## 数値実験の結果
PF : Perspective Formulation
NF : Natural Formulation
00_nn : $|V| = 00$のnn番目のインスタンス
----
| | [PF] $T$ | [PF] $N$ | [PF] SI | [NF] $T$ | [NF] $N$ | [NF] SI |
| ----- | ---------- | ---------- | ------- | ---------- | ---------- | ------- |
| 20_01 | 4.69 | 1281 | 95361 | 1.77 | 411 | 43562 |
| 20_02 | 6.93 | 1747 | 189683 | 2.92 | 725 | 92871 |
| 20_03 | 4.48 | 1270 | 114792 | 2.31 | 642 | 83211 |
| 20_04 | 14.63 | 2670 | 457010 | 12.49 | 1917 | 483096 |
| 20_05 | 0.39 | 34 | 6803 | 0.67 | 30 | 7385 |
| 20_06 | 7.03 | 1285 | 162885 | 8.73 | 1380 | 238941 |
| 20_07 | 4.59 | 882 | 55295 | 1.42 | 250 | 33936 |
| 20_08 | 4.69 | 1083 | 91882 | 2.06 | 432 | 48533 |
| 20_09 | 13.26 | 3065 | 490405 | 13.04 | 1784 | 380865 |
| 20_10 | 4.15 | 836 | 49913 | 1.30 | 270 | 29325 |
| 20_11 | 9.61 | 1946 | 272836 | 10.77 | 1882 | 399267 |
| 20_12 | 0.72 | 30 | 8679 | 1.09 | 362 | 25267 |
| 20_13 | 0.61 | 102 | 10245 | 0.70 | 93 | 10149 |
| 20_14 | 2.67 | 837 | 43078 | 1.28 | 345 | 27502 |
| 20_15 | 9.37 | 1125 | 246032 | 10.24 | 1282 | 309292 |
$T$ : 計算時間
$N$ : 展開済ノード数
SI : Simplex Iterations
----
#### $|V| = 20$でカットなしの場合
| | [PF] $T$ | [PF] $N$ | [PF] SI | [NF] $T$ | [NF] $N$ | [NF] SI |
| ----- | ---------- | ---------- | ------- | ---------- | ---------- | ------- |
| 20_01 | 19.66 | 12867 | 1792511 | 32.02 | 19419 | 2840229 |
| 20_02 | 49.89 | 28196 | 4782532 | 75.02 | 32877 | 6829954 |
| 20_03 | 30.80 | 16381 | 2759728 | 129.81 | 30139 | 8342751 |
| 20_04 | 879.79 | 157591 | 51063297 | 1152.71 | 230860 | 71843744 |
| 20_05 | 2.26 | 2338 | 94999 | 5.60 | 1387 | 179591 |
| **20_06** | 610.61 | 96704 | 31374826 | 517.99 | 151310 | 37762889 |
| 20_07 | 5.75 | 4533 | 427982 | 10.76 | 3941 | 741947 |
| 20_08 | 21.31 | 12300 | 1896086 | 29.87 | 16254 | 2518701 |
| 20_09 | 526.82 | 96728 | 27911220 | 650.49 | 199041 | 47286354 |
| 20_10 | 7.96 | 6260 | 673507 | 22.50 | 7428 | 1468356 |
| 20_11 | 79.16 | 32766 | 7192287 | 225.40 | 75946 | 19041948 |
| 20_12 | 0.63 | 722 | 18668 | 0.91 | 645 | 33863 |
| **20_13** | 7.35 | 7102 | 616557 | 6.93 | 6693 | 639098 |
| 20_14 | 2.77 | 2609 | 185414 | 4.92 | 4089 | 383728 |
| 20_15 | 538.01 | 112587 | 31235298 | 1211.96 | 171570 | 51872446 |
$T$ : 計算時間
$N$ : 展開済ノード数
SI : Simplex Iterations
----
| | [PF] $\overline{z}$ | [PF] $\underline{z}$ | [NF] $\overline{z}$ | [NF] $\underline{z}$ |
| ----- | ------------------- | -------------------- | ------------------- | -------------------- |
