations such as Dirichlet conditions and Neumann conditions are used to calculate the objective function. As a result, even if the boundary conditions are not clearly defined when calculating the objective function, the calculated value of the objective function is automatically optimized by the change in the solution of the differential equation which is the set calculation condition.

[0015] The optimization device 100 of the present embodiment shown in FIG. 1 is configured by a personal computer (PC). The optimization device 100 includes a monitor 30 that displays various images, an input unit 40 that receives inputs from a user, a transmission / reception unit 50 that transmits and receives various information to and from other devices by wire or wirelessly, a storage unit 20, and a CPU (Central Processing Unit) 10 that executes various programs. The input unit 40 is composed of a keyboard and a mouse. The storage unit 20 is composed of a hard disk drive (HDD) or the like. The storage unit 20 stores the three-dimensional data of the CAD model acquired in advance as the calculation target and the evaluation result of the objective function described later.

[0016] The CPU 10 executes the functions of various programs by expanding the programs stored in a ROM (Read Only Memory), not shown, into a RAM (Random Access Memory). The CPU 10 functions as an acquisition unit 11 that acquires various input information via the input unit 40 and the transmission / reception unit 50, a calculation unit 12 that calculates the solution of the differential equation used to calculate the objective function, an evaluation unit 13 that calculates the objective function using the solution calculated by the calculation unit 12, and an optimization unit 14 that solves the optimization problem.

[0017] The acquisition unit 11 acquires an objective function for evaluating the calculation target for which optimization is to be performed, constraint conditions that the objective function should satisfy, and a convergence condition for determining the end of optimization. Examples of the calculation target include a CAD model or geometry for determining the shape of a structure. Examples of the constraint conditions include that the design variables obtained from the calculated value of the objective function are within the design region and the upper limit of the expanding volume due to thermal expansion.

[0018] The calculation unit 12 calculates a solution of calculation conditions for minimizing an objective function within a calculation region determined by a calculation target. Specifically, the calculation unit 12 calculates a solution that gives the shape of a boundary condition in a differential equation such as a Dirichlet condition or a Neumann condition as the calculation conditions. In the present embodiment, the Dirichlet condition represents a prescribed condition for a physical quantity, and the Neumann condition represents an inflow condition of the physical quantity acting on the boundary of the calculation region. In other words, the calculation unit 12 sets the solution of the differential equation represented by the calculated Dirichlet condition and Neumann condition as the initial coordinate position, the magnitude of the initial physical quantity, etc., which are the initial conditions of the objective function. The solution of the differential equation calculated by the calculation unit 12 changes due to the optimization of the objective function performed by the optimization unit 14 described later. Therefore, it can be said that the calculation unit 12 searches for the solution of the differential equation as the calculation conditions in the process of optimization. In the present embodiment, the design region in which the calculation conditions are searched is expressed by a mathematical formula. Parameters s and t, which will be described later and are included in the mathematical formula, are used as part of the design variables.

[0019] The evaluation unit 13 obtains design variables from the calculated value of the objective function and evaluates whether the design variables satisfy the constraint conditions. The optimization unit 14 repeats the calculation of the solution by the calculation unit 12 and the evaluation of the objective function and the constraint conditions by the evaluation unit 13 until the calculated value of the objective function converges to less than a preset threshold value in order to solve the optimization problem. The optimization unit 14 repeats the calculation of the solution by the calculation unit 12 and the evaluation by the evaluation unit 13 until the calculated value of the objective function converges to less than a preset threshold value. The optimization unit 14 of the present embodiment obtains the sensitivity, which is the ratio of the solution between the calculated value of the objective function and the differential equation that is the calculation condition calculated by the calculation unit 12. The optimization unit 14 repeats the calculation of the solution of the differential equation by the calculation unit 12 and the evaluation by the evaluation unit 13 until the sensitivity converges to less than the threshold value as the convergence condition acquired by the acquisition unit 11. The optimization unit 14 outputs the design variable obtained from the objective function when the sensitivity converges to less than the threshold value as the optimized value. Further, the optimization unit 14 stores the optimized design variable in the storage unit 20. When the sensitivity is greater than or equal to the threshold value, the calculation unit 12 changes the solution of the differential equation, and the evaluation unit 13 calculates the objective function again using the changed solution. The evaluation unit 13 obtains the sensitivity using the design variable obtained from the calculated value of the objective function. In the present embodiment, the optimization executed by the optimization unit 14 is performed by the calculation method MMA (method of moving asymptotes) mounted on the optimization module of COMSOL Multiphysics 5.4.

