ZOOM聴講無料です。スケジュールナースが使用している基本技術に関する講演です。講演分野の3/４は、実際に使用しています。
人工知能学会 第134回人工知能基本問題研究会(SIG-FPAI)
人工知能学会 合同研究会2025（SIGAIs 2025） | 2025年12月1日（月）～3日（水） 慶應義塾大学 日吉キャンパス
LLMとモデリングについては、これからだと思います。来年以降に期待したいと思います。
2025年11月19日水曜日
Q 年末年始の勤務表については12月1日～翌年1月10日までの勤務表を作りたい場合 制約条件が今月となっているため、うまくいきません。
Q.年末年始のシフト勤務表については12月1日～翌年1月10日までの勤務表を作りたい場合
制約条件が「今月」となっているため、うまくいきません。
この場合はどこを設定し直す必要があるでしょうか。
Ans.
年末年始に関しては、以下のブログを参考にしてください。
実装１
実装２
実装３
ご質問は、実装３の内容になるかと思いますが、1年に一回しか必要ないので、まずは、通常月と同じ方法の実装１を参考にされると良いと思います。慣れたら実装３に挑戦する、というステップを踏むと良いのではないかと思います。
2025年11月18日火曜日
Q.特定の看護師の夜勤を（木）（金）（土）に設定する 現在は予定入力に特定の看護師の夜勤を入力してから求解しています。
Ans.
シフト制約を書くやり方と、シフト予定で入力するやり方の二つの方法があります。まずは、予定で入力する方法です。
＜シフト予定で入力する方法＞
１）そのスタッフ（Staff22）の予定を入力してロックします。
２）夜勤禁止というラベルを作って今月全部に貼り付けます。（ロック部は書き換わりません）
３）木金土を選択してクリアします
以上で、特定の看護師の夜勤を（木）（金）（土）に設定することが出来ます。木金土以外は、夜勤禁止のハード制約となるので、夜勤が入る箇所は木金土に限定されます。予め決まっている木金土予定は阻害されません。
＜制約で行う方法＞
１）グループ定義で、木金土以外夜勤禁止という属性項目を追加します。
２）スタッフプロパティシートで設定します。
３）木金土以外という集合を作ります。
木金土にハード制約予定が入っているとハードエラーとなってしまいますので、本制約をソフト制約としています。（レベル４）
以上、どちらの方法でも、特定の看護師の夜勤を（木）（金）（土）に設定することが出来ます。
以上二つのやり方を述べました。どちらの記述でも良いのですが、他のスタッフへの適用の可能性を勘案すると、今後、他のスタッフへ流用できる可能性は低いです。何がなんでも制約で記述しなければならない、ということではありません。制約を記述する手間と将来に渡る予定記述の手間とを天秤にかけてメリットがある方を選んでください。
一般に、何かを制約する場合は、ある集合に関して禁止するというパターンを多用します。制約において禁止とは、フィルタにかけて欲しい集合を抽出する操作です。
■「木金土を夜勤にする」としてしまいがちですが、その場合、必ず木金土が夜勤になってしまいます。木金土が例えば、日勤や休みになることはありません。
■一方、「木金土以外の夜勤を禁止にする」とすれば、「木金土は夜勤になるかもしれないし、ならないかもしれません。しかし、木金土以外の夜勤はありえません。」
本当に欲しい仕様は、どちらでしょうか？ 制約を書く前に「特定の看護師の夜勤を（木）（金）（土）に設定する」の仕様の意味を推し量ることが必要です。これらをAIに指示するときも、より直接的な指示が必要となるでしょう。これは、スケジュールナースが常々言っている、人に正確に意図を伝える技術、国語力が重要、ということでもあります。
2025年11月17日月曜日
Q.連続した遅勤務３（日遅）、準夜（準）、遅勤務３（日遅）の組合せは禁止
Ans. 「連続した」が何処にかかるのか、確認しました。意図は、日遅→準→日遅パターンの禁止だそうです。
ちなみに、生成AIでのモデリングをするとき、当然ですが、言語は日本語になります。人間が聞いても曖昧な表現は、尚更生成AIでも注意を要します。仕様を書くときは、誤解を生まない記述を心がけましょう。
2025年11月16日日曜日
COPT Barrier Solverの組み込み
coin-or/Osi: Open Solver Interface
の実装があると、直ぐに組み込めて1日もあれば、開発ソースに組み込むことが出来ます。で、サポートに聞いてみたのですが、「残念ながら無い」ということでした。
そうなると、自前で実装するしかありません。ただし、実際に全てを実装する必要がある訳ではなく、実際に開発ソース中でOSIをCALLしているAPIだけを実装すればとりあえずは十分です。組み込んだとしても、評価ライセンス期間中しか動かすことはないし、それも自分のマシンでしか動かすことは出来ません。それでも世界記録更新のためには、必要な作業と割り切って進めることにします。（OSIがいつからあるか分からないのですが、少なくとも、CLP,CLPEX,MOSEK,Gurobi等の実装は公開されており、これらのソルバ群については、簡単に置き換えることが出来ます。（ソルバDLLが供給されていれば）ちなみに、HighsのOSIラッパは、現在はサポートされていないので、自前で書いています。）
COPTのマニュアルは、中国語と英語の各々1400ページ位あり、C,C++,C#,Python,Ample..と様々な言語をサポートしています。当初C++APIで記述しようと思ったのですが、C++APIはサポートされていないものが多く、C APIによらざるを得ません。このため、記述はC++ですがAPIは、C APIを使用して記述中です。
2025年11月15日土曜日
COPT 評価ライセンス取得
Highs barrier solverが期待はずれだったので、COPTでinstance23/24用の開発を進めることにしました。
Cuopt WSL2の道もありますが、Windows環境からLinuxへの移植への時間がかかってしまい本題から逸れてしまう懸念がありました。GPU使用が前提となってしまい、市井のGPUしか持ち合わせていないことを考えると、トップ性能が得られるという保証はありません。それで本題の解を得られないかもしれないリスクを考えると、COPTで取り組む方が開発スピードが速いと判断しました。Cuoptは、解が得られた後、余裕があれば取り組むことしました。
また、AI Modelingにおいても業界をリードしています。解いた後の残りの評価期間も遊べます。
Cardinal-Operations/ORLM: ORLM: Training Large Language Models for Optimization Modeling
<COPT personalライセンス取得方法>
COPT personalライセンスは１８０日間です。使用するマシン上で、echo %username%で、ユーザ名を得て、それを申請WEBサイトに書き込みます。
その後メールで、二つのファイルが送られてきます。インストールを実行後、unsernamフォルダ上に、coptフォルダを作成してその二つのファイルを置くだけです。
＜COPT command lineの使用方法＞
Highs ipx/ipm(hipo)で速度比較を行ったログです。crossover無し、Barrier Solverでの比較になります。例えば、instance23での比較では、
Highs ipx 951sec
Highs ipm(hipo) 128sec
Copt barrier 8sec
と驚愕的な速度差があります。Highs新内点法ソルバ(hipo)に期待をしていた訳ですが、それでも未だ10倍以上差があります。
流石にGurobiを超える世界最高の内点法ソルバであると思います。Highsにしても同じメロートラの予測子修正子法 - Wikipediaの筈でありBlasやMetisを使用しているのも多分同じです。こんなにも違いがある原因が良く分かりません。
ちなみに、GPU版の内点法よりもCPU版の方が速く、GPU版PDLPは、未だPDLPXを実装していないと思われ、上の内点法結果には及びませんでした。
それにしても、数年前に評価したときは、内点法の実装はなく、Simplexのみでした。そのときに、あなたのインスタンス群では、内点法の方が良いよ、と彼らからアドバイスをもらっていました。その後、内点法が出来たと、連絡を受けてはいたのですが見ていませんでした。今回評価してみて、僅か数年で、世界トップに躍り出た研究開発力に恐れ入った次第です。Stanfordの4人のPh.Dが立ち上げた会社のようです。
C:\Users\xxxxx.PC\highs_test>highs --solver ipx --run_crossover off instance21.mps
Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option solver to "ipx"
Set option run_crossover to "off"
Set option log_file to "HiGHS.log"
LP instance21 has 1556 rows; 9235 cols; 603232 nonzeros
Coefficient ranges:
Matrix [1e+00, 1e+00]
Cost [1e+00, 1e+02]
Bound [1e+00, 1e+00]
RHS [1e+00, 9e+00]
Presolving model
1556 rows, 9235 cols, 603232 nonzeros 0s
Dependent equations search running on 1551 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
1551 rows, 9225 cols, 448385 nonzeros 0s
Presolve reductions: rows 1551(-5); columns 9225(-10); nonzeros 448385(-154847)
Solving the presolved LP
IPX model has 1551 rows, 9225 columns and 448385 nonzeros
Input
Number of variables: 9225
Number of free variables: 0
Number of constraints: 1551
Number of equality constraints: 1551
Number of matrix entries: 448385
Matrix range: [1e+00, 1e+00]
RHS range: [1e+00, 9e+00]
Objective range: [1e+00, 1e+02]
Bounds range: [1e+00, 1e+00]
Preprocessing
Dualized model: no
Number of dense columns: 0
Range of scaling factors: [1.00e+00, 1.00e+00]
Scaled cost norm: 100
Scaled bounds norm: 9
IPX version 1.0
Interior point solve
Iter primal obj dual obj pinf dinf gap time
0 2.12706705e+03 -2.72670044e+05 4.65e-01 4.29e-01 2.03e+00 0s
1 6.03005099e+04 -2.03276434e+05 1.13e-01 5.97e-02 3.69e+00 0s
2 5.12726393e+04 -1.64232453e+05 7.18e-02 3.45e-02 3.82e+00 0s
3 3.37863879e+04 -5.68654688e+04 3.53e-02 3.45e-08 7.86e+00 0s
4 1.61508412e+04 -2.05606678e+04 1.16e-02 1.19e-08 1.66e+01 0s
Constructing starting basis...
