JPH04362785A - Combination optimizing device - Google Patents

Combination optimizing device

Info

Publication number
JPH04362785A
JPH04362785A JP3181505A JP18150591A JPH04362785A JP H04362785 A JPH04362785 A JP H04362785A JP 3181505 A JP3181505 A JP 3181505A JP 18150591 A JP18150591 A JP 18150591A JP H04362785 A JPH04362785 A JP H04362785A
Authority
JP
Japan
Prior art keywords
cost
arrangement
conversion
data
conversion means
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP3181505A
Other languages
Japanese (ja)
Other versions
JP2893144B2 (en
Inventor
▲たて▼野 峰夫
Mineo Tateno
Ryuichi Mato
隆一 間藤
Hitoshi Araki
均 荒木
Hitoshi Kato
等 加藤
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
National Institute of Advanced Industrial Science and Technology AIST
Original Assignee
Agency of Industrial Science and Technology
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Filing date
Publication date
Application filed by Agency of Industrial Science and Technology filed Critical Agency of Industrial Science and Technology
Priority to JP3181505A priority Critical patent/JP2893144B2/en
Publication of JPH04362785A publication Critical patent/JPH04362785A/en
Application granted granted Critical
Publication of JP2893144B2 publication Critical patent/JP2893144B2/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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Abstract

PURPOSE:To shorten processing time by adjusting the applicable ratio of plural arrangement conversion means based on the decision result by a conversion validity decision means deciding the validity. CONSTITUTION:In an applicable ratio adjusting means 5, plural arrangement conversion means are ranked in order of high validity based on a decision result of a conversion validity decision means 6 deciding the validity every temperature at first. Next, the arrangement conversion means are divided into higher ranking arrangement conversion means and lower ranking arrangement conversion means. As for the higher ranking arrangement conversion means, the applicable ratio is increased and as for the lower ranking arrangement means, the applicable ratio is decreased. Further, the higher the ranking becomes, the more the increase rate is increased and the lower the ranking becomes, the more the decrease rate is increased. Based on the increase and decrease rates, the applicable ratio in a next temperature is decided. Namely, the higher the validity decided by the conversion validity decision means 6 deciding the validity of each arrangement conversion means stored in a data base 1 that an arrangement conversion means has is, the more the applicable ratio is increased. Thus, the processing time can be shortened.

Description

【発明の詳細な説明】[Detailed description of the invention]

【0001】0001

【産業上の利用分野】本発明は、設計分野、特に論理回
路設計における組合せ最適化問題を高速実行する装置に
関するものである。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for high-speed execution of combinatorial optimization problems in the field of design, particularly in logic circuit design.

【0002】0002

【従来の技術】最近、組合せ最適化装置は論理回路設計
などの分野で盛んに利用されるようになってきた。この
組合せ最適化装置としては、例えば、S.Kirkpa
trick, C.D.Gelatt, M.P.Ve
cchi ”Optimization by Sim
ulated Annealing”(Science
,Vol.220,No.4598,pp671−68
0,1983)などに記載されているシミュレーティッ
ド・アニーリングという構成が知られている。
2. Description of the Related Art Recently, combinatorial optimization devices have come into widespread use in fields such as logic circuit design. As this combination optimization device, for example, S. Kirkpa
trick, C. D. Gelatt, M. P. Ve
cchi ”Optimization by Sim
"Annealing" (Science
, Vol. 220, No. 4598, pp671-68
A configuration called simulated annealing, which is described in, for example, 0, 1983), is known.