[0020] 2. Example: Hereinafter, the optimization of the optimization device 100 will be described using the optimization flowchart and an example to which the above embodiment is applied. FIG. 2 is a flowchart of the optimization method. In the optimization flow shown in FIG. 2, first, the acquisition unit 11 performs an acquisition step of acquiring a calculation model as a calculation target via the input unit 40 or the transmission / reception unit 50 (step S1).

[0021] Figures 3 and 4 are schematic perspective views of the calculation model (object of calculation) 110 of the embodiment. The calculation model 110 shown in FIGS. 3 and 4 is a model of the pedestal portion where the machine tool is installed. In FIG. 3, among the calculation model 110, the upper surface (the surface orthogonal to the X 3 axis) where the machine tool is installed is shown. In FIG. 4, among the calculation model 110, the lower surface on which the calculation model 110 is installed is shown. Note that the orthogonal coordinate system CS shown in FIG. 3 corresponds to the orthogonal coordinate system CS shown in the figures after FIG. 4.

[0022] As shown in FIGS. 3 and 4, the calculation model 110 includes a main body portion 111, four upper installation members 112 arranged on the positive X 3 axis side with respect to the main body portion 111, and a lower installation member 113 arranged on the negative X 3 axis side with respect to the main body portion 111. As shown in FIG. 3, the four upper installation members 112 have the same thickness along the X 3 axis direction and have a flat plate shape extending in the longitudinal direction. The four upper installation members 112 are arranged spaced apart from each other. The upper surface (the hatched portion in FIG. 3) of the upper installation member 112 comes into contact with the arranged machine tool.

[0023] The lower installation member 113 hatched in FIG. 4 is configured by connecting a plurality of flat plates. The whole of the lower installation member 113 has the same thickness along the X 3 axis direction. The optimization unit 14 of the present embodiment defines an optimization problem for minimizing the amount of deformation due to thermal expansion of the calculation model 110 (step S2). In this embodiment, in order to minimize the amount of deformation, the arrangement of a plurality of legs arranged on the lower installation member 113 is obtained. Each leg is arranged within the range of the design region Γ 3 on the lower surface side (negative X floor axis side) of the lower installation member 113 as shown in FIG. 4.

[0024] The calculation unit 12 expresses the design region Γ floor for calculating the calculation conditions by a mathematical formula (step S3). The calculation unit 12 of the present embodiment calculates the calculation conditions of the Dirichlet condition and the Neumann condition, and thus the design region Γfloor is expressed as in the following formula (1). The design region Γ shown in the following formula (1) floor is, for example, a case where the number of disk-shaped legs having a circular shape parallel to the X 1 X 2 plane is eight. For the parameters s and t shown in the following formula (1), the relational expression shown in the following formula (2) is used.

[0025]

Number

Number

[0026] FIG. 5 is an explanatory diagram of the design region Γ expressed by formula (1). The design region Γ shown in FIG. 5 floor is the region of the entire surface on the negative X floor axis side of the lower installation member 113. In this embodiment, the calculation region Ω is the three-dimensional coordinate space of the entire calculation model 110 shown in FIGS. 3 and 4. 3

[0027] When the process of step S2 in FIG. 2 is performed, the evaluation unit 13 sets an objective function for solving the optimization problem (step S4). The evaluation unit 13 sets an objective function for obtaining a numerical solution of the optimization problem shown in the following formula (3) on the calculation region Ω having the design region Γ floor shown in formula (1).

