CN101515304B - Multi-objective optimum designs support device using mathematical process technique, its method and program - Google Patents
Multi-objective optimum designs support device using mathematical process technique, its method and program Download PDFInfo
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Abstract
The present invention discloses a multi-objective optimum designs support device using mathematical process technique, method and program thereof. A unit (101) calculates a plurality of sets of objective functions of sample sets of input parameters. A unit (102) approximates the objective functions using a polynomial on the basis of the calculation result of the unit (101). A unit (103) calculates a logical expression indicating a logical relation between arbitrary two or three objective functions, of the plurality of mathematically approximated objective functions as an inter-objective function logical expression by a QE method. A unit (104) displays areas that the values of the objective functions can take as usable areas according to the inter-objective function logical expression. Units (105) and 106 determine an optimum set of design parameters by limiting the sets of design parameters to corresponding sets of design parameters in the neighborhood of a Pareto boundary on the basis of the Pareto boundary of an objective function recognized from the usable areas displayed.
Description
Technical field
The present invention relates to the multi-objective optimum designs support device that in the design of slide block shape of hard disk etc., uses.
Background technology
Be accompanied by the densification/high capacity of hard disk, the distance between disk and the magnetic head is more and more littler.Need have the slider designs than moderate fluctuation (flying) variable quantity, this floats and changes because difference in height and disk radial location cause.
Shown in 1601 among Fig. 1, slide block is installed in the bottom, top of actuator 1602, moves on the disk of actuator 1602 in hard disk, and calculates the position of magnetic head based on the shape of slide block 1601.
When confirming the optimum shape of slide block 1601, need be used for minimizing simultaneously effective calculating of the function (that is so-called multiple goal optimization) of flying height (Fig. 1 1603), inclination (1604) and trim (1605).
Past replaces directly processing multiple goal optimization problem, and fill order's target optimization wherein shown in following mathematic(al) representation 1, through each objective function f_i multiply by linearity and the f that weight m_i obtains each item, and is calculated its minimum value.
[mathematic(al) representation 1]
f＝m_1*f_1+...+m_t*f_t
Then, calculate the slide block shape, wherein revising the parameter p that is used for confirming slide block shape S as shown in Figure 2, q, r etc. gradually through program when so that the minimized mode of functional value f value is come computing function f.
In above equality, f depends on weight vectors { m_i}.In actual design, { calculate minimum value in the m_i}, and through comprehensive its minimum value of judgement and { balance between the m_i} is confirmed the slide block shape further revising to the f of each modification value.
Be used for calculating the method for Pareto (Pareto) curved surface (optimal surface) of multiple goal optimization, promptly so-called normal state border intersection point (normal boundary intersection:NBI) method etc. is known.
Patent documentation 1: the open No.2002-117018 of Japanese patent application
But, in the optimization technique of above-mentioned traditional single goal function f, must repeat time-consuming unsteady calculating.Particularly, when detecting the detail section of slide block shape, the quantity of input parameter (corresponding with p as shown in Figure 2, q, r etc.) becomes about 20, and needs 10,000 times or more floating calculated.This will spend the plenty of time makes its optimization, and this is a problem.
For example, Fig. 3 is the operational flowchart of prior art systems.Set (step S1802) afterwards in specification setting (step S1801) and weight vectors, in the calculating (step S1803) that the optimization of single goal function is handled, need carry out the unsteady calculating of flood tide tens thousand of input parameter groups.
In addition, in the method, the minimum value of f (and input parameter value at that time) depend on and how to confirm weight vectors (m_1 ..., m_t).In actual design, expectation makes the f optimization to each group weight vectors and the situation that they compare is often taken place.Because according to above-mentioned prior art, all need to carry out again once more optimization at every turn when revising weight vectors and calculate, be accompanied by expensive unsteady calculating, repeating step S1804 to S1802 as shown in Figure 3.Therefore, the kind of the weight vectors of experiment usefulness is restricted.Confirming final weight vectors (the step S1805 among Fig. 3) afterwards, the cost great amount of time is exported best slide block shape (optimal parameter group) (the step S1806 among Fig. 3).
In addition,, once can only on the Pareto curved surface, obtain a point because in minimization function value f, thus the best relation between the objective function difficult to calculate, and can not give design with these information feedback, these all are problems.
In addition; In the prior art that is used for calculating through the numerical analysis method Pareto curved surface, it can not be found the solution when the Free Region right and wrong are protruding, and when as the point (end points) in the source in the calculating of Pareto curved surface nearby the time; Can not successfully carry out the algorithm computing, these all are problems.
Summary of the invention
The objective of the invention is to realize in the short time visual (demonstration on Pareto border etc.) of based target function; With can be visual/hold intuitively based on the relation between its objective function, to optimized restriction prediction and in the suitable selection of carrying out weight coefficient ratio under the optimized situation by single goal, and realize according at short notice the detailed optimization of unsteady calculating etc. under the state that the hunting zone is narrowed down based on its result.