【0003】以下、図3を参照しながら従来の組合せ最
適化装置について説明する。図3において、細線は制御
信号を、2重線は主にデータの参照関係を、太線は制御
信号及びデータの流れを主に示す。図3において、31
は配置データを生成する配置変換手段を複数記憶したデ
ータベース、32はデータベース31から配置変換手段
を無作為に選択し、配置変換手段により生成された新し
い配置データのコストを計算する変換適用手段、33は
従来の配置データのコストと新しい配置データのコスト
を比較して、従来の配置データと新しい配置データのい
ずれを採用するかを決定するコスト評価手段、34は温
度と呼ばれるパラメータを管理・変更する温度管理手段
、35は配置データの変動を観察し、変動がなくなった
ら処理を終了する処理終了判定手段、36は初期値を設
定、及び生成する初期化する手段である。
A conventional combinatorial optimization device will be explained below with reference to FIG. In FIG. 3, thin lines indicate control signals, double lines mainly indicate data reference relationships, and thick lines mainly indicate control signals and data flows. In FIG. 3, 31
32 is a database storing a plurality of layout conversion means for generating layout data; 32 is a conversion application means for randomly selecting a layout conversion means from the database 31 and calculating the cost of new layout data generated by the layout conversion means; 33 34 is a cost evaluation means that compares the cost of the conventional layout data and the cost of the new layout data to decide whether to adopt the old layout data or the new layout data, and 34 manages and changes a parameter called temperature. Temperature management means 35 is a process termination determining means for observing fluctuations in the arrangement data and terminating the process when the fluctuations disappear; 36 is an initializing means for setting and generating initial values.

【0004】以上のような図3の構成において、以下、
その動作について図4に示したフローチャートとともに
説明する。
[0004] In the configuration of FIG. 3 as described above, the following is performed.
The operation will be explained with reference to the flowchart shown in FIG.

【0005】まず、401では初期化手段により初期値
の組合せを生成し、初期値の組合せのコストを計算し、
温度管理手段34で管理されている温度というパラメー
タを初期化する。
First, in step 401, the initialization means generates a combination of initial values, calculates the cost of the combination of initial values,
A parameter called temperature managed by the temperature management means 34 is initialized.

【0006】次に、402では、変換適用手段32を用
いてデータベース31に記憶されている配置変換手段を
無作為に選択し、選択した配置変換手段を適用して新配
置データを生成する。403では、コスト評価手段33
により402で生成した配置データのコストを計算する
Next, in step 402, a layout conversion means stored in the database 31 is randomly selected using the conversion application means 32, and new layout data is generated by applying the selected layout conversion means. At 403, the cost evaluation means 33
The cost of the placement data generated in step 402 is calculated by.

【0007】404では、403で計算した新配置デー
タのコストと従来配置データのコストと温度管理手段3
4で管理している温度に基づいて、新配置データを採用
するかをコスト評価手段33により決定する。以下にそ
の方法を示す。
In 404, the cost of the new layout data calculated in 403, the cost of the conventional layout data, and the temperature management means 3
Based on the temperature managed in step 4, the cost evaluation means 33 determines whether to adopt the new layout data. The method is shown below.

【0008】新配置データのコストが従来配置データの
コストより減少した場合は、新配置データを採用する。 逆に、新配置データのコストが従来配置データのコスト
より増加した場合は、0以上1未満の乱数を発生させ、
その乱数が exp(−△C/T) より大きい時に新配置データを採用する。ここで、△C
は新配置データのコストと従来配置データのコストの差
、Tは温度管理手段34で管理している温度である。
[0008] If the cost of the new placement data is lower than the cost of the conventional placement data, the new placement data is adopted. On the other hand, if the cost of the new placement data is higher than the cost of the conventional placement data, a random number between 0 and 1 is generated,
When the random number is greater than exp(-ΔC/T), new arrangement data is adopted. Here, △C
is the difference between the cost of the new layout data and the cost of the conventional layout data, and T is the temperature managed by the temperature management means 34.

【0009】新配置データを採用する場合は405で配
置データを更新し、採用しない場合は従来の配置データ
のまま406へ飛ぶ。
If the new layout data is to be adopted, the layout data is updated in step 405; if not, the process jumps to step 406, leaving the existing layout data as is.

【0010】406では、コスト評価手段33により配
置データを生成した回数を管理し、その回数が設定した
値を越えたら温度管理手段34で管理している温度を下
げる。逆に、その回数が設定値以内の場合は402へ戻
る。
At step 406, the cost evaluation means 33 manages the number of times placement data has been generated, and when the number of times exceeds a set value, the temperature managed by the temperature management means 34 is lowered. Conversely, if the number of times is within the set value, the process returns to 402.

【0011】407では、処理終了判定手段35を用い
て、各温度における最終コストが3回続けて同じ場合に
処理を終了する。そうでない場合は402に戻る。
In step 407, the process termination determining means 35 is used to terminate the process if the final cost at each temperature is the same three times in a row. Otherwise, the process returns to 402.