| 20_01 | 1.522496149286e+02 | 1.522496149286e+02 | 1.522496149227e+02 | 1.522496149227e+02 |
| 20_02 | 1.603391800846e+02* | 1.603391800846e+02 | 1.603391800846e+02 | 1.603391800846e+02 |
| 20_03 | 1.465559992380e+02 | 1.465559992380e+02 | 1.465559992380e+02 | 1.465559992380e+02 |
| 20_04 | 1.514721323506e+02 | 1.514721323506e+02 | 1.514721323506e+02 | 1.514721323506e+02 |
| 20_05 | 1.774423866617e+02 | 1.774423866617e+02 | 1.774423866617e+02 | 1.774423866617e+02 |
| 20_06 | 1.483179749466e+02 | 1.483179749466e+02 | 1.483179749466e+02 | 1.483179749466e+02 |
| 20_07 | 1.683353499458e+02 | 1.683353499458e+02 | 1.683353499458e+02 | 1.683353499458e+02 |
| 20_08 | 1.465573863116e+02 | 1.465573863116e+02 | 1.465573863116e+02 | 1.465573863116e+02 |
| 20_09 | 1.503331377640e+02 | 1.503331377640e+02 | 1.503331377640e+02 | 1.503331377640e+02 |
| 20_10 | 1.744912713440e+02* | 1.744912713440e+02 | 1.744912713440e+02 | 1.744912713440e+02 |
| 20_11 | 1.580244743739e+02 | 1.580244743739e+02 | 1.580244743739e+02 | 1.580244743739e+02 |
| 20_12 | 1.802631752459e+02 | 1.802631752459e+02 | 1.802631752459e+02 | 1.802631752459e+02 |
| 20_13 | 1.787550345772e+02 | 1.787550345772e+02 | 1.787550345772e+02 | 1.787550345772e+02 |
| 20_14 | 1.554377708450e+02 | 1.554377708450e+02 | 1.554377708450e+02 | 1.554377708450e+02 |
| 20_15 | 1.511485964753e+02 | 1.511485964753e+02 | 1.511485964753e+02 | 1.511485964753e+02 |
`*` : `Warning: max constraint violation (.) exceeds tolerance`
$\overline{z}$ : 最適値の上界(暫定解の目的関数値)
$\underline{z}$ : 最適値の下界
**太字** : 最適解を求められたが、最適値の上下界が一致しなかった
*斜字* : 制限時間(4時間)内に最適解を求められなかった
----
| | [PF] $T$ | [PF] $N$ | [PF] SI | [NF] $T$ | [NF] $N$ | [NF] SI |
| ----- | ---------- | ---------- | ------- | ---------- | ---------- | ------- |
| 30_01 | 276.37 | 7948 | 5628476 | 310.56 | 6996 | 5927515 |
| 30_02 | 101.76 | 4623 | 1949279 | 121.05 | 2862 | 2123233 |
| 30_03 | 7.31 | 524 | 111218 | 9.70 | 546 | 142294 |
| 30_04 | 355.33 | 8710 | 7019366 | 990.52 | 16311 | 17649979 |
| 30_05 | 91.86 | 3395 | 1461482 | 143.56 | 2714 | 2321701 |
| 30_06 | 7328.34 | 67455 | 141860428 | 14400.01+ | 96463 | 165128050 |
| 30_07 | 215.35 | 4812 | 3964392 | 519.15 | 7078 | 7945233 |
| 30_08 | 7.20 | 399 | 118022 | 11.32 | 388 | 147811 |
| 30_09 | 359.06 | 8845 | 7019359 | 738.37 | 13077 | 13555596 |
| 30_10 | 2.43 | 1 | 19740 | 5.18 | 30 | 27264 |
| 30_11 | 114.95 | 3788 | 2353858 | 184.05 | 5659 | 3938410 |
| 30_12 | 70.08 | 1764 | 1149987 | 89.74 | 1513 | 1266615 |
| **30_13** | 285.91 | 7783 | 4835452 | 197.09 | 5414 | 3981541 |
