JP4867332B2 - Pareto new area search device, medium on which Pareto new area search program is recorded, Pareto new area search display device, and Pareto new area search method - Google Patents

Description

  The present invention relates to an optimization technique using a computer, and more particularly to an optimization technique using a Pareto surface.

Conventionally, a technique described in Patent Document 1 has been disclosed as a system that supports optimization. This publication discloses a technique for supporting design work for optimizing the value of each characteristic when a design object determined by a plurality of design variables has a plurality of characteristics. In this publication, sampling is generated using a genetic algorithm, a Pareto plane showing the relationship between characteristics is created, and a design variable having a desired characteristic is created by using design variables existing on the Pareto plane. I have identified.
Unexamined-Japanese-Patent No. 2002-230514.

  As described above, when the Pareto surface is created, when the Pareto surface exists in a narrow range, that is, when the design space is narrow, the range needs to be enlarged. However, in the above prior art, it is necessary to repeat the calculation from the beginning by resetting the input conditions such as the design variables given to the model at the initial stage of the calculation, and there is a problem that the calculation time becomes long. Further, since it is not known how to change the design variable when resetting, there is a problem that there is no compensation for the appearance of a new Pareto region even if recalculation is performed.

  The present invention has been made based on the above problems, and an object of the present invention is to provide a Pareto new area search technique capable of searching for a new Pareto area while suppressing unnecessary calculations.

  In order to achieve the above object, in the Pareto new region search device of the present invention, when there is a system having responses of a first characteristic value and a second characteristic value corresponding to a plurality of limiting elements, the limiting element of the system and the Two-dimensional plot creating means for generating a plurality of samplings that are combinations with characteristics, creating a two-dimensional plot in a two-dimensional coordinate system having the first axis as the first characteristic value and the second axis as the second characteristic value And classifying means for classifying the sampling according to the similarity of the characteristic values to form a plurality of clusters, and among the samplings on the two-dimensional plot, a cluster that realizes the set system optimization is used as an initial Pareto plane. The initial pareto surface creation means to be extracted is compared with the limiting elements of each cluster constituting the initial pareto surface. An extraction unit that extracts a tendency of a common limiting element as a Pareto principle, a search direction setting unit that arbitrarily sets a search direction of a Pareto new area on the two-dimensional coordinate system, and between each cluster when going to the search direction Based on the difference in the existence range of the limiting element, the change tendency extracting means for extracting the changing tendency of the limiting element, and the Pareto principle as a reference, sampling is generated in the direction along the changing trend, and a new And a search means for searching for a Pareto group.

  Therefore, by extracting the Pareto principle from the existing initial Pareto surface and generating sampling along the changing tendency based on the Pareto principle, it is possible to compensate for the presence of new sampling on the Pareto surface. Therefore, a new Pareto group can be searched efficiently.

  Hereinafter, the best mode for realizing the Pareto surface search device of the present invention will be described based on the embodiments shown in the drawings.

[Technical concept of Example 1]
First, define the word “system”. A system is a processing system or order that exists between input results that produce a specific result when there is a specific input. A specific event (phenomenon) is realized by defining a specific system to a certain value (corresponding to a system defined by a plurality of limiting elements). And the unique system works in a limited number, range, and nature, not processing everything or giving order to everything. Therefore, even if the types of events are the same, if there are various types with different limitations, there is a system corresponding to each. Furthermore, there are host systems that handle these uniformly according to the type of event.

  Such a layered system structure related to a specific event can be applied to almost all events such as economy, culture, design, and biology. It is accepted as a classification method that is easy to catch.

  For example, in an automobile suspension, the abstract system is a suspension, the individual system is a multilink or torsion beam, the concrete system is a specific multilink or torsion beam determined by the specific geometry value or bush stiffness value taken by the individual system, etc. It is.

  However, this classification is not intended to specifically understand systems in the same hierarchy or upper and lower systems. As the analysis (understanding) of the events shown by the lowest-level system progresses (matures), in order to make new efforts and discoveries, it is necessary to accurately understand the relationships between systems and the commonality that defines the overall system. Must be used. Here, the top layer system is called an “abstract system”, the middle layer system is called a “formal system”, and the bottom layer system is called a “concrete system”.

  In this embodiment, in order to enable understanding of the entire system, a “trend system” is introduced as a system in which a trend or range is limited between an abstract system and a formal system, and between a concrete system and a formal system. By deciding (systems classified by Cluster), it became possible to consider the understanding of the whole system, the understanding of characteristics between systems, the further understanding of events, the possibility of creating a new system, and so on. FIG. 1 shows these relationships.

  It was stated that the three-layer system structure is classified based on some commonality. When a complex event (phenomenon) is considered to be realized as a result of a combination of several events (phenomena), the characteristic of a complex event (phenomenon) is the characteristic of a certain event (phenomenon) It is thought that the characteristics of the combination have an influence. Such a feature is related to the commonality described above, and can be defined as a “common concept” of the system for realizing the phenomenon.

  In a certain formal system, various phenomena that occur as a result of changing various parameters of a concrete system are governed by a common concept peculiar to that formal system, and this concept realizes the tendency of various phenomena. It is thought that there is. And the specific tendency of each phenomenon shown by the concrete system is realized by taking a specific form derived from it based on a common concept.

  Here, the common concept is the value of specific parameters that can best explain the tendency of various complex phenomena, the combination of specific parameters, the relationship between specific parameters, the tendency of specific parameters, the value of specific parameters. Any of the ranges, or some combination of these. On the other hand, based on the common concept, the value of a specific parameter other than the common concept, the combination of specific parameters, the relationship between specific parameters, the tendency of specific parameters, the range of specific parameter values, or Some combinations of these can be defined as unique forms.

  Note that the common concept may exist between different systems that exist to realize a certain phenomenon. That is, various systems that exist in the formal system hierarchy exist in order to realize a specific phenomenon, and therefore there is a common concept (that is, in an abstract system) at the upper level of the formal system. The trend of the phenomenon is realized. And the phenomenon peculiar phenomenon is realized by adding the peculiar form of the formal system or the concrete system to the common concept.

  The first embodiment is configured based on the concept as described above in order to understand complicated phenomena. FIG. 2 shows a common concept extraction concept of the embodiment. In FIG. 2, common concept 0 is a concept that prescribes all phenomena, common concept 1 is a concept that prescribes phenomena only in the hatched area, and common concept 2 prescribes phenomena only in the hatched area. It is a concept. Common concept 0 includes common concepts 1 and 2, and when each common concept is overlapped with another common concept, a region is further defined.