【0012】0012

【発明が解決しようとする課題】しかし、以上の方法で
は、配置変換手段を無作為に適用するため、無駄な配置
変換手段を適用する可能性が大きくなり、処理時間がか
かる。本発明は上記課題に鑑み、配置変換手段を効率的
に適用して処理時間を短縮することを目的とする。
However, in the above method, since the arrangement conversion means are applied at random, there is a high possibility that the arrangement conversion means will be applied unnecessarily, and the processing time is increased. In view of the above problems, it is an object of the present invention to efficiently apply a layout conversion means to shorten processing time.

【0013】[0013]

【課題を解決するための手段】この目的を達成するため
、本発明は、配置変換手段の有効性を判定する変換有効
性判定手段と、複数の配置変換手段の適用比率を上記変
換有効性判定手段の判定結果に基づいて調整する適用比
率調整手段とを有している。
[Means for Solving the Problems] In order to achieve this object, the present invention provides a conversion effectiveness determining means for determining the effectiveness of a layout conversion means, and an application ratio of a plurality of layout conversion means for determining the conversion effectiveness. and an application ratio adjusting means for adjusting based on the determination result of the means.

【0014】[0014]

【作用】本発明において、配置転換手段の適用比率を管
理する適用比率調整手段は配置変換手段の有効性を温度
毎に判定する変換有効性判定手段のデータに基づき、次
の温度における適用比率を決定する。この比率に基づき
次の温度に対し、有効性の高い配置変換手段を優先的に
適用することにより、無駄な配置変換手段を適用する回
数を減少させるようにしたものである。
[Operation] In the present invention, the application ratio adjusting means for managing the application ratio of the arrangement changing means adjusts the application ratio at the next temperature based on the data of the conversion effectiveness determining means for determining the effectiveness of the arrangement changing means for each temperature. decide. Based on this ratio, the highly effective placement conversion means is preferentially applied to the next temperature, thereby reducing the number of times the placement conversion means is applied in vain.

【0015】[0015]

【実施例】以下、図1を参照しながら本発明の一実施例
について説明する。
DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to FIG.

【0016】図1において、細線は制御信号を、2重線
は主にデータの参照関係を、太線は制御信号及びデータ
の流れを主に示す。図1において、1は配置データを生
成する配置変換手段を複数記憶したデータベース、6は
配置変換手段の有効性を判定する変換有効性判定手段、
5は複数の配置変換手段の適用比率を変換有効性判定手
段6の判定結果に基づいて調整する適用比率調整手段、
2は適用比率調整手段5によって決定された適用比率に
基づいてデータベース1から選択した配置変換手段を適
用し、適用された配置変換手段により生成された新しい
配置データのコストを計算する変換適用手段、3は従来
の配置データのコストと新しい配置データのコストを比
較して、従来の配置データと新配置データのいずれを採
用するかを決定するコスト評価手段、4は温度と呼ばれ
るパラメータを管理・変更する温度管理手段、7は配置
データの変動を観察し、変動がなくなったら処理を終了
する処理終了判定手段、8は初期値を設定、及び生成す
る初期化手段である。
In FIG. 1, thin lines indicate control signals, double lines mainly indicate data reference relationships, and thick lines mainly indicate control signals and data flows. In FIG. 1, reference numeral 1 denotes a database storing a plurality of arrangement conversion means for generating arrangement data; 6, conversion effectiveness determination means for determining the effectiveness of the arrangement conversion means;
5 is an application ratio adjustment means for adjusting the application ratio of a plurality of arrangement conversion means based on the determination result of the conversion effectiveness determination means 6;
2 is a conversion application means that applies the placement conversion means selected from the database 1 based on the application ratio determined by the application ratio adjustment means 5, and calculates the cost of new placement data generated by the applied placement conversion means; 3 is a cost evaluation means that compares the cost of the conventional placement data and the cost of the new placement data to decide whether to adopt the old placement data or the new placement data, and 4 is a method for managing and changing a parameter called temperature. Reference numeral 7 indicates a temperature control means for observing the fluctuations in the arrangement data and terminates the processing when the variation disappears. Reference numeral 8 indicates an initialization means for setting and generating initial values.