| 30_14 | 813.45 | 18074 | 15275970 | 1528.60 | 21207 | 25019692 |
| 30_15 | 115.60 | 3017 | 1719773 | 292.59 | 5929 | 5162465 |
$T$ : 計算時間
$N$ : 展開済ノード数
SI : Simplex Iterations
----
| | [PF] $\overline{z}$ | [PF] $\underline{z}$ | [NF] $\overline{z}$ | [NF] $\underline{z}$ |
| ----- | ------------------- | -------------------- | ------------------- | -------------------- |
| 30_01 | 3.577840706824e+02 | 3.577840706824e+02 | 3.577840404548e+02 | 3.577840404548e+02 |
| 30_02 | 3.661960630241e+02 | **3.661769647259e+02** | 3.661960630241e+02 | 3.661960630241e+02 |
| 30_03 | 3.966341059665e+02* | 3.966341059665e+02 | 3.966341059665e+02 | 3.966341059665e+02 |
| 30_04 | 3.606178762563e+02 | 3.606178762563e+02 | 3.606178762563e+02 | **3.605951876083e+02** |
| 30_05 | 3.401503142677e+02 | **3.401210710443e+02** | 3.401503142677e+02 | **3.401412896349e+02** |
| 30_06 | 3.275836445864e+02 | **3.275645361953e+02** | *3.275836445864e+02* | *3.270025973698e+02* |
| 30_07 | 3.298490275722e+02 | 3.298490275722e+02 | 3.298490275722e+02 | 3.298490275722e+02 |
| 30_08 | 3.754866622325e+02 | 3.754866622325e+02 | 3.754866622325e+02 | **3.754818369293e+02** |
| 30_09 | 3.248521698259e+02 | **3.248235568239e+02** | 3.248521698259e+02 | **3.248287793671e+02** |
| 30_10 | 4.374213369353e+02 | 4.374213369353e+02 | 4.374213369353e+02 | 4.374213369353e+02 |
| 30_11 | 3.851213893555e+02 | 3.851213893555e+02 | 3.851213893555e+02 | **3.851187583897e+02** |
| 30_12 | 3.498200242865e+02 | 3.498200242865e+02 | 3.498200242865e+02 | 3.498200242865e+02 |
| 30_13 | 3.451956277154e+02 | **3.451719145850e+02** | 3.451956277154e+02 | **3.451640206953e+02** |
| **30_14** | 3.239359634548e+02* | 3.239359634548e+02 | 3.240004708431e+02 | 3.240004708431e+02 |
| 30_15 | 3.337604011871e+02 | 3.337604011871e+02 | 3.337604010163e+02 | **3.337422325265e+02** |
`*` : `Warning: max constraint violation (.) exceeds tolerance`
$\overline{z}$ : 最適値の上界(暫定解の目的関数値)
$\underline{z}$ : 最適値の下界
**太字** : 最適解を求められたが、最適値の上下界が一致しなかった
*斜字* : 制限時間(4時間)内に最適解を求められなかった
30_06N : 0.1774 %
----
| | [PF] $T$ | [PF] $N$ | [PF] SI | [NF] $T$ | [NF] $N$ | [NF] SI |
| ----- | ---------- | ---------- | ------- | ---------- | ---------- | ------- |
| 40_01 | 1478.54 | 11959 | 16539327 | 2924.22 | 12553 | 26728091 |
| 40_02 | 6873.34 | 31248 | 58387306 | 14400.01+ | 22616 | 81518452 |
| 40_03 | 14400.08+ | 23969 | 68557 | 14400.01+ | 29716 | 98789161 |
| 40_04 | 12186.01 | 31703 | 76424071 | 14400.01+ | 26047 | 98121063 |