5 1.85501457e+04 -1.46245866e+04 9.44e-03 9.37e-09 1.69e+01 0s
6 2.13687731e+04 -9.03790229e+03 7.01e-03 5.66e-09 4.93e+00 0s
7 2.21673245e+04 1.21064777e+03 5.04e-03 2.58e-09 1.79e+00 0s
8 2.24386703e+04 9.17672428e+03 2.27e-03 1.05e-09 8.39e-01 0s
9 2.20273418e+04 1.51707876e+04 5.80e-04 3.07e-10 3.69e-01 1s
10 2.16272941e+04 1.89206170e+04 1.58e-04 6.98e-11 1.33e-01 1s
11 2.13978016e+04 2.03146608e+04 4.29e-05 2.07e-11 5.19e-02 1s
12 2.13198715e+04 2.07229894e+04 1.81e-05 5.71e-12 2.84e-02 1s
13 2.12518144e+04 2.09114424e+04 6.95e-06 1.21e-12 1.61e-02 1s
14 2.12118634e+04 2.09905615e+04 3.46e-06 4.77e-13 1.05e-02 1s
15 2.11767514e+04 2.10554525e+04 1.47e-06 1.73e-13 5.74e-03 1s
16 2.11584276e+04 2.10876570e+04 6.57e-07 6.88e-14 3.35e-03 2s
17 2.11496461e+04 2.11047009e+04 3.37e-07 2.63e-14 2.13e-03 2s
18 2.11438790e+04 2.11158504e+04 1.80e-07 1.24e-14 1.33e-03 3s
19 2.11402167e+04 2.11208941e+04 9.83e-08 1.27e-14 9.14e-04 3s
20 2.11381599e+04 2.11254641e+04 6.27e-08 1.33e-14 6.01e-04 4s
21 2.11361933e+04 2.11282845e+04 3.48e-08 1.07e-14 3.74e-04 4s
22 2.11347482e+04 2.11301100e+04 1.80e-08 1.21e-14 2.19e-04 4s
23 2.11340537e+04 2.11307440e+04 1.11e-08 1.20e-14 1.57e-04 5s
Finish factorization 25: fill factor = 8.86 5s
24 2.11331024e+04 2.11315304e+04 3.55e-09 1.25e-14 7.44e-05 5s
25 2.11327908e+04 2.11318566e+04 1.95e-09 1.08e-14 4.42e-05 6s
26 2.11326528e+04 2.11319940e+04 1.27e-09 1.29e-14 3.12e-05 7s
27 2.11326633e+04 2.11320231e+04 1.23e-09 1.27e-14 3.03e-05 7s
28 2.11323872e+04 2.11322790e+04 1.67e-10 1.64e-14 5.12e-06 8s
29 2.11323367e+04 2.11323224e+04 1.03e-11 1.37e-14 6.79e-07 8s
30 2.11323344e+04 2.11323294e+04 3.22e-12 1.11e-14 2.37e-07 8s
31 2.11323340e+04 2.11323322e+04 1.89e-12 1.93e-14 8.47e-08 9s
32 2.11323337e+04 2.11323331e+04 9.09e-13 1.41e-14 2.71e-08 9s
33* 2.11323333e+04 2.11323333e+04 2.44e-15 1.31e-14 3.66e-09 9s
Summary
Runtime: 9.38s
Status interior point solve: optimal
Status crossover: not run
objective value: 2.11323333e+04
interior solution primal residual (abs/rel): 2.31e-14 / 2.31e-15
interior solution dual residual (abs/rel): 1.33e-12 / 1.31e-14
interior solution objective gap (abs/rel): 7.73e-05 / 3.66e-09
Ipx: IPM optimal
Performed postsolve
Model name : instance21
Model status : Optimal
IPM iterations: 33
Objective value : 2.1132333334e+04
P-D objective error : 8.2002286617e-10
HiGHS run time : 9.58
C:\Users\xxxxx.PC\highs_test>highs --solver ipm --run_crossover off instance21.mps
Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option solver to "ipm"
Set option run_crossover to "off"
Set option log_file to "HiGHS.log"
LP instance21 has 1556 rows; 9235 cols; 603232 nonzeros
Coefficient ranges:
Matrix [1e+00, 1e+00]
Cost [1e+00, 1e+02]
Bound [1e+00, 1e+00]
RHS [1e+00, 9e+00]
Presolving model
1556 rows, 9235 cols, 603232 nonzeros 0s
Dependent equations search running on 1551 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
1551 rows, 9225 cols, 448385 nonzeros 0s
Presolve reductions: rows 1551(-5); columns 9225(-10); nonzeros 448385(-154847)
Solving the presolved LP
HiPO model has 1551 rows, 9225 columns and 448385 nonzeros
Running HiPO
BLAS: Unknown
Threads: 8
Rows: 1.6e+03
Cols: 9.2e+03
Nnz: 4.5e+05
Range of A: [1.0e+00, 1.0e+00], ratio 1.0e+00
Range of b: [1.0e+00, 9.0e+00], ratio 9.0e+00
Range of c: [1.0e+00, 1.0e+02], ratio 1.0e+02
Range of bounds: [1.0e+00, 1.0e+00], ratio 1.0e+00
Scaling coefficients: [0.0e+00, 0.0e+00], ratio -
Newton system: NE preferred
Parallelism: Node preferred
Factorisation statistics
Size: 1.55e+03
Nnz: 1.12e+06
Fill-in: 1.04
Serial memory: 1.5e+02 MB
Flops: 1.1e+09
iter primal obj dual obj pinf dinf gap time
0 -2.77257683e+04 -5.39928666e+05 4.62e-01 8.02e-01 1.80e+00 0.6
1 2.12128558e+05 -4.54383344e+05 5.47e-02 8.02e-05 5.50e+00 0.9
2 6.09787090e+04 -1.75452264e+05 1.48e-02 8.02e-09 4.13e+00 1.2
3 3.07683490e+04 -5.36850870e+04 3.68e-03 2.21e-09 7.37e+00 1.6
4 2.34282491e+04 1.26507882e+03 6.15e-04 4.25e-10 1.79e+00 1.9
5 2.19331035e+04 1.49518999e+04 1.84e-04 1.14e-10 3.79e-01 2.2
6 2.13587172e+04 2.00049064e+04 4.84e-06 1.86e-11 6.55e-02 2.5
7 2.12467020e+04 2.06829678e+04 5.91e-07 7.59e-12 2.69e-02 2.9
8 2.11900253e+04 2.09673071e+04 1.57e-07 2.72e-12 1.06e-02 3.1
9 2.11548363e+04 2.10713876e+04 4.00e-08 9.47e-13 3.95e-03 3.4
10 2.11405328e+04 2.11072795e+04 1.25e-08 3.62e-13 1.57e-03 3.7
11 2.11360661e+04 2.11227496e+04 5.34e-09 1.25e-13 6.30e-04 4.0
12 2.11343219e+04 2.11281636e+04 2.55e-09 5.23e-14 2.91e-04 4.3
13 2.11331879e+04 2.11308340e+04 9.83e-10 1.83e-14 1.11e-04 4.6
14 2.11328289e+04 2.11315992e+04 5.25e-10 1.36e-14 5.82e-05 4.9
15 2.11325219e+04 2.11319496e+04 1.91e-10 1.55e-14 2.71e-05 5.3
16 2.11324196e+04 2.11320829e+04 1.06e-10 1.24e-14 1.59e-05 5.6
17 2.11324211e+04 2.11321221e+04 1.01e-10 1.46e-14 1.41e-05 5.9
18 2.11323616e+04 2.11322227e+04 3.30e-11 1.04e-14 6.57e-06 6.2
19 2.11323352e+04 2.11323302e+04 3.75e-13 1.40e-14 2.38e-07 6.4
iter primal obj dual obj pinf dinf gap time
20 2.11323335e+04 2.11323331e+04 2.08e-13 1.36e-14 1.85e-08 6.7
21 2.11323333e+04 2.11323333e+04 2.98e-13 1.43e-14 2.12e-10 7.0
=== Primal-dual feasible point found
Summary
HiPO runtime: 6.82
Status: primal-dual feasible
HiPO iterations: 21
Primal residual rel/abs: 2.98e-13 / 2.98e-12
Dual residual rel/abs: 1.43e-14 / 1.44e-12
Primal objective 2.11323333e+04
Dual objective 2.11323333e+04
Primal-dual gap: 2.12e-10
Hipo: Solved
Performed postsolve
Model name : instance21
Model status : Optimal
IPM iterations: 21
Objective value : 2.1132333335e+04
P-D objective error : 6.4311203345e-11
HiGHS run time : 7.02
C:\Users\xxxxx.PC\highs_test>highs --solver ipx --run_crossover off instance22.mps
Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option solver to "ipx"
Set option run_crossover to "off"
Set option log_file to "HiGHS.log"
LP instance22 has 3690 rows; 15856 cols; 1859219 nonzeros
Coefficient ranges:
Matrix [1e+00, 1e+00]
Cost [1e+00, 1e+02]
Bound [1e+00, 1e+00]
RHS [1e+00, 5e+00]