  The abstract system and the format system may be set as appropriate while paying attention only to the upper limit relationship between all layers. Therefore, the abstract system is not limited to the upper layer. Moreover, the order which connects between the abstract system, the formal system, and the concrete system which were set suitably is defined as a tendency system.

  FIG. 3 shows a Pareto new area search concept according to the first embodiment. For example, after categorizing sampling on the Pareto surface into a system of each hierarchy by hierarchization based on characteristics (formal system, trend system, concrete system, etc.), for example, a common concept existing in an existing trend system (Pareto principle described later) The main purpose of the first embodiment is to generate a new sampling using a change tendency of limiting elements other than the common concept and search for a new Pareto region from this sampling.

[Pareto New Area Search Flow]
In the first embodiment, a plurality of samplings are generated, and a two-dimensional plot is created in a two-dimensional coordinate system in which two characteristics (for example, a first characteristic value and a second characteristic value) set by the designer among the plurality of characteristics are set. To do. Then, this two-dimensional plot is classified according to the similarity of characteristic values to form a plurality of clusters. Next, out of sampling on the two-dimensional plot, a cluster that realizes the set system optimization is extracted as an initial Pareto plane, and an initial Pareto plane is created. At this time, this initial Pareto surface is a Pareto surface showing a rough tendency that the system will be optimal among the samplings that have occurred.

  After extracting the Pareto principle as a common concept that defines complex phenomena on the initial Pareto surface, the parameters that make up the Pareto principle and other parameters are changed in various directions to the direction of the new area that the designer wants Extract the corresponding structure. In order to extract this Pareto principle, it is necessary to prepare several combinations (hereinafter referred to as sampling) of phenomena (hereinafter referred to as characteristics) on the Pareto surface and parameters (hereinafter referred to as limiting elements) taken by a system that realizes the phenomenon. is there. Then, the Pareto principle that best explains all the phenomena is extracted by classifying these characteristics into several categories and comparing the limiting factors.

  Next, the restriction elements constituting the Pareto principle are changed after following the tendency of the restriction elements of the Pareto principle. In addition, the restriction elements other than the Pareto principle are changed by changing the restriction elements constituting the Pareto principle and then changing other restriction elements based on the changed Pareto principle.

From the above, in Example 1, as shown in FIG.
Step [1] Prepare the sampling and create the initial Pareto plane (Create the initial Pareto plane)
Step [2] Site to classify initial Pareto surface sampling (formation of multiple clusters)
Step [3] Part step for comparing the limiting elements and extracting the Pareto principle [4] Part step for setting the region direction to be obtained [5] Extracting the characteristics (change tendency) of the limiting elements other than the principle of the region direction to be obtained Part step [6] Pareto principle and part step [7] for generating sampling based on the features extracted in step [5] The sampling of step [6] is composed of seven steps for structural analysis. In this way, sampling can be efficiently generated using the Pareto principle, which is a common concept, so that a new Pareto region can be searched. Hereinafter, this Pareto new area search flow will be described by applying a specific example.

(Determination of optimal spring-S / ABS specifications for sedan vehicles in light bottoming)
Applying the above concept to the optimization process when determining the optimal spring-S / ABS specification for a sedan vehicle in light bottoming driving will be explained. Note that light bottoming refers to a state in which the vehicle nose-dives during braking, and “optimum spring-S / ABS specification” refers to a combination of the spring constant of the coil spring of the suspension and the damping characteristics of the shock absorber. Represents a decision. As a response model, a sedan vehicle model with a suspension was constructed, and each design variable was set.

  As the evaluation characteristics, the standard deviation of the front seat vertical acceleration was taken as the characteristic 1, and the standard deviation of the rear seat vertical acceleration was taken as the characteristic 2. Also, as the spring-S / ABS specifications (limitation factors) to be determined, on the front wheel side and rear wheel side, blow-by expansion side, orifice characteristic expansion side, valve characteristic inclination expansion side, blow-by compression side, orifice characteristic compression side, valve characteristic Eight limiting elements were taken up: tilt reduction, spring load, and stabilizer roll stiffness. Therefore, on the Pareto surface, parameter values for the spring-S / ABS specification in which the characteristics 1 and 2 are good are derived.

  FIG. 4 is a characteristic diagram showing the characteristics of the suspension. The horizontal axis represents the relationship between the piston speed and the vertical axis represents the damping force. The evaluation characteristic “blow-by” represents the piston speed when the slope of this relationship changes (point B). The “valve characteristic gradient” represents the gradient of the area expressed by a linear function (point C).

(Preparation for sampling and creation of initial Pareto surface)
At the stage of sampling preparation at step [1] and initial pareto plane creation at step [2], sampling satisfying the Pareto optimal values of characteristic 1 and characteristic 2 (a set of solutions considered to be system optimal) may be prepared. In FIG. 5, a two-dimensional plot is created in a two-dimensional coordinate system with the horizontal axis as the first axis as characteristic 1 (first characteristic value) and the vertical axis as the second axis as characteristic 2 (second characteristic value). 2D plot creation means), an initial Pareto plane which is a set of samplings that realize the set system optimization. In the first embodiment, the sampling satisfying the system optimum desired by the designer as the initial Pareto plane is plotted on the two-dimensional plane, and then this sampling is classified. However, a plurality of samplings are classified in advance to form a cluster. Then, the initial Pareto plane may be set by extracting a cluster that is considered to be a set of Pareto optimal values from each cluster, and arranging the clusters on a two-dimensional plane, which is not particularly limited. In this step, description is omitted because a Pareto plane may be appropriately created by an existing optimization method.

  If you have a simulator that simulates a system defined by multiple limiting elements and reproduces the characteristics that represent the relationship between input and output, link it with the simulator to work efficiently. It is desirable. The simulator may be in the same arithmetic device, or may be connected to another device with a cable or the like.

(Classification of Pareto surface sampling)
In the part for classifying the initial Pareto plane in step [3], hierarchical clustering is used. Clustering is an object of gathering groups that are similar to each other to create a community (hereinafter referred to as a cluster) in order to efficiently organize a meaningful system from a group of people with different characteristics. It is a general term for the method of classifying. Among these, hierarchical clustering is a method of generating hierarchies so that groups are nested. In the first embodiment, clustering is performed based on “similarity of characteristic tendency” as “similar”.