[0028]

Number

[0029] In this embodiment, the total number of design variables in the above formula (3) is defined as N, and the design variable F i , i ≦ N is the partial boundary of the design region Γ floor (a part of the design region Γ floor ). Further, the contact surface with the machine tool on which the calculation model 110 is installed is defined as Γ ceiling . In this case, the object to be optimized is the contact surface Γ​ceiling In the calculation domain Ω above, the deformation amount u along the vertical direction (X 3 axis direction) due to thermal expansion 3 is defined as the integral value of, and the objective function f 0 (u) to be optimized in the above formula (3) is set as in the following formula (4).

[0030]

Number

[0031] Note that in the above formula (4), the following formula (5) holds.

Number

[0032] Objective function f 0 (u) is set, and the calculation unit 12 sets a differential equation necessary for calculating the objective function (step S5). The calculation unit 12 sets a linear elastic equation with thermal expansion expressed by a mathematical formula as in the following formula (6) in order to evaluate the objective function. Note that the solution of the linear elastic equation in the following formula (6) represents the deformation amount u represented by the above formula (5).

Number

[0033] In the above equation (6), "·" represents the inner product, "b" on the right side represents the body force acting on the calculation domain Ω, and "∇" is represented as in the following formula (7).

Number

[0034] In particular, in this embodiment, the vertical gravity acting on the calculation domain Ω is expressed as in the following formula (8) using σ(u) representing the stress tensor.

Number

[0035] In the above formula (8), α T represents the coefficient of thermal expansion, T represents the assumed temperature, and T ref represents the reference temperature. Further, each of the Lamé constants λ e , μ is expressed by the following relational expressions (9) and (10) using the Young's modulus E and the Poisson's ratio ν.

[0036]

Equation

Equation

[0037] Also, δ in the above formula (8) ij is expressed as in the following formula (11).

Equation

[0038] The Kronecker symbol ε(u) = ε in the above formula (8) ij (u) represents the strain tensor and is expressed as in the following formula (12).

Equation

[0039] Figure 6 is an explanatory diagram of the boundary conditions. In Figure 6, an example of the restraint positions Γ 1 ~Γ 10 where the deformation amount u satisfies the boundary conditions with N = 10 in the linear elastic equation of the above formula (6) is shown. In the example shown in Figure 6, complete restraint conditions are given to the partial boundaries Γ floor of the design region Γ 1 , ···, Γ i , i = 4. On the other hand, only vertical restraint (in other words, X floor is applied to the partial boundaries Γ i+1 , ···, Γ N on the design region Γ 3A roller restraint that can rotate around an axis is provided. In Fig. 6, the positions of the four feet under the complete restraint condition are shown as white circles, and the positions of the six feet of the roller restraint are shown as black circles. Note that free boundary conditions are given to the remaining boundaries of the calculation domain Ω.

[0040] When the process of step S5 in Fig. 2 is performed, the acquisition unit 11 sets the initial conditions acquired via the input unit 40 or the transmission / reception unit 50 (step S6). Figs. 7 and 8 are explanatory diagrams of the initial conditions. In Fig. 7, various parameters set as the initial conditions are shown in a table. In the example shown in Fig. 7, the total number N of design variables, which is the number of feet, is set to 10, and for each foot, the radius r on a plane parallel to the X 1 X 2 plane is 0.0125 (m). As shown in Fig. 7, the right side of the linear elastic equation is set. In this example, the optimization unit 14 optimizes the deformation amount u of thermal expansion when the temperature rises from the normal temperature T = 283.15 (K) to the temperature T = 323.15 (K). The coefficient of thermal expansion α T the Young's modulus E, and the Poisson's ratio ν were used as the numerical values registered in the optimization module of COMSOL Multiphysics 5.4.