Presolving model
3690 rows, 15856 cols, 1859219 nonzeros 0s
Dependent equations search running on 3617 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.01s (limit = 1000.00s)
3617 rows, 15710 cols, 1472358 nonzeros 0s
Presolve reductions: rows 3617(-73); columns 15710(-146); nonzeros 1472358(-386861)
Solving the presolved LP
IPX model has 3617 rows, 15710 columns and 1472358 nonzeros
Input
Number of variables: 15710
Number of free variables: 0
Number of constraints: 3617
Number of equality constraints: 3617
Number of matrix entries: 1472358
Matrix range: [1e+00, 1e+00]
RHS range: [1e+00, 5e+00]
Objective range: [1e+00, 1e+02]
Bounds range: [1e+00, 1e+00]
Preprocessing
Dualized model: no
Number of dense columns: 0
Range of scaling factors: [1.00e+00, 1.00e+00]
Scaled cost norm: 100
Scaled bounds norm: 5
IPX version 1.0
Interior point solve
Iter primal obj dual obj pinf dinf gap time
0 1.27634489e+03 -7.40028735e+05 7.31e-01 8.55e-01 2.01e+00 0s
1 2.43044628e+05 -5.82333365e+05 3.09e-01 1.95e-01 4.87e+00 0s
Constructing starting basis...
2 1.54036035e+05 -2.91883491e+05 7.22e-02 1.95e-07 6.47e+00 1s
3 8.84560961e+04 -1.05049686e+05 3.33e-02 5.05e-08 2.33e+01 1s
4 5.99681280e+04 -6.08399276e+04 1.38e-02 2.93e-08 2.77e+02 1s
5 5.00562889e+04 -2.95147837e+04 7.65e-03 1.70e-08 7.75e+00 1s
6 4.29932788e+04 -1.07750240e+04 3.50e-03 9.71e-09 3.34e+00 2s
7 3.59514296e+04 6.77933828e+03 1.16e-03 4.62e-09 1.37e+00 2s
8 3.25653500e+04 1.75815380e+04 3.55e-04 2.11e-09 5.98e-01 3s
9 3.12273470e+04 2.52976496e+04 1.27e-04 6.67e-10 2.10e-01 5s
Start factorization 18: nonzeros in basis = 241212 6s
10 3.06707777e+04 2.84728268e+04 2.80e-05 1.23e-10 7.43e-02 7s
11 3.04222662e+04 2.96289176e+04 9.27e-06 3.55e-11 2.64e-02 9s
12 3.03437840e+04 3.00369026e+04 4.14e-06 5.75e-12 1.02e-02 11s
Start factorization 21: nonzeros in basis = 281121 12s
13 3.03103076e+04 3.01064065e+04 2.35e-06 2.17e-12 6.75e-03 14s
14 3.02849406e+04 3.01764924e+04 1.25e-06 4.94e-13 3.59e-03 16s
Finish factorization 23: fill factor = 6.42 18s
15 3.02640964e+04 3.02098003e+04 5.23e-07 7.47e-14 1.80e-03 18s
16 3.02555974e+04 3.02190302e+04 2.69e-07 7.17e-14 1.21e-03 22s
Start factorization 26: nonzeros in basis = 302572 23s
17 3.02483651e+04 3.02292931e+04 1.21e-07 7.42e-14 6.31e-04 25s
Finish factorization 28: fill factor = 6.65 29s
18 3.02449486e+04 3.02334611e+04 6.24e-08 8.19e-14 3.80e-04 30s
19 3.02423562e+04 3.02351222e+04 2.28e-08 7.64e-14 2.39e-04 34s
Start factorization 31: nonzeros in basis = 306741 34s
20 3.02409372e+04 3.02374697e+04 1.06e-08 6.54e-14 1.15e-04 36s
Finish factorization 33: fill factor = 6.56 40s
21 3.02402917e+04 3.02380350e+04 5.28e-09 5.96e-14 7.46e-05 41s
22 3.02397864e+04 3.02385339e+04 2.03e-09 8.61e-14 4.14e-05 43s
Finish factorization 36: fill factor = 6.41 46s
23 3.02395166e+04 3.02388009e+04 9.14e-10 5.91e-14 2.37e-05 47s
24 3.02394137e+04 3.02389267e+04 5.41e-10 6.77e-14 1.61e-05 51s
Finish factorization 39: fill factor = 6.45 52s
25 3.02393104e+04 3.02390434e+04 2.82e-10 8.00e-14 8.83e-06 53s
26 3.02392522e+04 3.02390742e+04 1.37e-10 6.61e-14 5.88e-06 55s
27 3.02392226e+04 3.02391136e+04 8.71e-11 7.28e-14 3.61e-06 57s
Start factorization 42: nonzeros in basis = 306429 58s
28 3.02392028e+04 3.02391212e+04 5.59e-11 6.47e-14 2.70e-06 60s
29 3.02391732e+04 3.02391296e+04 8.93e-12 7.07e-14 1.44e-06 62s
Finish factorization 44: fill factor = 6.33 64s
30 3.02391705e+04 3.02391311e+04 7.03e-12 6.04e-14 1.30e-06 64s
31 3.02391610e+04 3.02391428e+04 2.74e-12 8.22e-14 6.04e-07 66s
32 3.02391603e+04 3.02391440e+04 2.34e-12 6.21e-14 5.40e-07 68s
Finish factorization 47: fill factor = 6.47 70s
33 3.02391577e+04 3.02391466e+04 1.43e-12 6.42e-14 3.66e-07 70s
34 3.02391567e+04 3.02391468e+04 8.93e-13 6.96e-14 3.26e-07 72s
35 3.02391544e+04 3.02391497e+04 3.74e-13 7.78e-14 1.56e-07 74s
Start factorization 50: nonzeros in basis = 312785 75s
36 3.02391539e+04 3.02391504e+04 2.07e-13 7.62e-14 1.16e-07 77s
37 3.02391534e+04 3.02391510e+04 1.17e-13 7.40e-14 7.79e-08 79s
Finish factorization 52: fill factor = 6.56 81s
38 3.02391528e+04 3.02391515e+04 4.86e-14 7.71e-14 4.13e-08 81s
39 3.02391528e+04 3.02391517e+04 4.54e-14 6.81e-14 3.61e-08 83s
40 3.02391525e+04 3.02391519e+04 1.88e-14 7.60e-14 1.81e-08 85s
Finish factorization 55: fill factor = 6.59 87s
41* 3.02391523e+04 3.02391521e+04 4.46e-15 8.31e-14 5.08e-09 88s
Summary
Runtime: 87.63s
Status interior point solve: optimal
Status crossover: not run
objective value: 3.02391523e+04
interior solution primal residual (abs/rel): 2.79e-10 / 4.65e-11
interior solution dual residual (abs/rel): 8.39e-12 / 8.31e-14
interior solution objective gap (abs/rel): 1.54e-04 / 5.08e-09
Ipx: IPM optimal
Performed postsolve
Model name : instance22
Model status : Optimal
IPM iterations: 41
Objective value : 3.0239152277e+04
P-D objective error : 1.9228163221e-09
HiGHS run time : 88.27
C:\Users\xxxxx.PC\highs_test>highs --solver ipm --run_crossover off instance22.mps
Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option solver to "ipm"
Set option run_crossover to "off"
Set option log_file to "HiGHS.log"
LP instance22 has 3690 rows; 15856 cols; 1859219 nonzeros
Coefficient ranges:
Matrix [1e+00, 1e+00]
Cost [1e+00, 1e+02]
Bound [1e+00, 1e+00]
RHS [1e+00, 5e+00]
Presolving model
3690 rows, 15856 cols, 1859219 nonzeros 0s
Dependent equations search running on 3617 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.01s (limit = 1000.00s)
3617 rows, 15710 cols, 1472358 nonzeros 0s
Presolve reductions: rows 3617(-73); columns 15710(-146); nonzeros 1472358(-386861)
Solving the presolved LP
HiPO model has 3617 rows, 15710 columns and 1472358 nonzeros
Running HiPO
BLAS: Unknown
Threads: 8
Rows: 3.6e+03
Cols: 1.6e+04
Nnz: 1.5e+06
Range of A: [1.0e+00, 1.0e+00], ratio 1.0e+00
Range of b: [1.0e+00, 5.0e+00], ratio 5.0e+00
Range of c: [1.0e+00, 1.0e+02], ratio 1.0e+02
Range of bounds: [1.0e+00, 1.0e+00], ratio 1.0e+00
Scaling coefficients: [0.0e+00, 0.0e+00], ratio -