| 40_05 | 6814.69 | 29481 | 54328178 | 14400.01+ | 31168 | 92941698 |
| 40_06 | 14400.01+ | 45221 | 103961575 | 14400.02+ | 13716 | 74288322 |
| 40_07 | 14400.01+ | 38365 | 93472565 | 14400.01+ | 17301 | 71245752 |
| 40_08 | 14400.01+ | 44909 | 95547005 | 14400.01+ | 19126 | 74078307 |
| 40_09 | 14400.01+ | 49581 | 99310587 | 14400.01+ | 28473 | 99590890 |
| 40_10 | 11748.23 | 49831 | 100907518 | 14400.00+ | 40731 | 111590291 |
| 40_11 | 14400.01+ | 37380 | 86718982 | 14400.01+ | 22415 | 87978335 |
| 40_12 | 14400.01+ | 38023 | 95859313 | 14400.01+ | 15090 | 74528860 |
| 40_13 | 12274.40 | 62270 | 107377575 | 14400.00+ | 39375 | 100147253 |
| 40_14 | 14400.01+ | 50055 | 105213521 | 14400.03+ | 24000 | 85261813 |
| 40_15 | 6379.29 | 18631 | 45097587 | 14400.00+ | 27361 | 92285005 |
$T$ : 計算時間
$N$ : 展開済ノード数
SI : Simplex Iterations
----
| | [PF] $\overline{z}$ | [PF] $\underline{z}$ | [NF] $\overline{z}$ | [NF] $\underline{z}$ |
| ----- | ------------------- | -------------------- | ------------------- | -------------------- |
| 40_01 | 6.369172474238e+02 | **6.368725828823e+02** | 6.369172474238e+02 | 6.369172474238e+02 |
| 40_02 | 5.683170014881e+02 | **5.682908507472e+02** | *5.683324795725e+02* | *5.676932595199e+02* |
| 40_03 | *5.476351419785e+02* | *5.444296620851e+02* | *5.475824562652e+02* | *5.425368061492e+02* |
| 40_04 | 5.758084120005e+02 | **5.758007224544e+02** | *5.758084120005e+02* | *5.748371239338e+02* |
| 40_05 | 6.041956898399e+02* | **6.041615775300e+02** | *6.041956898399e+02* | *6.038049006639e+02* |
| 40_06 | *5.307664512571e+02* | *5.306937874420e+02* | *5.307664512571e+02* | *5.291054386393e+02* |
| 40_07 | *5.358641766367e+02* | *5.348268572159e+02* | *5.365157534928e+02* | *5.325321186835e+02* |
| 40_08 | *5.591229713517e+02* | *5.581330497611e+02* | *5.590763762183e+02* | *5.566717042408e+02* |
| 40_09 | *5.440201270986e+02* | *5.432926187952e+02* | *5.440201270986e+02* | *5.426330552261e+02* |
| 40_10 | 5.342147854389e+02 | **5.341774034561e+02** | *5.342147854389e+02* | *5.335118301275e+02* |
| 40_11 | *5.436017375290e+02* | *5.425993564114e+02* | *5.438165899050e+02* | *5.408366253225e+02* |
| 40_12 | *5.554749221849e+02* | *5.551646543876e+02* | *5.555797800742e+02* | *5.536019805558e+02* |
| 40_13 | 6.041845449053e+02 | **6.041310201456e+02** | *6.041845449053e+02** | *6.038408656778e+02* |
| 40_14 | *5.079152242421e+02* | *5.063775445982e+02* | *5.080760355234e+02* | *5.049444295104e+02* |