【0017】以上のような図1の構成において、以下、
その動作について図2に示したフローチャートとともに
説明する。
In the configuration of FIG. 1 as described above, the following is performed.
The operation will be explained with reference to the flowchart shown in FIG.

【0018】まず、201では初期化手段8により初期
値の組合せを生成し、初期値の組合せコストを計算し、
温度管理手段4で管理している温度というパラメータと
、適用比率調整手段5で管理している適用比率というパ
ラメータを初期化する。
First, in step 201, the initialization means 8 generates a combination of initial values, calculates the cost of the combination of initial values,
The parameter of temperature managed by temperature management means 4 and the parameter of application ratio managed by application ratio adjustment means 5 are initialized.

【0019】次に、202では、変換適用手段2により
適用比率調整手段5で管理している適用比率の大小に基
づいてデータベース1に記憶されている配置変換手段を
1つ選択する。適用比率が大きい配置変換手段ほど優先
的に選択される。
Next, in step 202, the conversion application means 2 selects one arrangement conversion means stored in the database 1 based on the magnitude of the application ratio managed by the application ratio adjustment means 5. The arrangement conversion means with a larger application ratio is selected preferentially.

【0020】203では、同じく変換適用手段2により
202で選択した配置変換手段を適用して新配置データ
を生成する。204では、コスト評価手段3により20
3で生成した配置データのコストを計算する。
At step 203, the arrangement conversion means selected at step 202 is similarly applied by the conversion application means 2 to generate new arrangement data. At 204, the cost evaluation means 3 calculates 20
Calculate the cost of the placement data generated in step 3.

【0021】205では、204で計算した新配置デー
タのコストと従来配置データのコストと温度管理手段4
で管理している温度に基づいて、新配置データを採用す
るかをコスト評価手段3により決定する。以下にその方
法を示す。
In step 205, the cost of the new arrangement data calculated in step 204, the cost of the conventional arrangement data, and the temperature management means 4 are calculated.
Based on the temperature managed by the cost evaluation means 3, it is determined whether to adopt the new layout data. The method is shown below.

【0022】新配置データのコストが従来配置データの
コストより減少した場合は、新配置データを採用する。 逆に、新配置データのコストが従来配置データのコスト
より増加した場合は、0以上1未満の乱数を発生させ、
その乱数が exp(−△C/T) より大きい時に新配置データを採用する。ここで、△C
は新配置データのコストと従来配置データのコストの差
、Tは温度管理手段4で管理している温度である。
[0022] If the cost of the new placement data is lower than the cost of the conventional placement data, the new placement data is adopted. On the other hand, if the cost of the new placement data is higher than the cost of the conventional placement data, a random number between 0 and 1 is generated,
When the random number is greater than exp(-ΔC/T), new arrangement data is adopted. Here, △C
is the difference between the cost of the new placement data and the cost of the conventional placement data, and T is the temperature managed by the temperature management means 4.

【0023】新配置データを採用する場合は206で配
置データを更新し、採用しない場合は従来の配置データ
のまま207へ飛ぶ。
If the new layout data is to be adopted, the layout data is updated in step 206; if the new layout data is not to be adopted, the process jumps to 207 with the conventional layout data unchanged.

【0024】コスト評価手段3により207では、配置
データを生成した回数を管理し、その回数が設定した値
を越えたら温度管理手段4で管理している温度を下げる
。逆に、その回数が設定値以内の場合は202へ飛ぶ。
At step 207, the cost evaluation means 3 manages the number of times placement data has been generated, and when the number of times exceeds a set value, the temperature managed by the temperature management means 4 is lowered. Conversely, if the number of times is within the set value, the process jumps to 202.

【0025】208では、適用比率調整手段5と変換有
効性判定手段6を用いて温度毎の適用比率を更新する。
At step 208, the application ratio for each temperature is updated using the application ratio adjustment means 5 and the conversion effectiveness determination means 6.