Newton system: NE preferred
Parallelism: Full preferred
Factorisation statistics
Size: 3.62e+03
Nnz: 6.49e+06
Fill-in: 1.15
Serial memory: 1.9e+02 MB
Flops: 1.5e+10
iter primal obj dual obj pinf dinf gap time
0 -2.23238887e+04 -9.13101589e+05 9.27e-01 1.03e+00 1.90e+00 2.7
1 8.74941050e+05 -7.90967906e+05 1.30e-01 2.51e-02 3.97e+01 4.0
2 2.28896513e+05 -3.62102614e+05 2.89e-02 2.51e-06 8.87e+00 5.5
3 8.34380115e+04 -9.92790785e+04 8.02e-03 5.22e-07 2.31e+01 7.2
4 4.39196895e+04 -1.32750405e+04 1.99e-03 1.40e-07 3.73e+00 8.9
5 3.24167669e+04 1.75576006e+04 3.00e-04 3.18e-08 5.95e-01 10.7
6 3.05436218e+04 2.77369549e+04 3.99e-05 4.35e-09 9.63e-02 12.4
7 3.03412164e+04 2.97887469e+04 9.85e-06 6.84e-10 1.84e-02 14.3
8 3.02817628e+04 3.00877444e+04 2.94e-06 2.20e-10 6.43e-03 16.1
9 3.02662147e+04 3.01785931e+04 1.69e-06 8.45e-11 2.90e-03 17.8
10 3.02511829e+04 3.02218180e+04 5.28e-07 1.95e-11 9.71e-04 19.5
11 3.02458568e+04 3.02311855e+04 2.51e-07 8.52e-12 4.85e-04 21.0
12 3.02426311e+04 3.02361828e+04 1.20e-07 2.92e-12 2.13e-04 22.6
13 3.02409862e+04 3.02382258e+04 6.05e-08 7.63e-13 9.13e-05 24.4
14 3.02399302e+04 3.02388356e+04 2.33e-08 1.87e-13 3.62e-05 26.2
15 3.02394982e+04 3.02390267e+04 9.91e-09 6.98e-14 1.56e-05 27.8
16 3.02393263e+04 3.02390995e+04 4.85e-09 7.71e-14 7.50e-06 29.6
17 3.02392299e+04 3.02391302e+04 2.12e-09 7.37e-14 3.30e-06 31.3
18 3.02392019e+04 3.02391422e+04 1.32e-09 6.80e-14 1.98e-06 33.0
19 3.02391638e+04 3.02391483e+04 2.79e-10 6.41e-14 5.13e-07 34.8
iter primal obj dual obj pinf dinf gap time
20 3.02391574e+04 3.02391506e+04 1.21e-10 6.97e-14 2.28e-07 36.5
21 3.02391563e+04 3.02391510e+04 6.43e-10 7.03e-14 1.74e-07 38.1
22 3.02391558e+04 3.02391512e+04 3.09e-09 6.94e-14 1.49e-07 39.3
23 3.02391547e+04 3.02391514e+04 2.17e-09 6.45e-14 1.09e-07 41.1
24 3.02391541e+04 3.02391515e+04 2.22e-09 5.59e-14 8.48e-08 42.6
25 3.02391538e+04 3.02391517e+04 4.30e-09 6.42e-14 7.16e-08 44.3
26 3.02391539e+04 3.02391518e+04 6.97e-08 5.55e-14 6.95e-08 46.0
27 3.02391536e+04 3.02391518e+04 6.01e-08 5.74e-14 5.97e-08 47.5
28 3.02391533e+04 3.02391519e+04 4.72e-08 5.66e-14 4.68e-08 49.0
29 3.02391529e+04 3.02391520e+04 2.84e-08 6.84e-14 2.96e-08 50.8
30 3.02391529e+04 3.02391520e+04 2.05e-08 6.14e-14 2.97e-08 52.2
31 3.02391528e+04 3.02391520e+04 2.59e-08 5.55e-14 2.41e-08 53.6
32 3.02391526e+04 3.02391521e+04 2.06e-08 6.45e-14 1.84e-08 55.7
33 3.02391526e+04 3.02391521e+04 1.83e-08 6.86e-14 1.51e-08 57.1
34 3.02391525e+04 3.02391521e+04 1.93e-08 5.84e-14 1.32e-08 58.6
35 3.02391525e+04 3.02391521e+04 1.49e-07 5.78e-14 1.19e-08 60.2
36 3.02391524e+04 3.02391521e+04 1.17e-07 6.75e-14 9.58e-09 61.8
37 3.02391522e+04 3.02391522e+04 1.96e-08 7.38e-14 1.95e-09 63.8
=== Primal-dual feasible point found
Summary
HiPO runtime: 63.16
Status: primal-dual feasible
HiPO iterations: 37
Primal residual rel/abs: 1.96e-08 / 1.17e-07
Dual residual rel/abs: 7.46e-14 / 7.53e-12
Primal objective 3.02391522e+04
Dual objective 3.02391522e+04
Primal-dual gap: 1.95e-09
Hipo: Solved
WARNING: Solution optimality conditions: Before postsolve
num/max 0 / 5.23e-12 (relative 0 / 8.71e-13) primal infeasibilities (tolerance = 1e-07)
num/max 0 / 0 (relative 0 / 0) dual infeasibilities (tolerance = 1e-07)
num/max 1 / 1.17e-07 (relative 0 / 1.96e-08) primal residual errors (tolerance = 1e-07)
num/max 0 / 5.55e-12 (relative 0 / 5.5e-14) dual residual errors (tolerance = 1e-07)
0 / 9.23e-10 P-D objective error (tolerance = 1e-07)
Performed postsolve
WARNING: Solution optimality conditions
num/max 1 / 1.17e-07 (relative 0 / 1.96e-08) primal infeasibilities (tolerance = 1e-07)
num/max 0 / 0 (relative 0 / 0) dual infeasibilities (tolerance = 1e-07)
num/max 0 / 0 (relative 0 / 0) primal residual errors (tolerance = 1e-07)
num/max 0 / 5.62e-12 (relative 0 / 5.56e-14) dual residual errors (tolerance = 1e-07)
0 / 9.23e-10 P-D objective error (tolerance = 1e-07)
Model name : instance22
Model status : Optimal
IPM iterations: 37
Objective value : 3.0239152234e+04
P-D objective error : 9.2294081509e-10
HiGHS run time : 63.83
C:\Users\xxxxx.PC\highs_test>highs --solver ipx --run_crossover off instance23.mps
Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option solver to "ipx"
Set option run_crossover to "off"
Set option log_file to "HiGHS.log"
LP instance23 has 5924 rows; 27740 cols; 2832110 nonzeros
Coefficient ranges:
Matrix [1e+00, 1e+00]
Cost [1e+00, 1e+02]
Bound [1e+00, 1e+00]
RHS [1e+00, 5e+00]
Presolving model
5924 rows, 27740 cols, 2832110 nonzeros 0s
Dependent equations search running on 5748 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.01s (limit = 1000.00s)
5748 rows, 27388 cols, 2012707 nonzeros 1s
Presolve reductions: rows 5748(-176); columns 27388(-352); nonzeros 2012707(-819403)
Solving the presolved LP
IPX model has 5748 rows, 27388 columns and 2012707 nonzeros
Input
Number of variables: 27388
Number of free variables: 0
Number of constraints: 5748
Number of equality constraints: 5748
Number of matrix entries: 2012707
Matrix range: [1e+00, 1e+00]
RHS range: [1e+00, 5e+00]
Objective range: [1e+00, 1e+02]
Bounds range: [1e+00, 1e+00]
Preprocessing
Dualized model: no
Number of dense columns: 0
Range of scaling factors: [1.00e+00, 1.00e+00]
Scaled cost norm: 100
Scaled bounds norm: 5
IPX version 1.0
Interior point solve
Iter primal obj dual obj pinf dinf gap time
0 1.79887102e+03 -1.48217069e+06 7.16e-01 9.12e-01 2.00e+00 0s
1 4.69368742e+05 -1.12335875e+06 2.31e-01 1.32e-01 4.87e+00 0s
2 4.44227759e+05 -9.85798883e+05 1.83e-01 8.96e-02 5.28e+00 1s
3 2.64708856e+05 -4.38912641e+05 5.95e-02 8.96e-08 8.08e+00 1s
4 6.75420983e+04 -1.71795055e+05 1.25e-02 2.67e-08 4.59e+00 2s
5 4.71645424e+04 -1.20643146e+05 5.79e-03 1.74e-08 4.57e+00 2s
6 3.89560641e+04 -8.56338014e+04 2.89e-03 1.15e-08 5.34e+00 3s
7 2.89466689e+04 -4.44709987e+04 1.16e-03 6.05e-09 9.46e+00 3s
8 2.31152088e+04 -1.16462351e+04 4.41e-04 2.27e-09 6.06e+00 4s
Constructing starting basis...