Aspect of the present invention has adopted a kind of design servicing unit; It is used for through importing a plurality of design parameters (input parameter) group; Calculate based on regulation a plurality of objective functions are calculated and said a plurality of objective functions carried out the multiple goal optimization handle, come the auxiliary best design parameter group of confirming.Said design parameter is the parameter of shape that for example is used for confirming the slide unit of hard disk magnetic memory apparatus.
Set of samples objective function computing unit (for example, 101 among Fig. 4) calculates a plurality of objective function groups of the design parameter set of samples of specified quantity.
Objective function is similar to unit (for example, 102 among Fig. 4) and asks mathematics to ask approximate to objective function based on the design parameter set of samples of specified quantity with a plurality of objective function groups that it calculates relatively.The approximate unit of this objective function through based on the design parameter set of samples of specified quantity and with a plurality of objective function groups that it calculates relatively, use repeatedly the polynomial expression of regression expression to carry out multiple regression analysis, come objective function is asked approximate.
Logical expression computing unit between objective function (for example, 103 among Fig. 4) will represent that the logical relation logical expression between any two or three objective functions in a plurality of objective functions of being asked mathematical approach calculates as logical expression between objective function.The logical expression computing unit is through the variable of the design parameter of any two or three objective functions in a plurality of objective functions of being asked mathematical approach of the mark elimination method of limiting the quantity of (QE method) cancellation between this objective function, and logical expression between calculating target function.
Logical expression shows that the value of any two or three functions can adopt the zone as Free Region between Free Region display unit (for example, 104 among Fig. 4) based target function.
Design auxiliary unit (for example, 105 among Fig. 4) is come Aided Design based on the demonstration of Free Region.This design auxiliary unit is through the Pareto border based on the objective function of discerning from the Free Region that is shown by the Free Region display unit; Set of design parameters is restricted to the corresponding set of design parameters of Pareto boundary vicinity and carries out the multiple goal optimization process, come the auxiliary best design parameter group of confirming.
According to the present invention, can ask approximate to objective function based on the mathematic(al) representation of some design parameter set of samples cause such as polynomial expressions of slide block shape of hard disk etc. etc., and can use mathematical processing methods to calculate this expression formula.
Therefore, because can under the situation of not carrying out any processing, operate input parameter, so logical relation between the easy master objective function and I/O relation.Therefore, through (confirming in the Pareto border especially) that in the auxiliary leading portion of design use is calculated like this and the objective function of mathematics manipulation, can realize very effective design aiding system.
Element and combination through in claim, specifically noting can realize the object of the invention, obtain advantage of the present invention.
Should be appreciated that aforementioned general remark and following detailed description are exemplary and indicative, do not limit the present invention.
Description of drawings
Fig. 1 shows the slide block of hard disk.
Fig. 2 shows the parameter of slide block shape.
Fig. 3 is the operational flowchart of prior art.
Fig. 4 shows the functional module structure of the preferred embodiments of the present invention.
Fig. 5 is the operational flowchart of the overall process of the preferred embodiments of the present invention.
Fig. 6 is the Free Region operation displayed process flow diagram (first) that carries out through mathematics manipulation.
Fig. 7 is the Free Region operation displayed process flow diagram (second) that carries out through mathematics manipulation.
Fig. 8 shows the set of samples of input parameter 107 and the example of each target function value corresponding with it.
Fig. 9 shows the example (first) that Free Region shows.
Figure 10 shows the example (second) that Free Region shows.
Figure 11 illustrates the center range of the operation of specifying input parameter.
Figure 12 A and 12B show the example (the 3rd) that Free Region shows.
Figure 13 A and 13B show the problem that Free Region shows.
Figure 14 shows how to improve the Free Region demonstration.
Figure 15 is the Free Region operation displayed process flow diagram (the 3rd) that carries out through mathematics manipulation.
Figure 16 A and 16B show the example (the 4th) that Free Region shows.
Figure 17 A and 17B show the example (the 5th) that Free Region shows.
Figure 18 shows an example of the hardware structure of computer that can realize system according to a preferred embodiment of the invention.
Embodiment
Below will illustrate and describe the preferred embodiments of the present invention.
Fig. 4 shows the functional module structure of the preferred embodiments of the present invention.
Actual computing unit 101 inputs of floating are used for the set of samples 107 of input parameter of the slide block shape of hard disk, carry out slide block to every group and float and calculate, and export each target function value.In the case, the quantity of the set of samples 107 of input parameter is at most hundreds of.