| 40_15 | 5.602270842849e+02 | **5.601881709840e+02** | *5.602270735171e+02* | *5.598917487576e+02* |
`*` : `Warning: max constraint violation (.) exceeds tolerance`
$\overline{z}$ : 最適値の上界(暫定解の目的関数値)
$\underline{z}$ : 最適値の下界
**太字** : 最適解を求められたが、最適値の上下界が一致しなかった
*斜字* : 制限時間(4時間)内に最適解を求められなかった
40_02N : 0.1125 %
40_03P : 0.5853 %
40_03N : 0.9214 %
40_04N : 0.1687 %
40_05N : 0.0647 %
40_06P : 0.0137 %
40_06N : 0.3129 %
40_07P : 0.1936 %
40_07N : 0.7425 %
40_08P : 0.1770 %
40_08N : 0.4301 %
40_09P : 0.1337 %
40_09N : 0.2550 %
40_10N : 0.1316 %
40_11P : 0.1844 %
40_11N : 0.5480 %
40_12P : 0.0559 %
40_12N : 0.3560 %
40_13N : 0.0569 %
40_14P : 0.3027 %
40_14N : 0.6164 %
40_15N : 0.0599 %
----
#### $|V| = 20$でPFの方が時間がかかったケース
`20_07`
```
Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (mac64[arm])
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 705 rows, 1900 columns and 5320 nonzeros
Model fingerprint: 0x46bc2ab4
Model has 76 quadratic constraints
Variable types: 1824 continuous, 76 integer (76 binary)
Coefficient statistics:
Matrix range [2e-04, 8e+02]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 4e+00]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 3e+02]
Presolve removed 153 rows and 79 columns
Presolve time: 0.01s
Presolved: 552 rows, 1821 columns, 5014 nonzeros
Presolved model has 76 quadratic constraint(s)
Variable types: 1747 continuous, 74 integer (74 binary)
Root relaxation: objective 6.933877e+01, 1226 iterations, 0.04 seconds (0.02 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 69.33877 0 61 - 69.33877 - - 0s
0 0 105.15801 0 52 - 105.15801 - - 0s
0 0 132.96068 0 46 - 132.96068 - - 0s
0 0 143.68980 0 38 - 143.68980 - - 0s
0 0 143.73790 0 39 - 143.73790 - - 0s
0 0 147.06550 0 39 - 147.06550 - - 0s
0 0 147.07912 0 37 - 147.07912 - - 0s
0 0 147.94496 0 39 - 147.94496 - - 0s
0 0 147.94521 0 39 - 147.94521 - - 0s
0 0 148.32026 0 37 - 148.32026 - - 0s
0 0 148.36095 0 37 - 148.36095 - - 0s
0 0 148.52858 0 37 - 148.52858 - - 0s
0 0 148.54852 0 39 - 148.54852 - - 0s
0 0 148.64228 0 38 - 148.64228 - - 0s
0 0 148.68450 0 38 - 148.68450 - - 0s
0 0 148.70942 0 39 - 148.70942 - - 0s
0 0 148.72633 0 38 - 148.72633 - - 0s
0 0 148.73688 0 39 - 148.73688 - - 0s
0 0 148.74311 0 38 - 148.74311 - - 0s
0 0 148.74639 0 38 - 148.74639 - - 0s
0 0 148.74841 0 39 - 148.74841 - - 0s
0 0 148.74986 0 38 - 148.74986 - - 0s
0 0 148.75093 0 39 - 148.75093 - - 0s
0 0 148.75167 0 39 - 148.75167 - - 0s
0 0 148.75205 0 37 - 148.75205 - - 0s