  Hierarchical clustering was adopted in the first embodiment because, as described in [Technical concept of the first embodiment], the system originally targeted by us is based on a hierarchical classification (i.e., most understood). This is because it is not possible to know in advance how many hierarchies and clusters exist in the trend system for understanding the relationship between the systems of each hierarchy. For example, when non-hierarchical clustering is performed, a threshold value or the like is set in advance, and operations within this threshold value are clustered. This threshold value may lead to the introduction of an existing concept. This is because when an existing concept is introduced, only a result confined to the existing concept is obtained, and the system cannot be classified correctly. The hierarchical clustering method is described below.

In hierarchical clustering, clusters are generated by joining individuals one by one based on similarity or dissimilarity, and gradually increasing from a small cluster to a larger cluster. Therefore, the cluster generation procedure is divided into two stages: definition of similarity (dissimilarity) and cluster generation. Here, the set of individuals x _i (1 ≦ i ≦ n), the set of all individuals X = {x ₁ , x ₂ , x ₃ ,..., X _n }, the similarity between individuals x _i and x _j Degrees d (x _i , x _j ) [1 ≦ x _i , x _j ≦ n, x _i ≠ x _j , x _i , x _j ∈X] are defined. Further, when an individual x _i is a cluster G _i , a cluster g including all the clusters is g = {G ₁ , G ₂ ,..., G _n }. At this time, the hierarchical clustering algorithm (Agglomerative Hierarchal Clustering: hereinafter referred to as AHC) is as follows.

(I) Define the following for the initial n clusters (individuals).

ここでG_qとG_rをgから取り除き、G'=G_q∪G_rをgに追加する。この際、クラスター数を一つ減らす。 (II) The cluster pair having the maximum similarity (or the minimum similarity) is combined.

Here, G _q and G _r are removed from g, and G ′ = G _q ∪G _r is added to g. At this time, the number of clusters is reduced by one.

(III) Recalculate the similarity d (G ′, G _i ) between clusters for all G _i ∈g and G _i ≠ G ′.

  (IV) Thereafter, (II) and (III) are repeated until the number of clusters becomes 1.

Various similarities (dissimilarities) taken up in (II) of the AHC have been proposed, but here, the Ward's Method is taken up. This method is based on the similarity based on the Euclid distance. That is, assuming that the value of the k-th element among the p elements constituting the individual x _i is x _i ^k , the Ward distance between the individuals x _{i and} x _j is expressed by Expression (3.4). Here, the element is a value included in the individual x _i .

At this time, if the center of gravity M (G) with respect to the cluster G is set as shown in formula (3.5), each component is expressed by formula (3.6).

Here, if the sum of squares E (G) of the difference between the center of gravity and the individual in the cluster G is defined as in the equation (3.7), the difference in distance between the two different clusters G _i and G _j is expressed by the equation ( It can be expressed as 3.8). Therefore, the coupling rule for the cluster of (II) of AHC selects G _q and G _r that minimize ΔE, as represented by the equation (3.9).

ここで、G'＝G_q∈G_rのとき

以上のように，AHCの（III）の再計算は、個体間の類似度を参照することなく、クラスター間の類似度のみを用いて再計算がなされる。図６に以上のアルゴリズムに基づくクラスターの生成方法を、図７に階層的クラスタリングの例を、図８に初期パレート面を分類した結果を示す。尚、図８には、分類されたクラスターの制限要素の関係を示す。 On the other hand, the recalculation of the similarity d (G ′, G _i ) of AHC (III) can be expressed using d (G _q , G _i ) and d (G _r , G _i ) before combining. If d (G _i , G _j ) = ΔE (G _i , G _j ) is defined, the initial cluster G _i = {x _i } can be expressed as shown in Expression (3.10).

Where G '= G _q ∈ G _r

As described above, the recalculation of (III) of AHC is performed by using only the similarity between clusters without referring to the similarity between individuals. FIG. 6 shows a cluster generation method based on the above algorithm, FIG. 7 shows an example of hierarchical clustering, and FIG. 8 shows the result of classifying the initial pareto plane. FIG. 8 shows the relationship of the restriction elements of the classified clusters.

Here, the cluster generation method is summarized as follows based on FIG.
(A) Sampling is clustered to generate clusters p, qr. In FIG. 6, it corresponds to a small circle.
(B) Calculate the center of gravity of each cluster.
(C) Combine clusters with small similarity (close distance). In FIG. 6, cluster p and cluster q are combined to generate a new cluster t.
(D) Calculate the center of gravity of the combined cluster t.
(E) Combine clusters with small similarity (close distance).
(F) Repeat (C) to (E) until there is one cluster.
In the step (A), not the cluster but the point information before clustering may be used, and there is no particular limitation.

[Extraction of Pareto principle]
In the part that compares the limiting elements and extracts the Pareto principle shown in step [4], after extracting the causal relationship between the characteristics and the characteristics between the limiting elements existing for each classified hierarchy, it is common to all the hierarchies. Find causality. The common causal relationship found here is called the Pareto principle.

(Extraction of the causal relationship between the characteristics and the relationship between the restriction elements that exist for each classified hierarchy)
Extract the physical causal relationship between the limiting elements and phenomena that exist for each classified phenomenon hierarchy. The feature that the phenomenon shows can only be said in a complete way that various limiting elements are involved. However, in other words, the phenomenon is realized through various forms of relationships while changing the relationship between the limiting elements. If this is a network of limiting elements leading to the realization of the phenomenon, this network can be considered as a causal relationship. Here, this network is called a “causal network”.

  When one path is considered, the formation of this path may be influenced by other limiting factors, and this influence may also be influenced by other limiting factors. When finding a route with such characteristics, rather than judging the route from pure connections after eliminating the influence of other restrictive elements, the route is based on the relationship of the restrictive elements that have the influence of other restrictive elements. It is better to judge.

  In other words, when a route is determined from a pure connection that eliminates the influence of other limiting elements, a determination is made based on the magnitude of the numerical value of the degree of influence between certain limiting elements or between a certain limiting element and a phenomenon. It will be. Therefore, it is difficult to say that the physical relationship between the cut-off restriction element and the path is cut off, and the whole represents a causal network without knowing whether the cut-off is correct. On the other hand, when judging a route that has the influence of other limiting factors, truncation based on the existing concept is not performed, so a causal network that can explain all the physical connections describing the phenomenon itself This is because it is considered to form.

  However, since it tends to be complicated, it is necessary to provide a numerical index in the path between the limiting elements. Here, Pearson's product-moment correlation coefficient is taken up as a measure for measuring the strength of the connection between two limiting elements that have the influence of other limiting elements. In order to extract the causal network from the limiting element to the phenomenon, each limiting element and the phenomenon are considered in the same dimension. Each limiting element and phenomenon placed in the same dimension will be called the fulcrum of the path that makes up the causal network.