Objective function polynomial approximation unit 102 is carried out multiple regression analysis through the polynomial expression that uses repeatedly regression equation and is come the computing unit 101 that floated by reality is asked approximate to each objective function that is used for the slide block shape of every set of calculated.
Limit the quantity of mark cancellation (quantifier elimination:QE) unit 103 based on the constraint condition of each parameter value of each objective function polynomial expression that calculates by objective function polynomial approximation unit 102 and input parameter set of samples 107 (input parameter group 108), calculate logical expression between any two objective functions through the QE method.
Free Region display unit 104 is based on the Free Region of display-object function on the graphoscope that in Fig. 4, is not specifically illustrated by logical expression between any two or more objective functions of QE computing unit 103 calculating.
The weight vector that single goal function optimization unit 105 is confirmed on Free Region display unit 104 based on each the objective function polynomial expression that is calculated by objective function polynomial approximation unit 102 and user calculate input parameter group 108, as the weighted linear of objective function and the single goal functional value of acquisition, and calculate input parameter group 108 candidates that its single goal functional value becomes minimum.The quantity of input parameter group 108 is 10,000 to 20,000 groups.
The actual calculating optimum unit 106 that floats carries out detailed unsteady calculating through input parameter group 108 candidates that its single goal functional value that is calculated by single goal function optimization unit 105 become minimum and conduct is calculated based on the weighted linear of the objective function of its calculating and the single goal functional value of acquisition, exports its single goal functional value and becomes minimum input parameter group 108.In the case; For each objective function; Use through actual floating and calculate the objective function that obtains, for weight vectors, use with single goal function optimization unit 105 in employed identical weight vectors or through it being carried out the weight vectors of some modifications acquisitions.
The operational flowchart of following basis shown in Fig. 5-7 and 15, and, the operation of the preferred embodiments of the present invention with said structure is described with reference to Fig. 8-11-14, Figure 16 A and 16B, 17A and 17B.
Fig. 5 is the operational flowchart by the overall process of the preferred embodiments of the present invention of the system's execution with functional module structure as shown in Figure 4.
At first; (the step S201 among Fig. 5) of actual hundreds of input parameter set of samples 107 conducts of computing unit 101 outputs design specification relevant of floating with the hunting zone of slide block shape; Carry out slide block to every group and float to calculate, and export each target function value (the step S202 among Fig. 5).
Therefore, form the input parameter set of samples 107 for example as shown in Figure 8 and the data file of target function value thereof.In Fig. 8, the value in the row of being represented by x1～x8 is an input parameter set of samples 107, and the value in the row of being represented by cost2 is the value group of certain objective function.
Then; The polynomial expression of objective function polynomial approximation unit 102 through using repeatedly regression expression comes each objective function of slide block shape is asked approximate (the step S203 among Fig. 5) to carrying out multiple regression analysis by input parameter set of samples 107 with to the data file that each target function value of every set of calculated is formed.
As a result, the following example of the polynomial expression of objective function.
[mathematic(al) representation 2]
f1：＝
99.0424978610709132-6.83556672325811121*x1
+14.0478279657713188*x2-18.6265540605823148*x3
-28.3737252180449389*x4-2.42724827545463118*x5
+36.9188200131846998*x6-46.7620704128296296*x7
+1.05958887094079946*x8+6.50858043416747911*x9
-11.3181110745759242*x10-6.35438297722882960*x11+
+4.85313298773917622*x12-11.142898807281405*x[13]
+35.3305897914634315*x14-53.2729720194943113*x15；
In the case, aspect slider designs, have following trend: along with the carrying out of work, it is many that the type of input parameter becomes.Estimate because the influence of other parameters exists for the lower parameter of the contribution of certain objective function.Therefore, through being used for to be attached to processing for the routine that the lower parameter of the contribution of certain objective function is got rid of, can be similar to through simpler polynomial expression through multiple regression analysis.When the deviser imported the number of parameters that is used to analyze, objective function polynomial approximation unit 102 reduced to the quantity of parameter the quantity of setting.Reduce through this parameter and to handle, can reduce the calculated amount when calculating through the QE method that will describe.
As a result, can obtain the polynomial expression of the objective function that its number of parameters of following example reduces.
[mathematic(al) representation 3]
f1：＝
100.236733508603720-.772229409006272793*x1
-20.7218054045105654*x3-5.61123555392073126*x5
+27.4287250065600468*x6-52.6209219228864030*x7
+2.86781289549098428*x8-1.51535612687246779*x11
-51.1537286823153181*x15；
(quantity of variable reduces to 8 from 15)
As stated, in a preferred embodiment of the invention, use hundreds of input parameter set of samples 107 at the most, can obtain to use repeatedly the polynomial expression of regression expression to ask approximate objective function.This is because in slider designs, at first has the original shape of slide block, and through using polynomial expression can ask approximate specified scope interscan (sweep) to be used for confirming carrying out optimization in the parameter of this original shape to objective function.This is because in this localized design modification scope, can be through obtaining enough effective optimization by the linear-apporximation of regression expression repeatedly.