[0041] In Fig. 8, when each of the design variables F i , i = 1, ···, 10 is defined as in the above formula (1), each numerical value of the parameters s and t given as the initial conditions is shown in a table. Note that in the above formula (1), the total number N of the design variables F i is 8, but as the initial conditions for the optimization to be performed later, an example where the total number N of the design variables F i is 10 is handled. Since the design variable F i changes with the parameters s and t, the parameters s and t can also be regarded as design variables.

[0042] When the process of step S6 in Fig. 2 is performed, the calculation unit 12 performs a calculation process of calculating the solution of the differential equation represented by the above formula (6) (step S7). The evaluation unit 13 uses the calculated solution of the differential equation to calculate the objective function f 0An evaluation step of evaluating the constraint conditions using the calculated value of (u) is performed (step S8). The evaluation unit 13 calculates the objective function f 0 (u) using the calculated solution. The evaluation unit 13 obtains each design variable F 0 using the parameters s and t obtained from the calculated value of the objective function f i . The evaluation unit 13 determines whether the coordinate position of the foot, which is each obtained design variable F i , satisfies the constraint condition included in the design region Γ floor .

[0043] The optimization unit 14 determines whether the calculated value of the objective function f 0 (u) calculated by the evaluation unit 13 satisfies the convergence condition (step S9). The optimization unit 14 obtains the sensitivity defined as the ratio of the change in the objective function f 0 (u) with respect to the change in the parameters s and t. The optimization unit 14 determines whether the obtained sensitivity is less than the acquired threshold value (step S9). When the sensitivity is greater than or equal to the threshold value, the optimization unit 14 determines that the convergence condition is not satisfied (step S9: NO), and updates the design variable Fi in the direction in which the sensitivity decreases (step S10). The calculation unit 12 updates the parameters s and t for obtaining the design variable Fi. The calculation unit 12 recalculates the solution of the differential equation represented by the above formula (6) using the updated parameters s and t (step S7), and the processes after step S8 are performed.

[0044] In the process of step S9, when the sensitivity is less than the threshold value, the optimization unit 14 determines that the convergence condition is satisfied (step S9: YES), outputs the design variable F i obtained from the parameters s and t to the monitor 30 (step S11), and the optimization flow ends. Each design variable F i represents the X floor coordinates of each foot arranged in the design region Γ 1 , X 2 coordinates.

[0045] Figure 9 shows the objective function f 0(u) is an explanatory diagram of the transition of the calculated value. As shown in FIG. 9, in this embodiment using the initial conditions shown in FIGS. 7 and 8, after the calculation by the calculation unit 12 and the evaluation by the evaluation unit 13 are repeated 155 times, the objective function f 0 (u) satisfies the convergence condition.

[0046] FIG. 10 is an explanatory diagram of the foot arrangement obtained by optimization. In FIG. 10, when the calculated value of the objective function f 0 (u) converges, the positions of the feet represented by the obtained design variables F i are shown. In this embodiment, by forming the 10 feet shown in FIG. 10 on the lower installation member 113, the deformation amount due to the thermal expansion of the calculation model 110 shown in the above formula (3) can be suppressed.

[0047] As described above, in the optimization device 100 of the present embodiment, the calculation unit 12 calculates the solution of the calculation condition (formula (6)) that gives the shape of the boundary condition in the calculation region Ω determined by the calculation target, in order to minimize the objective function f 0 (u). The evaluation unit 13 calculates the objective function f 0 (u) using the solution of the calculation condition, and obtains the design variable F 0 from the calculated value of the objective function f i . The evaluation unit 13 evaluates whether the design variable F i satisfies the constraint condition. The optimization unit 14 repeats the calculation of the solution by the calculation unit 12 and the evaluation by the evaluation unit 13 until the calculated value of the objective function f 0 (u) converges to less than a preset threshold value. In this embodiment, as the numerical values required to calculate the objective function f 0 (u), the solution of the differential equation calculated by the calculation unit 12 is given instead of the specified fixed value. Until the objective function f 0 (u) converges to less than the threshold value, the calculation unit 12 searches for the solution of the differential equation, and the objective function f 0(u) is given the solutions of a plurality of automatically searched differential equations. As a result, for example, in the automatic search for optimal fixing positions during the design of a structure and the automatic search for optimal joining positions between structures, conditions such as physical properties that were conventionally given in advance by designers and the like can be automatically searched by the optimization device of the present embodiment.