The number of data one fulcrum with n, 1 single fulcrum x, average x fulcrum x ^-, the other fulcrum y, the mean of the fulcrum y y ^- if that, the are two fulcrums x, between y A correlation coefficient r (xy) representing the strength of connection is expressed by equation (5.2).

  By applying the formula (5.2) between all the fulcrums, all the causal networks up to the phenomenon can be extracted together with the strength of connection including the influence of other limiting factors (see Fig. 9). . By applying this to a phenomenon cluster of all layers, it becomes possible to grasp a phenomenon process that is gradually hierarchized from a complicated phenomenon to a simple phenomenon together with a change in the causal network.

(Extraction of Pareto principle)
Complex phenomena have a hierarchical structure in which they are gradually divided into simple phenomena based on physical characteristics. Therefore, it is considered that the causal network changes along the hierarchy accordingly. The factors that determine a single phenomenon in a hierarchy and the factors that determine its complexity are: a causal network that is common to single phenomena in all hierarchies, the target phenomenon, and its upper and lower hierarchies. It can be defined as a heterogeneous causal network that exists between these phenomena.

  In the case of hierarchization accompanied by feature differentiation of complex phenomena using hierarchical clustering, the lowest layer is a cluster composed of one sample. Since it becomes a hierarchy which emphasizes the complexity of a phenomenon as it goes to the lowest layer, there is a feature that commonality fades. On the other hand, the cluster is composed of more samples as it goes to the top layer, but since the number of clusters included in the hierarchy is reduced, there is a feature that there is a lot of commonness including noise.

  Therefore, it can be considered that there is a most suitable hierarchy for extracting the Pareto principle from this relationship. Here, a hierarchy from which the Pareto principle can be extracted is specified, and a method for extracting the Pareto principle from here is described.

First, a hierarchy suitable for extracting the Pareto principle is specified. Here, the sensitivity S and SN ratio η of the correlation coefficient of a certain path p are used. The hierarchy of interest i, when the number of clusters included in the layer n, the correlation coefficient in the path p in the m-th cluster included in the layer and r _ipm, the correlation coefficient superposed r _ip ^- in the formula ( It is expressed as 5.3).

If one of the common causal networks in this hierarchy is the path p, the sensitivity S of the correlation coefficient can be expressed as in equations (5.3) to (5.4).

Further, the total variation S _t of the correlation coefficient in the path p for each cluster included in the layer i is expressed by equation (5.5).

Further, the correlation coefficient variation S _β of the path p is expressed by Expression (5.6), where Euclidean distance d _im for dividing each cluster and average Euclidean distance are di ⁻ .

Therefore, the error variance V _e in the path p can be expressed by Equation (5.7).

Therefore, the SN ratio η of the correlation coefficient in the path p of each cluster included in the hierarchy i can be expressed by Expression (5.8).

  Since the Pareto principle is a common causal network that can explain all phenomena, the sensitivity S expressed by equation (5.4) is large and the SN ratio η expressed by equation (5.8) is large in all common paths. The hierarchy is a hierarchy suitable for extraction of the Pareto principle. However, the Pareto principle extraction hierarchy must be examined in a hierarchy that is less than or equal to the maximum Euclidean distance that causes a branch when searching from the top layer to the bottom layer of the tree diagram.

  In the hierarchy suitable for Pareto principle extraction obtained as described above, the common causal network that becomes the Pareto principle corresponds to the path p with a high correlation coefficient sensitivity expressed by the equation (5.4). FIG. 10 shows an example in which the Pareto principle is indicated by a thick solid line as a front wheel limiting element. FIG. 11 shows an example in which the Pareto principle is indicated by a thick solid line as a rear wheel limiting element. As can be seen from FIG. 10, on the front wheel side, there is a strong causal relationship among the blow-by extension side, the orifice characteristic extension side, the valve characteristic inclination extension side, and the blow-by contraction side. Further, there is a strong causal relationship between the valve characteristic inclination reduction side and the spring load, and these tendencies can be understood as the Pareto principle on the front wheel side.

  Further, as can be seen from FIG. 11, on the rear wheel side, there is a strong causal relationship between the blow-by extension side and the orifice characteristic extension side. In addition, there is a strong causal relationship between the blow-by compression side and the orifice characteristic compression side. There is also a strong causal relationship between spring load and stabilizer roll stiffness. These tendencies can be understood as the Pareto principle on the rear wheel side.

(Setting the desired area direction)
In the setting of the region direction to be obtained shown in step [4], the designer previously determines a region for searching for a new Pareto region. FIG. 12 is a conceptual diagram showing setting of a region for searching for a new Pareto region. For example, when it is desired to search whether or not a Pareto region exists in a region where the value of the characteristic 1 is higher, the cluster toward the new region changes from cluster 3 to cluster 4 to cluster 5. From this, a new region is derived by changing the limiting element according to the same tendency shown in step [5].

(Sampling based on the Pareto principle)
In the extraction of the change tendency shown in step [5], the change tendency of the limiting elements other than the Pareto principle is extracted based on the Pareto principle. In the search for a new Pareto surface shown in Step [6], this is a part for obtaining a new sampling by following the Pareto principle and the changing tendency. First, the limiting elements constituting the Pareto principle are changed. Here, the limiting element is changed after following the causal relationship of the Pareto principle such as the value of the limiting element of the extracted Pareto principle or the range, the tendency of the relationship between the limiting elements. This compensates for the nature (trend) of the resulting sampling characteristics.

  Next, the limiting elements other than the Pareto principle are changed. Here, it is possible to grasp how the cluster direction is changed by setting the desired region direction. Understand how the limiting factors are changing due to the change of the cluster, that is, change tendency. FIG. 13 is a diagram showing a changing tendency of limiting elements other than the Pareto principle of the front wheels, and FIG. 14 is a diagram showing a changing tendency of limiting elements other than the Pareto principle of the rear wheels. The arrows in FIGS. 13 and 14 indicate the changing tendency of the limiting element, that is, the changing direction.

  Therefore, in addition to the change of the limiting element of the Pareto principle, a new sampling is generated by adding a change along the changing tendency of the limiting elements other than the Pareto principle. Calculation is performed based on the combination of the limiting elements obtained here, and the characteristics of this structure are obtained. That is, sampling is performed. Here, it is efficient to generate a distance model based on the changed limiting element.

(Distance model generation method)
The extracted Pareto principle is represented by a combination of limiting element values representing a causal relationship with a characteristic, a combination of ranges, a tendency of a relationship between limiting elements, and a combination thereof. This cannot be changed when the Pareto principle is a combination of only limiting element values. Further, when the Pareto principle is expressed in the range of the limiting element, model generation may be performed using, for example, an orthogonal table or a random number within this range.