In a preferred embodiment of the invention, through the objective function of such calculating of (particularly, in confirming the Pareto border) use and mathematics manipulation in the leading portion of slider designs, can realize very effective design aiding system.
Particularly, QE computing unit 103 as shown in Figure 4 calculates logical expression (part of step S204 among Fig. 5) between two or more objective functions arbitrarily based on constraint condition, the use QE method of each parameter value of each objective function polynomial expression that is calculated by objective function polynomial approximation unit 102 and input parameter set of samples 107 (input parameter group 108).
The algorithm of QE method among the step S204 below will be described according to operational flowchart as shown in Figure 6.
At first, the user specifies two objective functions (the step S301 among Fig. 6) of its Free Region of desired display.Suppose that these functions are f1 and f2.Wherein specify the preferred embodiment of three objective functions also to be fine.
Then, QE computing unit 103 uses the constraint condition of each parameter value of approximation polynomial and the input parameter set of samples 107 (input parameter group 108) of two or more intended target functions that calculated by objective function polynomial approximation unit 102 to be formulated this problem (the step S303 among Fig. 6).Therefore, for example, can obtain the formula of following example.Though in this example, the quantity of parameter is 15, does not obtain reducing, and this quantity can access minimizing.
[mathematic(al) representation 4]
y1＝f1(x1，...，x15)，y2＝f2(x1，...，x15)
AND?y1＝f1(x1，...，x15)AND?y2＝f2(x1，...，x15)
Input parameter x1 ..., x15 moves between 0≤x_i≤1.
Then, QE computing unit 103 is found the solution (the step S303 among Fig. 6) according to QE method certificate to the formula F that is exemplified as mathematic(al) representation 4.As a result, like the input parameter x1 of following example ..., x15 is by cancellation, and exports the logical expression of two objective function y1 and y2.Be under three the situation in the quantity of objective function, the logical expression of output three objective function y1, y2 and y3.
[mathematic(al) representation 5]
y2＜y1+1AND?y2＞2AND?y2＞2*y1-3
Though omitted the details of QE method here; But the known technology that the application's inventor HirokazuAnai and Kazuhiro Yokoyama are known " Introduction to Calculationreal algebraic geometry:Summary of CAD and QE " (Mathematic Seminar.No.11; The 64th～70 page; 2007) disclosed its disposal route, this disposal route can be used for the preferred embodiments of the present invention without modification.
Then, Free Region display unit 104 as shown in Figure 4 is based on the next Free Region (the step S204 among Fig. 5 and the step S304 among Fig. 6) that on graphoscope, shows two objective functions of logical expression between any two objective functions that calculated by QE computing unit 103.
Particularly, Free Region display unit 104 carries out painted to the point of the logical expression establishment of two objective function y1 wherein being calculated and be exemplified as mathematic(al) representation 5 by QE computing unit 103 and y2 when scanning (sweep) is about each point in the two-dimensional graphics plane of two objective function y1 and y2 in succession.As a result, can for example show Free Region with the form shown in the painted areas among Fig. 9.
Be under three the situation, can to show by three dimensional constitution in the quantity of objective function.
Another detailed example of Free Region display process is below described.
Following example supposes that the approximation polynomial of two objective functions is made up of three input parameter x1, x2 and x3.
[mathematic(al) representation 6]
y1＝f1(x1，x2，x3)＝x1-2*x2+3*x3+6
y2＝f2(x1，x2，x3)＝2*x1+3*x2-x3+ 5
When with formulate mathematic(al) representation 6, obtain following expression formula.
[mathematic(al) representation 7]
AND?y
1＝x
1-2x
2+3x
3AND?y
2＝2x
1+3x
2-x
3+5
When mathematic(al) representation 7 is used the QE method, obtain following expression formula.
[mathematic(al) representation 8]
(3*y1+2*y2-35＞＝0AND?3*y1+2*y2-42＜＝0AND?y1+3*y2-28＞＝0ANDy1+3*y2-35＜＝0)OR(3*y1+2*y2-28＞＝0AND?3*y1+2*y2-35＜＝0AND?2*y1-*y2-7＜＝0AND?2*y1-y2＞＝0)OR(2*y1-y2-7＞＝0AND?2*y1-y2-14＜＝0ANDy1+3*y2-21＞＝0AND?y1+3*y2-28＜＝0)
When drawing Free Region, for example, can obtain Free Region shown in figure 10 based on mathematic(al) representation 8.In Figure 10, angled straight lines is represented each logical boundary of mathematic(al) representation 8, and painted areas is the Free Region of two objective functions.