[0048] Also, the optimization unit 14 of the present embodiment obtains the sensitivity that is the ratio of the calculated value of the objective function f 0 (u) to the solution of the differential equation that is the calculation condition calculated by the calculation unit 12. The optimization unit 14 repeats the calculation of the solution of the differential equation by the calculation unit 12 and the evaluation by the evaluation unit 13 until the sensitivity converges to less than the threshold value as the convergence condition acquired by the acquisition unit 11. In the present embodiment, each time the calculation of the objective function f 0 (u) is repeated, the solution calculated by the calculation unit 12 and given to the objective function f 0 (u) is different. Therefore, the convergence condition is determined using the sensitivity obtained from both the solution calculated by the calculation unit 12 and the calculated value of the objective function f 0 (u) as an index, and the calculated value of the objective function f 0 (u) converges with a small number of calculation repetitions.

[0049] Also, the design domain Γ of the present embodiment floor is expressed by a mathematical formula as shown in the above formula (1), and the parameters s and t included in the mathematical formula are used as part of the design variables F i . Therefore, in the present embodiment, the relevance between the solution of the differential equation calculated by the calculation unit 12 and the parameters s and t is high, and the calculation target can be optimized more preferably.

[0050] Also, since the calculation conditions of the present embodiment are default values and default displacements that give Dirichlet conditions and Neumann conditions, the solution of the differential equation can be easily calculated.

[0051] <Modification Example of the Above Embodiment> The present invention is not limited to the above-described embodiments, and can be implemented in various forms without departing from the gist thereof. For example, the following modifications are possible.

[0052] [Modification Example 1] The optimization device 100 of the above embodiment is an example, and the configuration of the optimization device 100 and the control content performed by each configuration can be modified. The optimization device 100 does not necessarily include the storage unit 20, the monitor 30, the input unit 40, and the transmission / reception unit 50. For example, after the objective function f 0 (u) satisfies the convergence condition, the design variables output by the optimization unit 14 may be transmitted as data to another device via the transmission / reception unit 50 without being displayed on the monitor 30. The optimization device 100 can be modified within the range of functioning as the acquisition unit 11, the calculation unit 12, the evaluation unit 13, and the optimization unit 14.

[0053] In the above embodiment, the calculation model 110 shown in FIGS. 3 and 4 is taken as an example for the calculation target for optimization, but a well-known CAD model or geometry can be adopted for the calculation target. The differential equation for which the calculation unit 12 calculates the solution is not limited to the linear elastic equation of the above formula (6), and other differential equations can be adopted. Further, in the above embodiment, the Dirichlet condition and the Neumann condition are adopted as the calculation conditions, but other conditions may be adopted. The objective function, the calculation region, and the design variables may change according to the calculation target and the calculation conditions. For example, the objective function may be a function defined in an integral form as the sum of any physical quantity among the deformation amount, the thermal resistance, and the rigidity on the calculation region or on the boundary of the calculation region.

[0054] The optimization unit 14 of the above embodiment uses the sensitivity obtained from the calculated value of the objective function f 0 (u) and the design variables to determine whether or not the calculated value of the objective function f 0 (u) converges to less than the threshold value, but other convergence conditions may be used for the determination of convergence. For example, the optimization unit 14 may determine convergence by comparing the calculated value of the objective function f 0 (u) with the threshold value without using the design variables.

[0055] The design region Γ of the above embodiment floor is expressed by a mathematical formula as in the above formula (1), and the parameters s and t used when obtaining each design variable F i could be regarded as design variables, but the parameters s and t do not have to be used as part of the design variables. The optimization flow of other embodiments, different from the optimization flow shown in FIG. 2, includes an acquisition step (step S1), a calculation step (step S7), and an evaluation step (step S8), and the calculation step and the evaluation step may be repeated until the objective function f 0 (u) converges.