  On the other hand, in the case of the Pareto principle based on other expressions, it is necessary to change the limiting element following the Pareto principle. Here, a distance model generation method is proposed to generate a model that efficiently follows the Pareto principle.

  The distance model generation method is a method for newly generating a model similar to the limiting element constituting the Pareto principle. This method uses a measure between individuals used in a clustering grouping algorithm. In the clustering grouping algorithm, the distance between individuals is used as a measure for the degree of similarity (dissimilarity) between individuals. Various types of scales have been proposed. Here, the Euclidean distance, which makes it easy to imagine the similarity between individuals and is easy to handle, is taken up.

The Euclidean distance defines the distance d between individuals (x _i −x _j ), ^where x _i ^k is the value of the kth element among the p elements that make up the individual x _i To do. Here, the element is a value included in the individual x _i .

The model is generated using uniform random numbers. Therefore, if the model generated by uniform random numbers is d _rand , the model expressed by the limiting elements constituting the Pareto principle is x _c , and the model not satisfying the threshold is x _o , the newly generated model and these distances are It is expressed by (4.2).

Then, to apply the limitation rule not to adopt an extremely similar model to the model x _c restriction elements constituting the Pareto principle. For example, when the Euclidean distance is 0.01 or less and you want to recognize that two individuals are almost the same, the Pareto model x _{c is} the newly generated model x _rand adopt. The new model adopted here adopts one model of the minimum distance that satisfies the equation (4.3). In addition, since the generation of the model can be greatly changed by changing the value of the restriction rule, the designer can decide according to the purpose. In addition, when there are several Pareto principle models, in order to prevent the generation of the same model, the other Pareto principle models and the generated model are used to calculate Equation (4.3), and this is not adopted if it does not match.

In the following, a model generation algorithm will be described. An image diagram of model generation is shown in FIG.
(i) Prepare a model of limiting elements that constitute the Pareto principle.
(ii) A model is generated using random numbers, the distance is calculated according to equation (4.2), and a model satisfying equation (4.3) is selected. The distance between the model generated at this time and the Pareto principle model is stored.
(iii) Again, a model is generated using random numbers based on the Pareto principle, and the distance is calculated using equation (4.2). Replace the minimum distance, which is the restriction law of equation (4.3), with the distance of (ii), and select a model that satisfies this. Here, the distance between the selected model and the Pareto principle model is stored. When generating random numbers, since it is necessary to generate the limit elements other than the Pareto principle so as to follow the change tendency, a random number generation area is designated.
(iv) Thereafter, the above (i) to (iii) are repeated.

(Structural analysis)
Next, in step [7], the structure analysis of the sampling generated in step [6] is performed, and the characteristic 1 and characteristic 2 of this structure are calculated and plotted on the Pareto surface. Thereafter, this operation is repeated to search for a new Pareto surface. Thereby, as shown in FIG. 12, a new area can be obtained in the set area direction to be obtained.

  As described above, in the first embodiment, the following effects can be obtained.

  (1) When there is a system having responses of a first characteristic value and a second characteristic value corresponding to a plurality of limiting elements, a plurality of samplings that are combinations of the limiting element and the characteristics of the system are generated, A two-dimensional plot is created in a two-dimensional coordinate system with the axis as the first characteristic value and the second axis as the second characteristic value (two-dimensional plot creation means), and the sampling is performed according to the similarity of the characteristic values. Classify and form multiple clusters (classification means). Then, out of the sampling on the two-dimensional plot, a cluster that realizes the set system optimization is extracted as an initial Pareto plane (initial Pareto plane creation means). The restriction elements of each cluster constituting the initial Pareto surface are compared, and the tendency of restriction elements common among the clusters among the restriction elements is extracted as a Pareto principle (extraction unit). The search direction of the Pareto new area is arbitrarily set on the two-dimensional coordinate system (search direction setting means), and the limit is determined based on the difference in the existence range of the limit elements between the clusters when moving in the search direction. The change tendency of the element is extracted (change tendency extraction means). Using the Pareto principle as a reference, sampling is generated in a direction along the change tendency to search for a new Pareto group (search means).

  Therefore, by extracting the Pareto principle from the existing initial Pareto surface and generating sampling along the changing tendency based on the Pareto principle, it is possible to compensate for the presence of new sampling on the Pareto surface. Therefore, a new Pareto surface can be searched efficiently. By the way, in the sampling generation method using genetic algorithms proposed in the prior art, the sampling is generated ignoring the Pareto principle etc., so it is necessary to grasp which limiting element works to create the Pareto surface. I can't. Therefore, even if the number of samplings is simply increased, whether or not sampling on the Pareto plane can be obtained is not compensated at all. On the other hand, in the present invention, since it is possible to generate a sampling of a desired region, it is possible to obtain a sampling that is impossible with the prior art, as well as greatly reducing the calculation time.

  (2) The search direction was set to extend the initial Pareto surface. As a result, the initial pareto surface can be extended, and the degree of freedom in designing can be expanded.

  (2) When a new sampling is generated based on the change tendency of the limiting element based on the extracted Pareto principle, a new sampling is generated by generating a distance model.

  Therefore, a new Pareto group can be searched based on the concept that defines the existing Pareto principle.

  (3) When searching for a new Pareto region, the limiting elements constituting the Pareto principle are changed within a common range. As a result, the tendency and characteristic of the new sampling can follow the tendency and characteristic of the existing Pareto region, and the existing characteristic can be compensated for while being a new sampling. It should be noted that when searching for a new Pareto region, the same effect can be obtained even if the tendency of the limiting elements constituting the Pareto principle is maintained and changed.

  Note that all of the above-described actions may be provided in a state described in a program or the like that can be read by the arithmetic device. Specifically, when there is a system having responses of a first characteristic value and a second characteristic value corresponding to a plurality of limiting elements, a plurality of samplings that are combinations of the limiting element and the characteristics of the system are generated, A two-dimensional plot creation command unit for outputting a command to create a two-dimensional plot in a two-dimensional coordinate system having the first axis as the first characteristic value and the second axis as the second characteristic value; and the sampling, A classification command unit that outputs a command for forming a plurality of clusters classified according to the similarity of characteristic values, and a cluster that realizes a set system optimization among samplings on the two-dimensional plot is extracted as an initial Pareto plane. The initial pareto surface creation command unit that outputs the command is compared with the limiting elements of each cluster that constitutes the initial pareto surface. An extraction command unit that outputs a command to extract a tendency of a common limiting element as a Pareto principle, a search direction setting command unit that outputs a search direction of a Pareto new region arbitrarily set on the two-dimensional coordinate system, Based on the Pareto principle, the change tendency extraction command unit that outputs a command to extract the change tendency of the restriction element based on the difference in the existence range of the restriction element of each cluster when going in the search direction, the change By generating a sampling in the direction along the trend and outputting a command for searching for a new Pareto group, a Pareto new area search program characterized by comprising a medium, The distribution can be improved.