Can know as Figure 10 is clear, in painted Free Region, can be intuitively and easily discern the border of the Pareto border of two objective functions as near the lower limb the true origin, and can discern optimized boundary zone.Under the situation of three objective functions,, can show with three dimensional constitution though the Pareto border becomes curved surface (Pareto curved surface).
When calculating the single goal function (seeing mathematic(al) representation 1) of weighted sum, can estimate the optimum value of the ratio of each weighted value between two objective functions in weight vectors through total slope of identification Free Region based on two objective functions.
Though in the case; Suppose in mathematic(al) representation 7; Each input parameter that constitutes the set of samples 107 of input parameter can freely be taked the arbitrary number between 0 and 1; If but in fact expection is searched for central point of specifying input parameter and the mode that moves this value within the specific limits, then can obtain better result.
In order to carry out this operation, the step S204 in Fig. 5, QE computing unit 103 carry out operating process as shown in Figure 7 with Free Region display unit 104 and replace the operating process among Fig. 6.
At first, the user specifies two objective functions (the step S401 among Fig. 7) of its Free Region of desired display.Suppose that these functions are f1 and f2.
Then, QE computing unit 103 extracts wherein roughly f2=f1 and apart from the nearest point of initial point from input parameter set of samples 107 and two intended target functions (f1 and f2) corresponding with it, for example by the point of 801 expressions among Figure 11.Suppose the input parameter corresponding with it be (p1 ..., P15) (the step S402 among Fig. 7).
Then, QE computing unit 103 uses the sweep length t of each parameter value of approximation polynomial and the input parameter set of samples 107 (input parameter group 108) of two intended target functions that calculated by objective function polynomial approximation unit 102 to be formulated this problem (the step S403 among Fig. 7).Therefore, for example, can obtain the formula of following example.
[mathematic(al) representation 9]
AND..AND?p15-t≤x15≤p15+t
AND?y1＝f1(x1，...，x15)AND?y2＝f2(x1，...，x15)
Each input parameter x_i moves between the width t around the p_i.
Then, QE computing unit 103 is found the solution (the step S404 among Fig. 7) according to the QE method according to the value F to the expression formula that is exemplified as mathematic(al) representation 9.As a result, input parameter x1 ..., x15 is by cancellation, and exports the logical expression of two objective function y1 and y2 and sweep length t.
Then, the Free Region display unit 104 among Fig. 4 based on logical expression between any two objective functions that calculate by QE computing unit 103, in the value of revising sweep length t, on graphoscope, show the Free Region (the step S405 among Fig. 7) of two objective functions.
In the case, preferably select t with set of samples 107 that comprises input parameter and the mode that also reduces its area.
Figure 12 A is the example that shows through the Free Region that uses the input parameter set of samples corresponding with actual slide block shape 107 to obtain.Figure 12 B is the example that the Free Region under the situation on the border of going back the display logic expression formula shows.In this example, it is that the amount of floating that wherein is in the slide block of low clearance (0m) is the first objective function f1, and the amount of floating that is in the slide block of high altitude (4200m) is the second objective function f2, and their relation is the figure of y1 and y2.
Because the slope of Pareto curve in the figure is about-1/8～-1/5, so if be about 1 to 8～1 to 5 just enough at the ratio that these two objective functions is carried out weighting and obtain the weighted value in the weight vectors under the situation of single goal function (seeing mathematic(al) representation 1).
Therefore, in the processing of Free Region display unit 104 as shown in Figure 4, the user can be carried out estimating under the optimized situation weighted value (the step S205 among Fig. 5) in the weight vectors in expection by single goal function (seeing mathematic(al) representation 1).The user can be through the Free Region in for example illustrating on the display overall slope (not specifically illustrating among the figure) etc., the ratio of the weighted value of weight vectors is announced to system.Perhaps, the ratio that the algorithm that system can be according to the rules comes automatic right to examin heavily to be worth.
In above Free Region display process, the user can be when specifying two objective functions in succession the ratio of the weighted value of specified weight vector effectively, and the Pareto border that is used for each objective function.
After above operation; The ratio of the weighted value in the weight vectors that single goal function optimization unit 105 is confirmed on Free Region display unit 104 based on each the objective function polynomial expression that is calculated by objective function polynomial approximation unit 102 and by the user calculates weighted linear and the single goal functional value (seeing mathematic(al) representation 1) that is obtained as the objective function of input parameter group 108, and calculates its single goal functional value and become minimum input parameter group 108 candidates (the step S207 among Fig. 5).The quantity of input parameter group 108 is about 10,000～20, and 000.
In the case, because when calculating each target function value, use approximation polynomial to replace the actual unsteady calculating of carrying out, so can calculate with very high speed.In addition; Because for the weight value group in the weight vectors that when calculating the single goal functional value, uses based on mathematic(al) representation 1; In the operation of Free Region display unit 104, use value, so need be such as the double counting revising weight vectors in succession by the suitable appointment of user.