9 1.98781076e+04 6.17861284e+03 1.41e-04 5.62e-10 1.05e+00 7s
Finish factorization 5: fill factor = 7.34 10s
10 1.86763348e+04 1.19666883e+04 5.92e-05 1.92e-10 4.38e-01 12s
Finish factorization 7: fill factor = 8.31 15s
11 1.82671320e+04 1.33890868e+04 2.57e-05 8.44e-11 3.08e-01 17s
12 1.78567059e+04 1.55983410e+04 9.19e-06 1.24e-11 1.35e-01 21s
Start factorization 9: nonzeros in basis = 277666 21s
13 1.75205147e+04 1.67451184e+04 2.66e-06 3.42e-12 4.53e-02 26s
Start factorization 10: nonzeros in basis = 296309 27s
14 1.74284596e+04 1.70157094e+04 1.06e-06 5.12e-13 2.40e-02 32s
Start factorization 11: nonzeros in basis = 310778 33s
Finish factorization 12: fill factor = 11.08 42s
15 1.73690457e+04 1.71259230e+04 4.44e-07 1.75e-13 1.41e-02 44s
Finish factorization 13: fill factor = 11.94 51s
Finish factorization 14: fill factor = 12.49 58s
Finish factorization 15: fill factor = 12.54 64s
16 1.73389245e+04 1.71842011e+04 1.69e-07 4.04e-14 8.96e-03 67s
Start factorization 16: nonzeros in basis = 363873 70s
Finish factorization 16: fill factor = 13.44 77s
Finish factorization 17: fill factor = 13.72 85s
17 1.73173632e+04 1.72280250e+04 7.79e-08 3.75e-14 5.17e-03 88s
Start factorization 18: nonzeros in basis = 392487 92s
Finish factorization 18: fill factor = 14.83 101s
Finish factorization 19: fill factor = 15.32 113s
Finish factorization 20: fill factor = 15.51 124s
18 1.73054204e+04 1.72503112e+04 3.59e-08 3.56e-14 3.19e-03 128s
Start factorization 21: nonzeros in basis = 421339 131s
Finish factorization 21: fill factor = 16.16 143s
Finish factorization 22: fill factor = 16.63 158s
Finish factorization 23: fill factor = 16.64 171s
19 1.72974102e+04 1.72632703e+04 1.53e-08 3.71e-14 1.98e-03 176s
Start factorization 24: nonzeros in basis = 454612 180s
Finish factorization 24: fill factor = 17.56 195s
Finish factorization 25: fill factor = 17.87 212s
20 1.72928995e+04 1.72710583e+04 7.25e-09 3.30e-14 1.26e-03 217s
Start factorization 26: nonzeros in basis = 475776 221s
Finish factorization 26: fill factor = 18.42 239s
Finish factorization 27: fill factor = 18.72 259s
21 1.72899150e+04 1.72769958e+04 3.49e-09 3.04e-14 7.47e-04 264s
Start factorization 28: nonzeros in basis = 489799 267s
Finish factorization 28: fill factor = 19.20 286s
Finish factorization 29: fill factor = 19.31 309s
Finish factorization 30: fill factor = 19.32 330s
22 1.72877050e+04 1.72796403e+04 1.22e-09 4.79e-14 4.67e-04 334s
Start factorization 31: nonzeros in basis = 497594 336s
Finish factorization 31: fill factor = 19.34 356s
Finish factorization 32: fill factor = 19.51 379s
Finish factorization 33: fill factor = 19.58 401s
23 1.72864249e+04 1.72815317e+04 5.62e-10 3.08e-14 2.83e-04 405s
Start factorization 34: nonzeros in basis = 503023 407s
Finish factorization 34: fill factor = 19.59 428s
Finish factorization 35: fill factor = 19.58 451s
Finish factorization 36: fill factor = 19.69 474s
24 1.72857218e+04 1.72826633e+04 2.89e-10 3.01e-14 1.77e-04 478s
Start factorization 37: nonzeros in basis = 501816 480s
Finish factorization 37: fill factor = 19.50 501s
Finish factorization 38: fill factor = 19.72 524s
Finish factorization 39: fill factor = 19.67 545s
25 1.72851972e+04 1.72833434e+04 1.41e-10 3.08e-14 1.07e-04 549s
Finish factorization 40: fill factor = 19.66 571s
Finish factorization 41: fill factor = 19.54 594s
Finish factorization 42: fill factor = 19.61 616s
26 1.72849075e+04 1.72836986e+04 7.31e-11 3.10e-14 6.99e-05 619s
Finish factorization 43: fill factor = 19.43 641s
Finish factorization 44: fill factor = 19.44 662s
Finish factorization 45: fill factor = 19.46 684s
27 1.72847168e+04 1.72839715e+04 4.38e-11 3.05e-14 4.31e-05 687s
Finish factorization 46: fill factor = 19.34 709s
Finish factorization 47: fill factor = 19.36 731s
28 1.72846938e+04 1.72839898e+04 3.85e-11 3.01e-14 4.07e-05 734s
Finish factorization 48: fill factor = 19.35 756s
29 1.72845132e+04 1.72840972e+04 1.20e-11 2.98e-14 2.41e-05 759s
Finish factorization 49: fill factor = 19.34 780s
Finish factorization 50: fill factor = 19.46 802s
30 1.72844802e+04 1.72841951e+04 9.02e-12 3.07e-14 1.65e-05 805s
Finish factorization 51: fill factor = 19.31 827s
31 1.72844355e+04 1.72842261e+04 5.29e-12 2.80e-14 1.21e-05 830s
Finish factorization 52: fill factor = 19.54 852s
32 1.72843706e+04 1.72842865e+04 1.36e-12 3.55e-14 4.86e-06 854s
Finish factorization 53: fill factor = 19.52 876s
33 1.72843385e+04 1.72843273e+04 1.69e-13 3.50e-14 6.51e-07 879s
Finish factorization 54: fill factor = 19.42 900s
34 1.72843335e+04 1.72843316e+04 5.27e-15 3.57e-14 1.08e-07 902s
Finish factorization 55: fill factor = 19.49 924s
35 1.72843333e+04 1.72843329e+04 2.78e-15 3.63e-14 2.31e-08 927s
Finish factorization 56: fill factor = 19.35 948s
36* 1.72843333e+04 1.72843333e+04 2.77e-15 3.69e-14 3.44e-09 951s
Summary
Runtime: 950.71s
Status interior point solve: optimal
Status crossover: not run
objective value: 1.72843333e+04
interior solution primal residual (abs/rel): 2.42e-09 / 4.04e-10
interior solution dual residual (abs/rel): 3.73e-12 / 3.69e-14
interior solution objective gap (abs/rel): 5.75e-05 / 3.33e-09
Ipx: IPM optimal
Performed postsolve
Model name : instance23
Model status : Optimal
IPM iterations: 36
Objective value : 1.7284333342e+04
P-D objective error : 8.5862158026e-10
HiGHS run time : 951.92
C:\Users\xxxxx.PC\highs_test>highs --solver ipm --run_crossover off instance23.mps
Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option solver to "ipm"
Set option run_crossover to "off"
Set option log_file to "HiGHS.log"
LP instance23 has 5924 rows; 27740 cols; 2832110 nonzeros
Coefficient ranges:
Matrix [1e+00, 1e+00]
Cost [1e+00, 1e+02]
Bound [1e+00, 1e+00]
RHS [1e+00, 5e+00]
Presolving model
5924 rows, 27740 cols, 2832110 nonzeros 0s