[0056] In the above embodiment, a part of the configuration assumed to be realized by hardware may be replaced with software, and conversely, a part of the configuration assumed to be realized by software may be replaced with hardware. The present invention is not limited to the above embodiments, and can be implemented in various modes without departing from the gist thereof.

[0057] As described above, this aspect has been described based on the embodiments and modified examples. The embodiments of the above-described aspects are for facilitating the understanding of this aspect and do not limit this aspect. This aspect can be changed and improved without departing from its gist and the scope of the claims, and equivalents thereof are included in this aspect. Also, if its technical features are not described as essential in this specification, they can be deleted as appropriate.

Description of Reference Numerals

[0058] 10... CPU 11... Acquisition unit 12... Calculation unit 13... Evaluation unit 14... Optimization unit 20... Storage unit 30... Monitor 40... Input unit 50... Transmission / reception unit 100... Optimization device 110…Calculation model (object of calculation) 111…Main body 112…Upper installation member 113…Lower installation member CS…Cartesian coordinate system E…Young's modulus F i …Design variable N…Total number of design variables r…Radius of the leg s, t…Parameters u, u 3 …Deformation amount α T …Coefficient of thermal expansion λ e …Lame constant f 0 (u)…Objective function Γ floor …Design domain Γ ceiling …Contact surface Γ i …Design variable Ω…Calculation domain ν…Poisson's ratio

Claims

1. An optimization device, comprising: an acquisition unit that acquires an objective function for evaluating a calculation target for performing optimization and constraint conditions that the objective function should satisfy; a calculation unit that calculates, within a calculation region determined by the calculation target, a calculation condition for minimizing the objective function and calculates a solution of the calculation condition that gives the shape of a boundary condition in a differential equation; an evaluation unit that calculates the objective function using the solution of the calculation condition and evaluates whether a design variable obtained from the calculated value of the objective function satisfies the constraint conditions; an optimization unit that repeats the calculation by the calculation unit and the evaluation by the evaluation unit until the calculated value of the objective function converges to be less than a preset threshold value; The optimization device comprising the above.

2. The optimization device according to Claim 1, wherein the optimization unit obtains a ratio between the calculated value of the objective function and a design variable obtained from the objective function, and repeats the calculation by the calculation unit and the evaluation by the evaluation unit until the obtained ratio converges to be less than the preset threshold value.

3. The optimization device according to Claim 1 or Claim 2, wherein the calculation region is expressed by a mathematical formula, and a parameter included in the mathematical formula is used as part of a design variable.

4. The optimization device according to Claim 3, wherein the calculation condition is a preset value and a preset displacement that give a Dirichlet condition and a Neumann condition.

5. An optimization method, wherein a computer performs an acquisition step of acquiring an objective function for evaluating a calculation target for performing optimization and constraint conditions that the objective function should satisfy, a calculation step of calculating, within a calculation region determined by the calculation target, a calculation condition for minimizing the objective function and calculating a solution of the calculation condition that gives the shape of a boundary condition in a differential equation, an evaluation step of calculating the objective function using the solution of the calculation condition and evaluating whether a design variable obtained from the objective function satisfies the constraint conditions, and the calculation step and the evaluation step are repeated until the calculated value of the objective function converges to be less than a preset threshold value.

6. A computer program, comprising: an acquisition function that acquires an objective function for evaluating a calculation target for performing optimization and constraint conditions that the objective function should satisfy; In the calculation region determined by the object of calculation, a calculation condition for minimizing the objective function, and a calculation function for calculating a solution of the calculation condition that gives the shape of the boundary condition in the differential equation. An evaluation function that calculates the objective function using the solution of the calculation condition and evaluates whether the design variables obtained from the objective function satisfy the constraint conditions. To be realized by a computer. The computer program in which the calculation function and the evaluation function are repeated until the calculated value of the objective function converges to less than a preset threshold value.

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