At last; The 106 pairs of single goal functional values that calculated by single goal function optimization unit 105 in the unsteady calculating optimum unit of reality as shown in Figure 4 become minimum input parameter group 108 candidates and carry out detailed unsteady calculating, and calculate as the weighted linear of objective function and the single goal functional value that is obtained (the step S208 among Fig. 5).In the case; For each objective function; The objective function that use float to calculate is obtained by reality, for weight vectors, use with single goal function optimization unit 105 in used identical weight vectors or use through it being carried out the weight vectors of some modifications acquisitions.
Then, actual float calculating optimum unit 106 with reference to the boundary value of scheduled target function in aforementioned Free Region display process judge this single goal functional value and at that time the optimization of each target function value whether restrain (the step S209 among Fig. 5).
If optimization does not restrain, and judge that the result of determination in step S209 is not, then flow process turns back to step S207, and the weighted value in the weight vectors is carried out some modifications.Then, the optimization among the execution in step S207 and 208 is handled once more.
When optimization convergence and the actual calculating optimum unit 106 that floats are judged to be in the judgement of step S209 when being, the single goal functional value that then obtains at that time become minimum input parameter group 108 by output as best slide block form parameter group 109 outputs (the step S210 among Fig. 5).
Another preferred embodiment of the operation of QE computing unit 103 and Free Region display unit 104 then, is below described.
In the operation of above QE computing unit 103 shown in the operational flowchart in Fig. 7 and Free Region display unit 104; With for example can be with wherein f2=f1 and (for example roughly apart from the nearest point of initial point at two objective functions (f1 and f2); Point by 801 among Figure 11 expression) is appointed as the central point of input parameter, and can uses said mode of in the scope of movable width t, searching for Free Region to be formulated logical expression F as the center.
Showing under the situation of Free Region, when drawing, shown in Figure 13 A based on the logical expression F that confirms like this; Along with movable width t reduces, the scope of Free Region diminishes, and shown in Figure 13 B; Along with movable width t increases, it is big that the scope of Free Region becomes.In the case, preferably make Free Region as far as possible accurately comprise input parameter, and make Free Region bigger,, and improve degree of freedom in design because can enlarge the range of choice of design parameter.
But, shown in the operational flowchart as shown in Figure 7, when a point that uses input parameter is detected Free Region as the center; Shown in Figure 13 A; If movable width is less, although then Free Region almost accurately comprises input parameter, the scope of Free Region diminishes.On the contrary, if movable width is bigger, although then the scope of Free Region becomes big, Free Region does not accurately comprise input parameter.In other words, in a method that point is detected Free Region as the center that is used for using input parameter, be difficult to find the movable width that matees with set of samples, this is a problem.
Therefore; In following preferred embodiment, replace using only point of input parameter to search for Free Region as the center, shown in figure 14; A plurality of points of use Pareto boundary vicinity (for example; Four some S1, S2, S3 and S4) as the center, setting movable width t with each matching mode of these points, and search and their each corresponding Free Region A1, A2, A3 and A4.The a plurality of Free Regions that obtain like this are combined and show.Therefore, can search for the Free Region that can comprise accurately that input parameter also also enlarges widely on the Pareto border.
Figure 15 shows in order to replace operational flowchart as shown in Figure 7 to realize the operation that above-mentioned functions, QE computing unit 103 and the Free Region display unit 104 step S204 in Fig. 5 carries out.
At first, the user specifies two objective functions (the step S1201 among Figure 15) of its Free Region of desired display.Suppose that these functions are f1 and f2.
Then, QE computing unit 103 as shown in Figure 4 extracts near the central point group S Pareto (for example, shown in figure 14 four central point S1, S2, S3 and S4) from input parameter set of samples 107.Particularly, extract this central point group S on by the plane of two objective functions (f1 and f2) appointment, as shown in figure 14 uniformly-spaced to be arranged near the groups of samples near the side the initial point.
Then; The central point input parameter variable { p_i}=(p1 of the input parameter of each central point that QE computing unit 103 uses the approximation polynomial of two intended target functions that calculated by objective function polynomial approximation unit 102, represent with variable to comprise among the central point group S; ...; P15) and movable width t (identical) with t as shown in Figure 7 be formulated this problem, thereby form logical expression (the step S1203 among Figure 15).Therefore, for example, can obtain to be exemplified as the following formula of mathematic(al) representation 9.Though in the description of above Fig. 7, (p1 ..., the p15) coordinate of a concrete central point of expression, in this preferred embodiment, the variable of a plurality of central points of its expression representative.