Dependent equations search running on 5748 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.01s (limit = 1000.00s)
5748 rows, 27388 cols, 2012707 nonzeros 1s
Presolve reductions: rows 5748(-176); columns 27388(-352); nonzeros 2012707(-819403)
Solving the presolved LP
HiPO model has 5748 rows, 27388 columns and 2012707 nonzeros
Running HiPO
BLAS: Unknown
Threads: 8
Rows: 5.7e+03
Cols: 2.7e+04
Nnz: 2.0e+06
Range of A: [1.0e+00, 1.0e+00], ratio 1.0e+00
Range of b: [1.0e+00, 5.0e+00], ratio 5.0e+00
Range of c: [1.0e+00, 1.0e+02], ratio 1.0e+02
Range of bounds: [1.0e+00, 1.0e+00], ratio 1.0e+00
Scaling coefficients: [0.0e+00, 0.0e+00], ratio -
Newton system: NE preferred
Parallelism: Full preferred
Factorisation statistics
Size: 5.75e+03
Nnz: 1.55e+07
Fill-in: 1.18
Serial memory: 7.4e+02 MB
Flops: 5.7e+10
iter primal obj dual obj pinf dinf gap time
0 -4.79996718e+04 -1.82732158e+06 7.63e-01 1.09e+00 1.90e+00 7.1
1 1.26253803e+06 -1.53315522e+06 7.09e-02 1.09e-04 2.07e+01 11.5
2 2.42033952e+05 -5.05056879e+05 1.35e-02 1.09e-08 5.68e+00 16.7
3 6.65457176e+04 -1.12401460e+05 3.19e-03 1.39e-09 7.80e+00 22.4
4 3.35239645e+04 -4.81719636e+04 9.90e-04 6.31e-10 1.12e+01 28.2
5 1.99904767e+04 -7.29542684e+03 1.52e-04 2.08e-10 4.30e+00 33.9
6 1.81460861e+04 9.90596672e+03 4.24e-05 5.53e-11 5.87e-01 39.8
7 1.75856830e+04 1.51772989e+04 1.07e-05 1.47e-11 1.47e-01 46.3
8 1.73840579e+04 1.67861176e+04 2.57e-07 3.56e-12 3.50e-02 52.9
9 1.73279989e+04 1.71423928e+04 4.90e-08 1.02e-12 1.08e-02 59.3
10 1.72994114e+04 1.72492102e+04 1.11e-08 2.33e-13 2.91e-03 66.2
11 1.72885648e+04 1.72754708e+04 2.18e-09 5.59e-14 7.58e-04 73.5
12 1.72855002e+04 1.72821663e+04 4.71e-10 3.69e-14 1.93e-04 80.8
13 1.72846850e+04 1.72838077e+04 1.21e-10 4.31e-14 5.08e-05 88.0
14 1.72845143e+04 1.72841030e+04 6.17e-11 3.19e-14 2.38e-05 94.0
15 1.72844066e+04 1.72842627e+04 2.42e-11 4.30e-14 8.33e-06 101.2
16 1.72843420e+04 1.72843263e+04 7.78e-12 3.54e-14 9.08e-07 109.5
17 1.72843364e+04 1.72843315e+04 1.23e-09 3.48e-14 2.85e-07 116.0
18 1.72843335e+04 1.72843332e+04 2.12e-09 4.14e-14 1.70e-08 123.4
19 1.72843333e+04 1.72843333e+04 5.18e-10 4.03e-14 1.14e-09 128.9
=== Primal-dual feasible point found
Summary
HiPO runtime: 127.79
Status: primal-dual feasible
HiPO iterations: 19
Primal residual rel/abs: 5.18e-10 / 3.11e-09
Dual residual rel/abs: 4.03e-14 / 4.07e-12
Primal objective 1.72843333e+04
Dual objective 1.72843333e+04
Primal-dual gap: 1.14e-09
Hipo: Solved
Performed postsolve
Model name : instance23
Model status : Optimal
IPM iterations: 19
Objective value : 1.7284333344e+04
P-D objective error : 5.1598549731e-10
HiGHS run time : 128.99
C:\Users\xxxxx.PC\highs_test>copt_cmd
Cardinal Optimizer v8.0.1. Build date Oct 22 2025
Copyright Cardinal Operations 2025. All Rights Reserved
COPT> set LpMethod 2
Setting parameter 'LpMethod' to 2
COPT> set crossover 0
Setting parameter 'Crossover' to 0
COPT> read instance19.mps
Reading from 'C:\Users\sugaw.PC\highs_test\instance19.mps'
Reading finished (0.02s)
COPT> opt
Model fingerprint: 7bf9a8ee
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
460 rows, 6085 columns and 254045 non-zero elements
The presolved problem has:
459 rows, 6083 columns and 254040 non-zero elements
Starting barrier solver using 8 CPU threads
Problem info:
Dualized in presolve: No
Range of matrix coefficients: [1e+00,1e+00]
Range of rhs coefficients: [1e+00,9e+00]
Range of bound coefficients: [1e+00,1e+00]
Range of cost coefficients: [1e+00,1e+02]
Factor info:
Number of free columns: 0
Number of dense columns: 0
Number of matrix entries: 8.862e+04
Number of factor entries: 1.056e+05
Number of factor flops: 3.234e+07
Iter Primal.Obj Dual.Obj Compl Primal.Inf Dual.Inf Time
0 +3.24302501e+05 -1.67720818e+05 2.95e+06 7.59e+03 1.13e+02 0.05s
1 +1.01164287e+05 -1.26415190e+05 3.23e+05 3.95e+02 4.57e-01 0.06s
2 +2.39146595e+04 -2.89651619e+04 6.86e+04 9.73e+01 8.10e-02 0.06s
3 +9.17968547e+03 -7.59553897e+03 2.21e+04 3.66e+01 2.24e-02 0.06s
4 +7.17427838e+03 -3.25563753e+03 1.48e+04 2.69e+01 1.31e-02 0.06s
5 +5.31526881e+03 -9.01277184e+02 9.06e+03 1.64e+01 7.95e-03 0.08s
6 +4.21816058e+03 +8.59174155e+02 4.97e+03 9.10e+00 4.29e-03 0.08s
7 +3.69866873e+03 +2.05071087e+03 2.47e+03 4.87e+00 1.93e-03 0.08s
8 +3.36330050e+03 +2.62229853e+03 1.05e+03 1.96e+00 8.64e-04 0.08s
9 +3.26440885e+03 +2.92108778e+03 4.84e+02 9.97e-01 3.75e-04 0.08s
10 +3.22470571e+03 +3.02035832e+03 2.94e+02 6.57e-01 2.10e-04 0.09s
11 +3.20042945e+03 +3.06977211e+03 1.91e+02 4.53e-01 1.28e-04 0.09s
12 +3.18248467e+03 +3.09746251e+03 1.25e+02 3.02e-01 8.18e-05 0.09s
13 +3.17510341e+03 +3.11897968e+03 8.79e+01 2.43e-01 4.47e-05 0.09s
14 +3.16481173e+03 +3.12867609e+03 5.75e+01 1.64e-01 2.71e-05 0.11s
15 +3.15838927e+03 +3.13714071e+03 3.50e+01 1.06e-01 1.44e-05 0.11s
16 +3.15483164e+03 +3.14093362e+03 2.34e+01 7.32e-02 8.76e-06 0.11s
17 +3.15244918e+03 +3.14317086e+03 1.60e+01 5.21e-02 5.30e-06 0.11s
18 +3.15055613e+03 +3.14536540e+03 9.48e+00 3.31e-02 2.44e-06 0.11s
19 +3.14928347e+03 +3.14633058e+03 5.57e+00 2.02e-02 1.21e-06 0.11s
20 +3.14855950e+03 +3.14678543e+03 3.40e+00 1.26e-02 6.81e-07 0.13s
21 +3.14824656e+03 +3.14705733e+03 2.37e+00 9.17e-03 3.84e-07 0.13s
22 +3.14807507e+03 +3.14720488e+03 1.81e+00 7.30e-03 2.20e-07 0.13s
23 +3.14786312e+03 +3.14731066e+03 1.17e+00 4.77e-03 1.30e-07 0.13s
24 +3.14770621e+03 +3.14737815e+03 6.90e-01 2.81e-03 7.86e-08 0.14s
25 +3.14762145e+03 +3.14741167e+03 4.43e-01 1.81e-03 4.92e-08 0.14s
26 +3.14758507e+03 +3.14744775e+03 3.04e-01 1.29e-03 2.76e-08 0.14s
27 +3.14754151e+03 +3.14746647e+03 1.66e-01 7.03e-04 1.51e-08 0.14s
28 +3.14752876e+03 +3.14747253e+03 1.24e-01 5.27e-04 1.13e-08 0.14s
29 +3.14750933e+03 +3.14749030e+03 4.32e-02 1.88e-04 3.58e-09 0.14s
30 +3.14750425e+03 +3.14749310e+03 2.32e-02 9.39e-05 2.45e-09 0.16s