  Further, when executing the Pareto new area search, when there is a system having responses of first characteristic values and second characteristic values corresponding to a plurality of limiting elements as display means for the designer, A plurality of samplings that are combinations of the limiting element and the characteristic are generated, a two-dimensional plot is created in a two-dimensional coordinate system in which the first axis is the first characteristic value and the second axis is the second characteristic value. The two-dimensional plot display means for displaying, the sampling is classified according to the similarity of the characteristic values, the classification display means for displaying the result of forming a plurality of clusters, and the sampling on the two-dimensional plot are set. The initial Pareto plane display means for extracting and displaying the cluster realizing the system optimization as the initial Pareto plane, and the limitation of each cluster constituting the initial Pareto plane An extraction unit that compares elements and extracts a tendency of a limiting element that is common among clusters among the limiting elements as a Pareto principle, and a search that arbitrarily sets a search direction for a new Pareto region on the two-dimensional coordinate system Based on the direction setting display means, the change tendency extraction means for extracting the change tendency of the restriction element based on the difference in the existence range of the restriction element between the clusters when going in the search direction, and the Pareto principle as a reference Providing a Pareto new area search and display device characterized by comprising a search result display means for generating a sampling in a direction along the change tendency and searching and displaying a new Pareto group It is possible to further improve the design ease of the person.

The technical ideas that can be grasped from the above embodiments will be listed below.
(4) When there is a set of characteristics indicating the relationship between input and output for a system defined by a plurality of limiting elements, the set is classified based on the tendency of the characteristics, and the limiting elements corresponding to the classified characteristics The restriction element for a given classification is compared with the restriction element for the other classification. In other words, by comparing the characteristics classified based on the tendency between the limiting elements that define this characteristic, it becomes possible to grasp the limiting elements that define the tendency, and to understand the technical meaning of the classification. it can.

  (5) A common concept (Pareto principle) was extracted based on the limiting elements common to each classification. Therefore, a common concept can be extracted from a complex phenomenon.

  (6) We used a hierarchical clustering method that clustered hierarchically based on trends. In other words, considering the fact that our target system is based on hierarchical classification, the most understandable system can be obtained by hierarchical clustering. Further, considering that the number of layers existing in the system is not known in advance, it is not necessary to set a threshold or the like in advance, and a result that is not bound by an existing concept can be obtained.

  (7) A common concept (Pareto principle) was extracted based on the limiting elements common to each layer. Therefore, it is possible to extract a common concept that defines between hierarchies.

  (8) The common concept (Pareto principle) was extracted based on the limiting elements common to only a certain hierarchy. Therefore, a common concept that defines a certain hierarchy can be extracted.

  (9) When sampling the system, based on the set range and the set trend, it was decided to sample without restriction on the combination of limiting elements. Therefore, the limiting elements can be compared without causing a bias in the characteristics. Moreover, a common concept can be extracted without causing a bias in characteristics.

  (10) When performing sampling, an orthogonal table is used. Therefore, when focusing on the specific level of an assigned limiting element, all the levels of other limiting elements are created so that they are combined evenly. it can. Moreover, a common concept can be extracted without causing a bias in characteristics.

  (11) The characteristics are classified based on the similarity according to the distance in the Euclidean space. Therefore, it becomes possible to express a multidimensional restriction element in an orthogonal coordinate system based on the similarity, and it is possible to easily compare in a form that can be understood by humans.

  (12) The classification is based on the similarity based on the distance between the center of gravity of a certain classification and each characteristic. Therefore, it becomes possible to observe complex phenomena on a scale of distance, and to compare in a form that can be understood by humans.

  (13) The limiting element is arranged on a two-dimensional plane. Therefore, it is possible to easily compare in a form that can be understood by humans.

  (14) All restricted elements are described. Therefore, since the truncation based on the existing concept is not performed, the physical connection describing the phenomenon itself can be accurately described.

  (15) The causal network representing the connection between the limiting element and the characteristic is arranged by arranging the limiting element and the characteristic in the same dimension. Therefore, the physical connection between the limiting element and the characteristic can be expressed in a form that can be understood by humans.

  (16) When the limiting factors and characteristics on the causal network are defined as fulcrums, the correlation coefficient representing the strength of the connection between each fulcrum is calculated between all the fulcrums and the causal network with a large correlation coefficient is extracted. It was decided to. Therefore, it is possible to grasp a phenomenon process that is gradually hierarchized from a complicated phenomenon to a simple phenomenon together with a change in the causal network.

  (17) The error variance representing the size of the variance area of the causal network is calculated, and the common concept is extracted in a hierarchy having a large correlation coefficient and a small error variance. Therefore, a numerical index can be provided in the path between the limiting elements, and even if all the limiting elements are compared, a causal network can be easily formed without complication.

  Next, Example 2 will be described. Since the basic configuration is the same as that of the first embodiment, only different points will be described. In Example 1, the search direction was set in the direction of extending the Pareto surface, and the Pareto surface was extended. On the other hand, the second embodiment is different in that the search direction is set in a direction in which the Pareto surface is advanced in the origin direction.

  FIG. 16 is a diagram illustrating the entire sampling according to the second embodiment. The sampling target is the same as in the first embodiment. In the first embodiment, only the sampling on the Pareto plane is shown, but in the second embodiment, all samplings other than the Pareto plane are shown.

[Pareto New Area Search Flow]
In the second embodiment, after extracting the Pareto principle as a common concept for defining a complex phenomenon on the Pareto surface, the parameters constituting the Pareto principle and other parameters are changed in various ways so that the Pareto surface is the origin. The structure corresponding to the direction of moving forward is extracted. In order to extract this Pareto principle, it is necessary to prepare several combinations (hereinafter referred to as sampling) of phenomena (hereinafter referred to as characteristics) on the Pareto surface and parameters (hereinafter referred to as limiting elements) taken by a system that realizes the phenomenon. is there. Then, the Pareto principle that best explains all the phenomena is extracted by classifying these characteristics into several categories and comparing the limiting factors.