Then, QE computing unit 103 is found the solution (the step S1204 among Figure 15) according to the QE method according to the value F to the expression formula that is exemplified as mathematic(al) representation 9.As a result, input parameter x1 ..., x15 is by cancellation, and can export two objective function y1 and y2, central point input parameter variable { the logical expression G of p_i} and movable width t.
Then; Processing when QE computing unit 103 selects to be included in each central point among the central point group S (for example, shown in figure 14 S1, S2, S3 and S4) one by one in the judgement of step S1205 shown in figure 15 among execution in step S1206～S1209.
At first, and the central point input parameter variable of the logical expression G that the input parameter substitution that QE computing unit 103 will be corresponding with selected central point is calculated in step S1204 { p_i}=(p1 ..., p15) (the step S1206 among Figure 15).
Then; QE computing unit 103 is through the value of reduction activity width t is simultaneously in order in the determination processing of step S1207 shown in figure 15; The Free Region corresponding with the central point of current selection calculated in logical expression G that the value substitution of the movable width t that repetition will be cut down at step S1208 shown in figure 15 obtains at step S1206 and the processing of calculating this value.
When in step S1207 shown in Figure 15, judging the processing of reduction activity width t in specialized range, the Free Region that QE computing unit 103 and selected central point will calculate relatively as stated is stored in the storer etc. as local Free Region.
QE computing unit 103 is via the judgement of step S1205 shown in Figure 15; Carry out the processing of calculating to being included in whole central points among the central point group S (for example, shown in Figure 14 S1, S2, S3 and S4) with the corresponding local Free Region of representing by above-mentioned step S1206-S1209 shown in Figure 15 of a central point.
Then; If be judged to be the computing of the local Free Region that is included in the whole central points among the central point group S at step S1205 shown in Figure 15; Free Region display unit 104 then as shown in Figure 4 will be corresponding with each central point in being included in central point group S (it is stored in storer etc.) each local Free Region (for example; Corresponding with S1, S2, S3 and S4 respectively Free Region A1, A2, A3 and A4 shown in Figure 14) superpose simultaneously, and they are presented at (the step S1210 among Figure 15) on the graphoscope.So the user can clearly obtain the trade-off relation between selected two objective functions.
Figure 16 A and 16B and 17A and 17B are the examples through the combination of four Free Regions demonstrations of specifying four central points acquisitions.
As stated, in above preferred embodiment,, be applied to many points and the accurate Free Region stack at each some place that will obtain, can improve the precision of overall Pareto structure through reducing the precision that movable width t improves local Free Region structure a little.
Figure 18 shows an example of the hardware structure of computer that can realize said system.
Computing machine shown in Figure 180 comprises portable storage media drive unit 1506 and the network connection device 1507 that CPU (CPU) 1501, storer 1502, input media 1503, output unit 1504, external memory 1505, portable storage media 1509 insert wherein, and above-mentioned member is connected to each other through bus 1508.Structure shown in Figure 180 is to realize an example of the computing machine of said system, and this structure is not subject to this computing machine.
Portable storage media drive unit 1506 holds portable storage media 1509 (for example CD, SDRAM, compact flash (compact flash, registered trademark) etc.), and plays a part auxiliary external memory 1505.
Can realize by the CPU1501 that execution has a program of functional module as shown in Figure 4 according to the system of this preferred embodiment.Program for example can be stored in also can distribute in external memory 1505 or the portable storage media 1509 etc.Perhaps, program can be obtained from network by network connection device 1507.
Though in above-mentioned preferred embodiment of the present invention, the present invention the invention is not restricted to this and uses, and can also be applied at the various devices of carrying out the optimized while Aided Design of multiple goal with the design servicing unit of the slider designs that acts on auxiliary hard disk.
Claims (10)
1. multiple goal design optimization servicing unit that uses mathematical processing methods; It is used for through importing a plurality of set of design parameters; Calculate based on regulation a plurality of objective functions are calculated and said a plurality of objective functions carried out the multiple goal optimization handle; Come the auxiliary best design parameter group of confirming, said multiple goal design optimization servicing unit comprises:
Set of samples objective function computing unit, it is used for a plurality of objective function groups of the design parameter set of samples of regulation are calculated;
Objective function is similar to the unit, and it is used for coming said objective function is asked mathematical approach based on the design parameter set of samples of said regulation with a plurality of objective function groups that it calculates relatively;
Logical expression computing unit between objective function, it is used for the logical expression of logical relation between any two or three objective functions of a plurality of objective functions of being asked mathematical approach of expression is calculated as logical expression between objective function;
The Free Region display unit, it is used for showing that based on logical expression between said objective function the value of said any two or three functions can adopt the zone as Free Region; And
The design auxiliary unit; It is used for confirming to be used for to confirm the best design parameter group of shape of the slide unit of hard disk magnetic memory apparatus based on the demonstration of said Free Region, and is used for Aided Design and has the sliding unit that uses the shape that said best design parameter group confirms.