31 +3.14750301e+03 +3.14749541e+03 1.72e-02 7.47e-05 1.33e-09 0.16s
32 +3.14750054e+03 +3.14749782e+03 5.66e-03 2.29e-05 5.37e-10 0.16s
33 +3.14750018e+03 +3.14749855e+03 3.58e-03 1.51e-05 3.04e-10 0.16s
34 +3.14750002e+03 +3.14749888e+03 2.67e-03 1.19e-05 1.88e-10 0.17s
35 +3.14749993e+03 +3.14749901e+03 2.24e-03 1.02e-05 1.39e-10 0.17s
36 +3.14749960e+03 +3.14749951e+03 2.65e-04 1.38e-06 9.19e-12 0.17s
37 +3.14749957e+03 +3.14749957e+03 1.46e-05 8.13e-08 9.28e-13 0.17s
Barrier status: OPTIMAL
Primal objective: 3.14749957e+03
Dual objective: 3.14749957e+03
Duality gap (abs/rel): 4.12e-06 / 1.31e-09
Primal infeasibility (abs/rel): 8.13e-08 / 9.04e-09
Dual infeasibility (abs/rel): 9.28e-13 / 9.28e-15
Postsolving
Solving finished
Status: Optimal Objective: 3.1474995696e+03 Iterations: 37(0) Time: 0.17s
COPT> read instance20.mps
Reading from 'C:\Users\sugaw.PC\highs_test\instance20.mps'
Reading finished (0.03s)
COPT> opt
Model fingerprint: e6a2d116
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
1142 rows, 6249 columns and 426542 non-zero elements
The presolved problem has:
1142 rows, 6249 columns and 426542 non-zero elements
Starting barrier solver using 8 CPU threads
Problem info:
Dualized in presolve: No
Range of matrix coefficients: [1e+00,1e+00]
Range of rhs coefficients: [1e+00,1e+01]
Range of bound coefficients: [1e+00,1e+00]
Range of cost coefficients: [1e+00,1e+02]
Factor info:
Number of free columns: 0
Number of dense columns: 0
Number of matrix entries: 5.822e+05
Number of factor entries: 6.527e+05
Number of factor flops: 4.971e+08
Iter Primal.Obj Dual.Obj Compl Primal.Inf Dual.Inf Time
0 +7.32200271e+05 -2.53533354e+05 4.88e+06 7.52e+03 1.24e+02 0.11s
1 +3.00691355e+05 -1.87513771e+05 7.33e+05 7.70e+02 6.83e-01 0.13s
2 +9.17881570e+04 -5.17716431e+04 1.97e+05 2.42e+02 7.88e-02 0.14s
3 +2.36533280e+04 -1.58989763e+04 5.21e+04 6.04e+01 2.24e-02 0.15s
4 +1.28297811e+04 -4.17199374e+03 2.31e+04 2.74e+01 8.76e-03 0.15s
5 +7.92819623e+03 +5.30459245e+02 9.93e+03 1.12e+01 3.79e-03 0.16s
6 +5.79583227e+03 +3.26482392e+03 3.32e+03 3.75e+00 1.16e-03 0.18s
7 +5.00763920e+03 +4.42547883e+03 7.26e+02 8.34e-01 2.29e-04 0.18s
8 +4.87845431e+03 +4.64373518e+03 2.92e+02 3.61e-01 8.39e-05 0.19s
9 +4.83113336e+03 +4.71110242e+03 1.52e+02 2.07e-01 3.70e-05 0.20s
10 +4.80814697e+03 +4.74113985e+03 8.74e+01 1.34e-01 1.67e-05 0.21s
11 +4.79074128e+03 +4.75448435e+03 4.79e+01 7.67e-02 8.07e-06 0.22s
12 +4.78086843e+03 +4.76267731e+03 2.48e+01 4.38e-02 2.95e-06 0.22s
13 +4.77467263e+03 +4.76634534e+03 1.16e+01 2.19e-02 1.05e-06 0.24s
14 +4.77271424e+03 +4.76766619e+03 7.27e+00 1.48e-02 4.47e-07 0.24s
15 +4.77063697e+03 +4.76855151e+03 3.11e+00 6.81e-03 1.12e-07 0.25s
16 +4.76913287e+03 +4.76896570e+03 2.61e-01 6.22e-04 4.08e-09 0.26s
17 +4.76900024e+03 +4.76899993e+03 5.17e-04 1.37e-06 1.99e-12 0.27s
18 +4.76900000e+03 +4.76900000e+03 2.29e-09 7.33e-12 2.12e-12 0.29s
Barrier status: OPTIMAL
Primal objective: 4.76900000e+03
Dual objective: 4.76900000e+03
Duality gap (abs/rel): 1.52e-09 / 3.19e-13
Primal infeasibility (abs/rel): 7.33e-12 / 7.33e-13
Dual infeasibility (abs/rel): 2.12e-12 / 2.12e-14
Solving finished
Status: Optimal Objective: 4.7690000000e+03 Iterations: 18(0) Time: 0.29s
COPT> read instance21.mps
Reading from 'C:\Users\sugaw.PC\highs_test\instance21.mps'
Reading finished (0.03s)
COPT> opt
Model fingerprint: 8d056eaa
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
1556 rows, 9235 columns and 603232 non-zero elements
The presolved problem has:
1556 rows, 9235 columns and 603232 non-zero elements
Starting barrier solver using 8 CPU threads
Problem info:
Dualized in presolve: No
Range of matrix coefficients: [1e+00,1e+00]
Range of rhs coefficients: [1e+00,9e+00]
Range of bound coefficients: [1e+00,1e+00]
Range of cost coefficients: [1e+00,1e+02]
Factor info:
Number of free columns: 0
Number of dense columns: 0
Number of matrix entries: 1.100e+06
Number of factor entries: 1.211e+06
Number of factor flops: 1.257e+09
Iter Primal.Obj Dual.Obj Compl Primal.Inf Dual.Inf Time
0 +1.82487175e+06 -3.36105687e+05 9.05e+06 9.59e+03 1.21e+02 0.19s
1 +5.61990160e+05 -2.68443148e+05 1.13e+06 6.56e+02 6.95e-01 0.21s
2 +1.42174475e+05 -5.39554732e+04 2.42e+05 1.64e+02 3.27e-02 0.21s
3 +6.93821989e+04 -1.22261971e+04 1.01e+05 6.70e+01 1.28e-02 0.23s
4 +3.77197444e+04 +9.04158441e+03 3.52e+04 2.41e+01 3.57e-03 0.24s
5 +2.74757110e+04 +1.60764040e+04 1.36e+04 9.58e+00 1.21e-03 0.26s
6 +2.19785460e+04 +1.96565416e+04 2.58e+03 1.57e+00 2.50e-04 0.27s
7 +2.14806151e+04 +2.06576401e+04 8.95e+02 5.52e-01 8.47e-05 0.29s
8 +2.13181699e+04 +2.09239832e+04 4.29e+02 2.86e-01 3.70e-05 0.30s
9 +2.12368399e+04 +2.10400720e+04 2.16e+02 1.64e-01 1.54e-05 0.32s
10 +2.11825845e+04 +2.10813543e+04 1.11e+02 8.12e-02 8.03e-06 0.32s
11 +2.11544377e+04 +2.11078822e+04 5.08e+01 3.75e-02 3.62e-06 0.33s
12 +2.11447967e+04 +2.11201501e+04 2.71e+01 2.21e-02 1.64e-06 0.35s
13 +2.11406387e+04 +2.11255534e+04 1.68e+01 1.50e-02 8.82e-07 0.36s
14 +2.11370120e+04 +2.11290786e+04 8.89e+00 8.64e-03 3.91e-07 0.38s
15 +2.11352809e+04 +2.11305792e+04 5.31e+00 5.54e-03 2.02e-07 0.40s
16 +2.11340526e+04 +2.11312080e+04 3.22e+00 3.38e-03 1.19e-07 0.41s
17 +2.11331141e+04 +2.11318181e+04 1.47e+00 1.62e-03 4.80e-08 0.43s
18 +2.11328380e+04 +2.11319824e+04 9.78e-01 1.11e-03 2.87e-08 0.43s
19 +2.11327251e+04 +2.11320454e+04 7.74e-01 8.62e-04 2.36e-08 0.45s
20 +2.11323456e+04 +2.11322572e+04 9.25e-02 3.76e-05 5.45e-09 0.46s
21 +2.11323334e+04 +2.11323328e+04 6.28e-04 3.86e-08 4.38e-11 0.48s
22 +2.11323333e+04 +2.11323333e+04 9.69e-10 6.22e-12 1.98e-12 0.49s
Barrier status: OPTIMAL
Primal objective: 2.11323333e+04
Dual objective: 2.11323333e+04
Duality gap (abs/rel): 1.70e-09 / 8.04e-14
Primal infeasibility (abs/rel): 6.22e-12 / 6.91e-13