  Next, the restriction elements constituting the Pareto principle are changed after following the tendency of the restriction elements of the Pareto principle. In addition, the restriction elements other than the Pareto principle are changed by changing the restriction elements constituting the Pareto principle and then changing other restriction elements based on the changed Pareto principle.

From the above, in the second embodiment, as shown in FIG. 4 basically described in the first embodiment,
Step [1] Site step for preparing sampling and creating initial Pareto surface [2] Region step for classifying initial Pareto surface sampling [3] Region step for comparing Pareto principles and extracting Pareto principle [4] Part step for setting region direction [5] Part step for extracting features of limiting elements other than the principle of region direction to be obtained [6] Part for generating sampling based on Pareto principle and features extracted in step [5] Step [7] The sampling of step [6] is composed of seven steps of the part for structural analysis. Here, in Example 2, the setting of the region direction to be obtained shown in Step [4] is the Pareto surface advance direction (the direction in which the initial Pareto surface advances toward the origin of the two-dimensional coordinate system), and Step [5] The feature extraction of the limiting element other than the principle shown is not a cluster on the Pareto surface but sampling other than the Pareto surface, and the extraction of the feature of the limiting element is performed between the sampling on the opposite side of the Pareto advance direction. What is done is different. Since Step [1] to Step [3] and Step [6] and Step [7] are the same as those in the first embodiment, only Step [4] and Step [5] will be described. Hereinafter, this Pareto new area search flow will be described by applying it to a specific example of the first embodiment.

(Determination of optimal spring-S / ABS specifications for sedan vehicles in light bottoming)
Since a specific example to be processed is the same as that of the first embodiment, description thereof is omitted.

(Setting the desired area direction)
In the setting of the region direction to be obtained shown in step [4], the designer previously determines a region for searching for a new Pareto region. In the second embodiment, the purpose is to advance the initial Pareto plane toward the origin of the two-dimensional coordinate system, and thus the direction in which the initial Pareto plane advances is set. FIG. 17 is a conceptual diagram showing setting of a region for searching for a new Pareto region (advance of the Pareto surface). For example, when it is desired to move the cluster 2 forward, it is considered that the sampling existing behind the cluster 2 in the forward direction changes so as to approach the Pareto plane. From this, the Pareto surface is advanced by changing the limiting element according to the same tendency.

(Sampling based on the Pareto principle)
The generation of sampling based on the Pareto principle shown in step [6] is a part for obtaining new sampling based on the changing tendency of the limiting elements other than the Pareto principle based on the Pareto principle. First, the limiting elements constituting the Pareto principle are changed. Here, the limiting element is changed after following the causal relationship of the Pareto principle such as the value of the limiting element of the extracted Pareto principle or the range, the tendency of the relationship between the limiting elements. This compensates for the nature (trend) of the resulting sampling characteristics.

  Next, the limiting elements other than the Pareto principle are changed. Here, the region direction to be obtained is grasped by the setting of the region direction to be obtained and how the sampling limiting element changes. Understand how the limiting factors are changing, that is, change trends. At this time, since the sampling existing behind the Pareto surface advance direction is not the Pareto optimal value, attention should be paid to the changing tendency of the limiting elements other than the principle.

  FIG. 18 is a diagram showing the relationship between the restricting element of the front wheel belonging to cluster 2 and the restricting element of the front wheel belonging to cluster 6 existing behind the Pareto surface advance direction, and FIG. FIG. 10 is a diagram illustrating a relationship with a limiting element of a rear wheel belonging to the cluster 6 existing behind the Pareto surface forward direction. As shown in FIGS. 18 and 19, since the cluster 6 is not the Pareto optimal value, the limiting element constituting the Pareto principle takes a value different from that of the Pareto principle. Therefore, it is only necessary to generate sampling by paying attention to the changing tendency of the limiting elements other than the limiting elements constituting the Pareto principle.

  Therefore, in addition to the change of the limiting element of the Pareto principle, a new sampling is generated by adding a change along the changing tendency of the limiting elements other than the Pareto principle. Calculation is performed based on the combination of the limiting elements obtained here, and the characteristics of this structure are obtained. That is, sampling is performed. Here, the generation based on the distance model based on the changed limiting element is efficient, but it is omitted because it has been described in the first embodiment.

(Structural analysis)
In the structural analysis shown in step [7], the structural analysis of the sampling generated in step [6] is performed, and the characteristics 1 and 2 of this structure are calculated and plotted on the Pareto surface. Thereafter, this operation is repeated to advance the Pareto surface. Thereby, the Pareto surface can be advanced as shown by the dotted line in FIG.

  As described above, the Pareto new area search device according to the second embodiment can obtain the following effects as compared with the actions and effects of the first embodiment.

  (18) The initial Pareto surface is searched in the direction of moving forward toward the origin of the two-dimensional coordinate system. As a result, it is possible to move forward with the Pareto surface toward the origin, and furthermore, it is possible to obtain a system optimum desired by the designer, that is, sampling with a good Pareto optimum value for both characteristics 1 and 2.

  (19) Using the sampling other than the Pareto optimal value located behind the initial Pareto surface in the forward direction, the tendency of change of the limiting factors other than the Pareto principle was extracted. Specifically, after extracting the Pareto principle, attention was paid to the fact that the changing tendency other than the limiting elements constituting the Pareto principle may be other than the Pareto optimal value. That is, the Pareto optimum value can be searched from samplings other than the Pareto optimum value, and the sampling data can be used effectively.

  Although not specifically shown in the first embodiment, it is industrially effective to use an information processing technique based on the logical configuration as a program medium that can be processed by a computer or the like. The program medium may be a medium such as a CD or a DVD, or may be configured to store the program in a server or the like and download the program as appropriate. Also, a device written in advance in a Flash memory or ROM may be provided.