【0026】変換有効性判定手段6では、データベース
1に記憶されている各配置変換手段の有効性を温度毎に
判定する。本実施例では、各配置変換手段の適用回数と
その配置変換手段を適用しコストが減少した回数の比率
が大きい程、有効性が高いと判定している。
The conversion effectiveness determining means 6 determines the effectiveness of each arrangement conversion means stored in the database 1 for each temperature. In this embodiment, it is determined that the effectiveness is higher as the ratio between the number of times each layout conversion means is applied and the number of times the cost is reduced by applying that layout conversion means is larger.

【0027】適用比率調整手段5では、まず、変換有効
性判定手段6の結果に基づいて、複数の配置変換手段を
有効性の高い順に順位付けする。次に順位の高い配置変
換手段と順位の低い配置変換手段に分ける。順位の高い
配置変換手段に対しては適用比率を増加させ、順位の低
い配置変換手段に対しては適用比率を減少させる。さら
に、増加率は順位が高い程大きくし、減少率は順位が低
い程大きくする。これらの増減率に基づいて、次の温度
における適用比率を決定する。
The application ratio adjustment means 5 first ranks the plurality of placement conversion means in descending order of effectiveness based on the results of the conversion effectiveness determination means 6. Next, it is divided into high ranking placement conversion means and low ranking placement conversion means. The application ratio is increased for a placement conversion means with a high rank, and the application ratio is decreased for a placement conversion means with a low rank. Further, the higher the rank, the higher the increase rate, and the lower the rank, the higher the decrease rate. Based on these rate of increase/decrease, determine the application ratio at the next temperature.

【0028】つまり、変換有効性判定手段によって判定
された有効性が高い配置変換手段ほど適用比率を大きく
し、有効性が低い配置変換手段ほど適用比率を小さくす
る。
That is, the higher the effectiveness determined by the conversion effectiveness determining means, the higher the application ratio is made, and the lower the effectiveness, the lower the application ratio.

【0029】本実施例では、配置変換手段数をN、最大
増減率幅をW、配置変換手段の優先順位をi、(N−1
)/2 の商を分割数nとし、各配置変換手段の適用比
率の増減率r(i)を以下のように定めている。Nが奇
数(N=2n+1)の場合は、 r(i) = +(W/n)×((n+1) − i)
    i ≦ nr(i) = 0        
              i = n+1r(i)
 = −(W/n)×(i − (n+1))    
i > n+1Nが偶数(N=2(n+1))の場合は
、r(i) = +(W/n)×((n+1) − i
)    i ≦ nr(i) = 0       
               i = n+1,n+
2r(i) = −(W/n)×(i − (n+2)
)    i > n+2としている。
In this embodiment, the number of arrangement conversion means is N, the maximum increase/decrease rate width is W, and the priority order of the arrangement conversion means is i, (N-1
)/2 is defined as the number of divisions n, and the increase/decrease rate r(i) of the application ratio of each arrangement conversion means is determined as follows. If N is an odd number (N=2n+1), r(i) = +(W/n)×((n+1) − i)
i ≦ nr(i) = 0
i = n+1r(i)
= −(W/n)×(i − (n+1))
i > n+1 If N is an even number (N=2(n+1)), r(i) = +(W/n)×((n+1) − i
) i ≦ nr(i) = 0
i = n+1, n+
2r(i) = −(W/n)×(i − (n+2)
) i > n+2.

【0030】209では、処理終了判定手段7を用いて
、各温度における最終コストが3回続けて同じ場合に処
理を終了する。そうでない場合は202に戻る。
At step 209, the process termination determining means 7 is used to terminate the process if the final cost at each temperature is the same three times in a row. If not, the process returns to 202.

【0031】以上のように、適用比率調整手段5と変換
有効性判定手段6を設けて、各温度毎に適用比率を調整
することにより、配置変換手段の効果的な適用が可能に
なる。
As described above, by providing the application ratio adjusting means 5 and the conversion effectiveness determining means 6 and adjusting the application ratio for each temperature, it becomes possible to effectively apply the arrangement conversion means.