Dual infeasibility (abs/rel): 1.98e-12 / 1.98e-14
Solving finished
Status: Optimal Objective: 2.1132333333e+04 Iterations: 22(0) Time: 0.51s
COPT> read instance22.mps
Reading from 'C:\Users\sugaw.PC\highs_test\instance22.mps'
Reading finished (0.09s)
COPT> opt
Model fingerprint: 44bcbef1
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
The presolved problem has:
3690 rows, 15856 columns and 1859219 non-zero elements
Starting barrier solver using 8 CPU threads
Problem info:
Dualized in presolve: No
Range of matrix coefficients: [1e+00,1e+00]
Range of rhs coefficients: [1e+00,5e+00]
Range of bound coefficients: [1e+00,1e+00]
Range of cost coefficients: [1e+00,1e+02]
Factor info:
Number of free columns: 0
Number of dense columns: 0
Number of matrix entries: 6.129e+06
Number of factor entries: 6.810e+06
Number of factor flops: 1.675e+10
Iter Primal.Obj Dual.Obj Compl Primal.Inf Dual.Inf Time
0 +1.78753868e+06 -5.17951890e+05 8.52e+06 7.72e+03 1.26e+02 0.84s
1 +7.22287609e+05 -3.30274994e+05 1.40e+06 8.90e+02 1.26e+00 0.95s
2 +1.64208363e+05 -8.31086340e+04 3.01e+05 1.87e+02 2.34e-01 1.06s
3 +9.38534398e+04 -2.96782704e+04 1.51e+05 9.37e+01 1.20e-01 1.16s
4 +4.17388199e+04 +1.27704170e+04 3.41e+04 1.73e+01 2.86e-02 1.27s
5 +3.16084890e+04 +2.60420456e+04 6.08e+03 2.19e+00 5.18e-03 1.38s
6 +3.04170084e+04 +2.97002260e+04 7.30e+02 2.42e-01 4.95e-04 1.49s
7 +3.03034597e+04 +3.01150144e+04 1.89e+02 7.51e-02 1.09e-04 1.58s
8 +3.02872428e+04 +3.01746588e+04 1.12e+02 5.58e-02 5.72e-05 1.68s
9 +3.02609774e+04 +3.02128712e+04 4.79e+01 2.42e-02 2.15e-05 1.80s
10 +3.02487250e+04 +3.02304347e+04 1.82e+01 1.01e-02 6.45e-06 1.90s
11 +3.02440929e+04 +3.02360233e+04 8.02e+00 5.22e-03 2.03e-06 1.99s
12 +3.02406656e+04 +3.02382117e+04 2.44e+00 1.67e-03 4.82e-07 2.11s
13 +3.02401386e+04 +3.02385940e+04 1.53e+00 1.12e-03 2.66e-07 2.20s
14 +3.02394915e+04 +3.02389595e+04 5.28e-01 3.96e-04 7.47e-08 2.33s
15 +3.02392771e+04 +3.02390797e+04 1.96e-01 1.53e-04 2.18e-08 2.44s
16 +3.02392233e+04 +3.02391164e+04 1.06e-01 8.89e-05 1.01e-08 2.53s
17 +3.02391742e+04 +3.02391324e+04 4.15e-02 3.09e-05 4.73e-09 2.64s
18 +3.02391604e+04 +3.02391457e+04 1.46e-02 1.13e-05 1.47e-09 2.75s
19 +3.02391566e+04 +3.02391497e+04 6.77e-03 6.15e-06 4.98e-10 2.86s
20 +3.02391542e+04 +3.02391512e+04 3.04e-03 3.05e-06 1.58e-10 2.99s
21 +3.02391534e+04 +3.02391516e+04 1.83e-03 1.85e-06 9.07e-11 3.10s
22 +3.02391529e+04 +3.02391520e+04 9.32e-04 1.12e-06 2.59e-11 3.22s
23 +3.02391525e+04 +3.02391521e+04 4.48e-04 5.43e-07 1.17e-11 3.33s
24 +3.02391522e+04 +3.02391522e+04 3.56e-05 4.42e-08 9.38e-12 3.44s
Barrier status: OPTIMAL
Primal objective: 3.02391522e+04
Dual objective: 3.02391522e+04
Duality gap (abs/rel): 3.34e-05 / 1.11e-09
Primal infeasibility (abs/rel): 4.42e-08 / 8.85e-09
Dual infeasibility (abs/rel): 9.38e-12 / 9.38e-14
Solving finished
Status: Optimal Objective: 3.0239152208e+04 Iterations: 24(0) Time: 3.45s
COPT> read instance23.mps
Reading from 'C:\Users\sugaw.PC\highs_test\instance23.mps'
Reading finished (0.16s)
COPT> opt
Model fingerprint: 248df987
Using Cardinal Optimizer v8.0.1 on Windows
Hardware has 8 cores and 16 threads. Using instruction set X86_NATIVE (1)
Minimizing an LP problem
The original problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
The presolved problem has:
5924 rows, 27740 columns and 2832110 non-zero elements
Starting barrier solver using 8 CPU threads
Problem info:
Dualized in presolve: No
Range of matrix coefficients: [1e+00,1e+00]
Range of rhs coefficients: [1e+00,5e+00]
Range of bound coefficients: [1e+00,1e+00]
Range of cost coefficients: [1e+00,1e+02]
Factor info:
Number of free columns: 0
Number of dense columns: 0
Number of matrix entries: 1.552e+07
Number of factor entries: 1.755e+07
Number of factor flops: 6.932e+10
Iter Primal.Obj Dual.Obj Compl Primal.Inf Dual.Inf Time
0 +3.73349161e+06 -1.04353509e+06 1.63e+07 5.32e+03 1.27e+02 1.86s
1 +1.16029401e+06 -6.89466052e+05 2.22e+06 3.33e+02 1.01e+00 2.21s
2 +3.02180174e+05 -1.76061151e+05 5.43e+05 9.53e+01 1.85e-01 2.50s
3 +1.17287615e+05 -8.35442472e+04 2.28e+05 3.78e+01 9.12e-02 2.79s
4 +6.33412308e+04 -3.11349242e+04 1.09e+05 1.82e+01 4.21e-02 3.09s
5 +2.41759009e+04 +3.05372148e+03 2.33e+04 2.98e+00 9.58e-03 3.43s
6 +1.82392525e+04 +1.44953604e+04 3.86e+03 4.43e-01 1.38e-03 3.77s
7 +1.74595485e+04 +1.68787459e+04 5.76e+02 4.97e-02 2.09e-04 4.10s
8 +1.73487970e+04 +1.71721093e+04 1.75e+02 1.34e-02 5.35e-05 4.44s
9 +1.73081441e+04 +1.72444735e+04 6.30e+01 3.94e-03 1.65e-05 4.78s
10 +1.72972626e+04 +1.72635648e+04 3.33e+01 2.08e-03 8.67e-06 5.08s
11 +1.72890010e+04 +1.72777565e+04 1.11e+01 6.63e-04 2.46e-06 5.43s
12 +1.72859829e+04 +1.72819675e+04 3.98e+00 2.15e-04 8.04e-07 5.77s
13 +1.72850001e+04 +1.72836402e+04 1.34e+00 8.22e-05 2.06e-07 6.11s
14 +1.72845933e+04 +1.72840511e+04 5.36e-01 3.36e-05 7.08e-08 6.46s
15 +1.72845787e+04 +1.72840681e+04 5.05e-01 3.14e-05 6.70e-08 6.77s
16 +1.72844526e+04 +1.72842241e+04 2.26e-01 1.58e-05 2.30e-08 7.11s
17 +1.72844360e+04 +1.72842457e+04 1.88e-01 1.36e-05 1.85e-08 7.41s
18 +1.72843817e+04 +1.72842949e+04 8.56e-02 6.49e-06 7.94e-09 7.70s
19 +1.72843347e+04 +1.72843318e+04 2.82e-03 1.93e-07 2.77e-10 8.03s
20 +1.72843333e+04 +1.72843333e+04 6.88e-07 2.26e-10 6.26e-12 8.34s
Barrier status: OPTIMAL
Primal objective: 1.72843333e+04
Dual objective: 1.72843333e+04
Duality gap (abs/rel): 6.63e-07 / 3.83e-11
Primal infeasibility (abs/rel): 2.26e-10 / 4.52e-11
Dual infeasibility (abs/rel): 6.26e-12 / 6.26e-14
Solving finished
Status: Optimal Objective: 1.7284333334e+04 Iterations: 20(0) Time: 8.36s
COPT>
2025年11月14日金曜日
Q 準夜(準)の翌日に、am日勤pm休（半２）、出張、am日勤pm出張（日出）及びam出張pm日勤（出日）の組合せは禁止
Ans.
意味を確認しました。
準半2禁止、準出禁止、準日出禁止、準出日禁止でOKです。
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