It is a figure showing the concept which introduce | transduces the tendency system which added the limitation of a tendency or a range between the abstract system of Example 1, and a format system, and between a concrete system and a format system. It is a conceptual diagram showing the relationship between the cluster of Example 1, and a common concept. It is a figure showing the Pareto new area | region search flow of Example 1. FIG. 6 is a diagram illustrating suspension characteristics in a specific example of Example 1. FIG. 3 is a diagram illustrating a Pareto surface in a specific example of Example 1. FIG. FIG. 6 is a diagram illustrating a specific example of clustering according to the first exemplary embodiment. 3 is a diagram illustrating a specific example of hierarchical clustering according to Embodiment 1. FIG. It is a figure showing the result of having classified the Pareto surface of Example 1. FIG. It is a figure showing an example of the display method of the causal network of Example 1. FIG. It is a figure showing the display method of the Pareto principle common to the causal network of the front wheel of Example 1. FIG. It is a figure showing the display method of the Pareto principle common to the causal network of the rear wheel of Example 1. 6 is a conceptual diagram illustrating search method setting processing in a specific example of Embodiment 1. FIG. It is a figure showing the change tendency of limiting elements other than the limiting element which comprises the Pareto principle of the front wheel in the specific example of Example 1. FIG. It is a figure showing the change tendency of limiting elements other than the limiting element which comprises the Pareto principle of the rear wheel in the specific example of Example 1. FIG. It is a schematic explanatory drawing showing the distance model production | generation process of Example 1. FIG. It is a figure showing both the sampling on the Pareto surface in the specific example of Example 2, and sampling other than the Pareto optimal value. FIG. 10 is a conceptual diagram illustrating sampling classification and search direction setting processing on a Pareto surface in a specific example of the second embodiment. FIG. 10 is a diagram showing a change tendency in comparison with a cluster, which is a limiting element other than the limiting element constituting the Pareto principle in the front wheel of cluster 2 in a specific example of Example 2. FIG. 9 is a diagram illustrating a change tendency in comparison with a cluster 6 that is a limiting element other than the limiting element that constitutes the Pareto principle in the rear wheel of the cluster 2 in the specific example of the second embodiment.

Explanation of symbols

p, q, r cluster
t cluster (cluster p + cluster q)

Claims (7)

When there is a system having responses of a first characteristic value and a second characteristic value corresponding to a plurality of limiting elements,
A two-dimensional plot in a two-dimensional coordinate system in which a plurality of samplings that are combinations of the limiting element and the characteristic of the system are generated, the first axis is the first characteristic value, and the second axis is the second characteristic value Two-dimensional plot creating means for creating
Classifying means for classifying the sampling according to the similarity of the characteristic values to form a plurality of clusters;
Of the sampling on the two-dimensional plot, an initial Pareto surface creation means for extracting a cluster that realizes the set system optimization as an initial Pareto surface;
An extraction unit that compares the limiting elements of each cluster constituting the initial Pareto surface, and extracts the tendency of the limiting elements common among the clusters among the limiting elements as a Pareto principle;
Search direction setting means for arbitrarily setting the search direction of the Pareto new area on the two-dimensional coordinate system;
A change tendency extracting means for extracting a change tendency of the limiting element based on a difference in the existence range of the limiting element between the clusters when traveling in the search direction;
Search means for generating a sampling in a direction along the change trend based on the Pareto principle and searching for a new Pareto group;
A Pareto new area search device characterized by comprising: In the Pareto new area search device according to claim 1,
The Pareto new area search device, wherein the search direction setting means is a means for setting the direction to extend the initial Pareto plane. In the Pareto new area search device according to claim 1,
The Pareto new area search device, wherein the search direction setting means is a means for setting the initial Pareto plane in a direction to advance toward the origin of the two-dimensional coordinate system. In the Pareto new area search device according to any one of claims 1 to 3,
The Pareto new area search device, wherein the classification means uses a hierarchical clustering technique. When there is a system having responses of a first characteristic value and a second characteristic value corresponding to a plurality of limiting elements,
Computer
A two-dimensional plot in a two-dimensional coordinate system in which a plurality of samplings that are combinations of the limiting element and the characteristic of the system are generated, the first axis is the first characteristic value, and the second axis is the second characteristic value and a two-dimensional plot creation part to create a,
The sampling, classified by the similarity of the characteristic values, a classification unit that form a plurality of clusters,
Of sampling on the two-dimensional plot, the initial Pareto surface creation unit that to extract clusters to achieve a system optimized set as an initial Pareto surface,
Comparing the limiting elements of each cluster constituting the initial Pareto surface, of said restricting element, an extraction unit that to extract the trend of limiting elements that are common between each cluster as Pareto principle,
A search direction setting tough for outputting a search direction of the arbitrarily set on the two-dimensional coordinate system Pareto new area,
When directed to the search direction, and on the basis of the difference in the existence range of the restricting element, said that to extract the change trend of the limiting element changes tend Extraction of each cluster,
The Pareto principle as a reference, to generate sampled in a direction along the changing trends, and the search unit you explore new Pareto group,
Medium Pareto new area search program is recorded for causing to function as. When there is a system having responses of a first characteristic value and a second characteristic value corresponding to a plurality of limiting elements,
A two-dimensional plot in a two-dimensional coordinate system in which a plurality of samplings that are combinations of the limiting element and the characteristic of the system are generated, the first axis is the first characteristic value, and the second axis is the second characteristic value 2D plot display means for creating and displaying
Classification display means for displaying the results of classifying the sampling according to the similarity of the characteristic values and forming a plurality of clusters;
Of the sampling on the two-dimensional plot, an initial Pareto plane display means for extracting and displaying a cluster that realizes the set system optimization as an initial Pareto plane;
An extraction unit that compares the limiting elements of each cluster constituting the initial Pareto surface, and extracts the tendency of the limiting elements common among the clusters among the limiting elements as a Pareto principle;
Search direction setting display means for arbitrarily setting the search direction of the Pareto new area on the two-dimensional coordinate system;
A change tendency extracting means for extracting a change tendency of the limiting element based on a difference in the existence range of the limiting element between the clusters when traveling in the search direction;
Search result display means for searching for and displaying a new Pareto group by generating sampling in a direction along the change trend based on the Pareto principle;
A Pareto new area search and display device characterized by comprising: When there is a system having responses of a first characteristic value and a second characteristic value corresponding to a plurality of limiting elements,
Computer
A two-dimensional plot in a two-dimensional coordinate system in which a plurality of samplings that are combinations of the limiting element and the characteristic of the system are generated, a first axis is the first characteristic value, and a second axis is the second characteristic value The steps of creating
Classifying the sampling according to the similarity of the characteristic values to form a plurality of clusters;
Of the sampling on the two-dimensional plot, extracting a cluster that realizes the set system optimization as an initial Pareto surface;
Comparing the limiting elements of each cluster constituting the initial Pareto surface, and extracting the tendency of the limiting elements common among the clusters among the limiting elements as a Pareto principle;
Arbitrarily setting the search direction of the Pareto new area on the two-dimensional coordinate system;
Extracting a change tendency of the limiting element based on a difference in the existence range of the limiting element between the clusters when going in the search direction;
Using the Pareto principle as a reference, generating sampling in a direction along the change trend, and searching for a new Pareto group;
A Pareto new region search method characterized by executing :

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