【0032】[0032]

【発明の効果】以上のように本発明は配置変換手段の有
効性を温度毎に判定する変換有効性判定手段と前記変換
有効性判定手段のデータに基づき、次の温度における配
置転換手段の適用比率を決定する適用比率調整手段を設
けることにより、無駄な配置変換手段を適用する回数を
減少させるので、その結果、高速処理が可能となる。
As described above, the present invention provides a conversion effectiveness determining means for determining the effectiveness of the relocation means for each temperature, and application of the relocation means at the following temperatures based on the data of the conversion effectiveness determining means. By providing the application ratio adjusting means for determining the ratio, the number of times the unnecessary arrangement conversion means is applied is reduced, and as a result, high-speed processing becomes possible.

【図面の簡単な説明】[Brief explanation of drawings]

【図1】本発明の実施例における構成図[Fig. 1] Configuration diagram in an embodiment of the present invention

【図2】実施例
におけるフローチャート
[Figure 2] Flowchart in the example

【図3】従来の組合せ最適化装
置における構成図
[Figure 3] Block diagram of a conventional combinatorial optimization device

【図4】従来の組合せ最適化装置にお
けるフローチャート
[Figure 4] Flowchart in a conventional combinatorial optimization device

【符号の説明】[Explanation of symbols]

1  データベース 2  変換適用手段 3  コスト評価手段 4  温度管理手段 5  適用比率調整手段 6  変換有効性判定手段 7  処理終了判定手段 8  初期化手段 1 Database 2. Conversion application means 3 Cost evaluation means 4 Temperature control means 5 Applicable ratio adjustment means 6 Conversion effectiveness determination means 7 Processing end determination means 8 Initialization means

Claims (1)

【特許請求の範囲】[Claims] 【請求項1】  新しい配置データを生成する複数の配
置変換手段と、各配置変換手段の有効性を判定する変換
有効性判定手段と、複数の配置変換手段を適用する比率
を上記変換有効性判定手段の判定結果に基づいて調整す
る適用比率調整手段と、上記適用比率調整手段で決定し
た適用比率に基づいて複数の配置変換手段のいずれかを
適用して生成される新しい配置データのコストを計算す
る変換適用手段と、従来の配置データのコストと新しい
配置データのコストを比較して従来の配置データと新し
い配置データのいずれを採用するかを決定するコスト評
価手段と、温度と呼ばれるパラメータを管理する温度管
理手段と、配置データのコストの変動がなくなったとき
処理を終了する処理終了判定手段を具備することを特徴
とする組合せ最適化装置。
Claim 1: A plurality of arrangement conversion means for generating new arrangement data, a conversion effectiveness determination means for determining the effectiveness of each arrangement conversion means, and a ratio of applying the plurality of arrangement conversion means for determining the conversion effectiveness. Calculate the cost of new placement data generated by applying an application ratio adjustment means that adjusts based on the determination result of the means and one of a plurality of placement conversion means based on the application ratio determined by the application ratio adjustment means. A cost evaluation means that compares the cost of the old placement data and the cost of the new placement data to decide whether to adopt the old placement data or the new placement data, and a parameter called temperature. 1. A combinational optimization device comprising: a temperature management means for controlling the cost of the arrangement data; and a processing end determining means for terminating the processing when there is no longer any variation in the cost of placement data.
JP3181505A 1991-06-10 1991-06-10 Combination optimization device Expired - Lifetime JP2893144B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP3181505A JP2893144B2 (en) 1991-06-10 1991-06-10 Combination optimization device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP3181505A JP2893144B2 (en) 1991-06-10 1991-06-10 Combination optimization device

Publications (2)

Publication Number Publication Date
JPH04362785A true JPH04362785A (en) 1992-12-15
JP2893144B2 JP2893144B2 (en) 1999-05-17

Family

ID=16101938

Family Applications (1)

Application Number Title Priority Date Filing Date
JP3181505A Expired - Lifetime JP2893144B2 (en) 1991-06-10 1991-06-10 Combination optimization device

Country Status (1)

Country Link
JP (1) JP2893144B2 (en)

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH02242474A (en) * 1989-03-16 1990-09-26 Hitachi Ltd Method and device for optimizing element arrangement and method and device for deciding optimum arrangement

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH02242474A (en) * 1989-03-16 1990-09-26 Hitachi Ltd Method and device for optimizing element arrangement and method and device for deciding optimum arrangement

Also Published As

Publication number Publication date
JP2893144B2 (en) 1999-05-17

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