2. the multiple goal design optimization servicing unit of use mathematical processing methods according to claim 1, wherein,
Said design auxiliary unit is through the Pareto border based on the said objective function of discerning from the Free Region of said Free Region display unit demonstration; Said set of design parameters is restricted in the corresponding set of design parameters of said Pareto boundary vicinity and carries out said multiple goal optimization and handle, confirm said best design parameter group.
3. the multiple goal design optimization servicing unit of use mathematical processing methods according to claim 1, wherein,
The approximate unit of said objective function through based on the design parameter set of samples of said regulation and with a plurality of objective function groups that it calculates relatively, use repeatedly the polynomial expression of regression expression to carry out multiple regression analysis, come said objective function is asked approximate.
4. the multiple goal design optimization servicing unit of use mathematical processing methods according to claim 1, wherein,
The logical expression computing unit is through the variable of the said design parameter of any two or three objective functions in the said a plurality of objective functions of being asked mathematical approach of the mark elimination method cancellation of limiting the quantity of between said objective function, and calculates logical expression between said objective function.
5. the multiple goal design optimization servicing unit of use mathematical processing methods according to claim 1, wherein,
The logical expression computing unit calculates in the logical expression between a plurality of said objective functions each as follows between said objective function: satisfy respectively in the said design parameter set of samples and each each corresponding design parameter set of samples as a plurality of central points of the Pareto boundary vicinity of the said objective function of object; And apart from each constraint condition of each movable width of each said central point, and
Said Free Region display unit superposes based on each of logical expression between a plurality of said objective function that is calculated by logical expression computing unit between said objective function and shows a plurality of said Free Regions.
6. multiple goal design optimization householder method of using mathematical processing methods; It is used for through importing a plurality of set of design parameters; Calculate based on regulation a plurality of objective functions are calculated and said a plurality of objective functions carried out the multiple goal optimization handle; Come the auxiliary best design parameter group of confirming, said multiple goal design optimization householder method comprises:
Set of samples objective function calculation procedure is calculated a plurality of objective function groups of design parameter set of samples of regulation;
The objective function approximating step comes said objective function is asked mathematical approach based on the design parameter set of samples of said regulation with a plurality of objective function groups that it calculates relatively;
Logical expression calculation procedure between objective function calculates the logical expression of the logical relation between any two or three objective functions in a plurality of objective functions of being asked mathematical approach of expression as logical expression between objective function;
The Free Region step display shows that based on logical expression between said objective function the value of said any two or three functions can adopt the zone as Free Region; And
The design additional step is confirmed to be used for to confirm the best design parameter group of shape of the slide unit of hard disk magnetic memory apparatus based on the demonstration of said Free Region, and is used for Aided Design and has the sliding unit that uses the shape that said best design parameter group confirms.
7. the multiple goal design optimization householder method of use mathematical processing methods according to claim 6, wherein,
In said design additional step; Through Pareto border based on the said objective function of discerning from the Free Region that said Free Region step display, shows; Said set of design parameters is restricted in the corresponding set of design parameters of said Pareto boundary vicinity and carries out said multiple goal optimization and handle, confirm the best design parameter group.
8. the multiple goal design optimization householder method of use mathematical processing methods according to claim 6, wherein,
In said objective function approximating step, through based on the design parameter set of samples of said regulation and with a plurality of objective function groups that it calculates relatively, use repeatedly the polynomial expression of regression expression to carry out multiple regression analysis, come said objective function is asked approximate.
9. the multiple goal design optimization householder method of use mathematical processing methods according to claim 6, wherein,
Between said objective function in the logical expression calculation procedure; Through the variable of the said design parameter of any two or three objective functions in the said a plurality of objective functions of being asked mathematical approach of the mark elimination method cancellation of limiting the quantity of, and calculate logical expression between said objective function.
10. the multiple goal design optimization householder method of use mathematical processing methods according to claim 6, wherein,
Between said objective function in the logical expression calculation procedure; As follows in the logical expression between a plurality of said objective functions each calculated: satisfy respectively in the said design parameter set of samples and each each corresponding design parameter set of samples as a plurality of central points of the Pareto boundary vicinity of the said objective function of object; And apart from each constraint condition of each movable width of each said central point, and
In said Free Region step display, each that is based on logical expression between a plurality of said objective function that is calculated in the logical expression calculation procedure between said objective function superposes and shows a plurality of said Free Regions.
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| JP2008147332A JP5062046B2 (en) | 2008-01-14 | 2008-06-04 | Multi-objective optimization design support apparatus, method, and program using mathematical expression processing technique |
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| JP5477242B2 (en) * | 2010-09-22 | 2014-04-23 | 富士通株式会社 | Optimization processing program, method and apparatus |
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