0 0 148.75234 0 38 - 148.75234 - - 0s
0 0 148.75297 0 39 - 148.75297 - - 0s
0 0 148.75339 0 39 - 148.75339 - - 0s
0 0 148.75377 0 38 - 148.75377 - - 0s
0 0 148.75437 0 39 - 148.75437 - - 0s
0 0 148.75485 0 37 - 148.75485 - - 0s
0 0 148.75520 0 38 - 148.75520 - - 0s
0 0 148.75592 0 37 - 148.75592 - - 0s
0 0 148.75660 0 38 - 148.75660 - - 0s
0 0 148.75714 0 39 - 148.75714 - - 0s
0 0 148.75755 0 37 - 148.75755 - - 0s
0 0 148.75819 0 39 - 148.75819 - - 0s
0 0 148.75863 0 39 - 148.75863 - - 0s
0 0 148.75906 0 38 - 148.75906 - - 0s
0 0 148.75935 0 38 - 148.75935 - - 0s
0 0 148.75962 0 39 - 148.75962 - - 0s
0 0 148.75982 0 39 - 148.75982 - - 0s
0 0 148.76012 0 38 - 148.76012 - - 0s
0 0 148.76044 0 37 - 148.76044 - - 0s
0 0 148.76067 0 38 - 148.76067 - - 0s
0 0 148.76091 0 39 - 148.76091 - - 0s
0 0 148.76144 0 39 - 148.76144 - - 0s
0 0 148.76195 0 39 - 148.76195 - - 0s
0 0 148.76229 0 37 - 148.76229 - - 0s
0 0 148.76280 0 38 - 148.76280 - - 0s
0 0 148.76324 0 38 - 148.76324 - - 0s
0 0 148.76386 0 39 - 148.76386 - - 0s
0 0 148.76433 0 39 - 148.76433 - - 0s
0 0 148.76458 0 39 - 148.76458 - - 0s
0 0 148.76474 0 37 - 148.76474 - - 0s
0 0 148.76501 0 39 - 148.76501 - - 0s
0 0 148.76524 0 39 - 148.76524 - - 0s
0 0 148.76542 0 38 - 148.76542 - - 0s
0 0 148.76564 0 37 - 148.76564 - - 0s
0 0 148.76595 0 38 - 148.76595 - - 0s
0 0 148.76641 0 38 - 148.76641 - - 0s
0 0 148.76682 0 37 - 148.76682 - - 0s
0 0 148.76728 0 39 - 148.76728 - - 0s
0 0 148.76758 0 37 - 148.76758 - - 0s
0 0 148.76786 0 39 - 148.76786 - - 0s
0 0 148.76817 0 38 - 148.76817 - - 0s
0 0 148.76841 0 38 - 148.76841 - - 0s
0 0 148.76870 0 37 - 148.76870 - - 0s
0 0 148.76901 0 39 - 148.76901 - - 0s
0 0 148.76933 0 39 - 148.76933 - - 0s
0 0 148.76961 0 39 - 148.76961 - - 0s
0 0 148.76998 0 39 - 148.76998 - - 0s
0 0 148.77022 0 39 - 148.77022 - - 0s
0 0 148.77041 0 39 - 148.77041 - - 0s
0 0 148.77068 0 38 - 148.77068 - - 0s
0 0 148.77090 0 38 - 148.77090 - - 0s
0 0 148.77105 0 39 - 148.77105 - - 0s
0 0 148.77160 0 38 - 148.77160 - - 0s
0 0 148.77196 0 38 - 148.77196 - - 0s
0 0 148.77231 0 36 - 148.77231 - - 0s
0 0 148.77265 0 39 - 148.77265 - - 0s
0 0 148.77294 0 39 - 148.77294 - - 0s
0 0 148.77331 0 38 - 148.77331 - - 0s
0 0 148.77367 0 38 - 148.77367 - - 0s
0 0 148.77392 0 39 - 148.77392 - - 0s
0 0 148.77412 0 39 - 148.77412 - - 0s
0 0 148.77437 0 38 - 148.77437 - - 0s
0 0 148.77467 0 37 - 148.77467 - - 0s
0 0 148.77492 0 39 - 148.77492 - - 0s
0 0 148.77516 0 39 - 148.77516 - - 0s
0 0 148.77556 0 39 - 148.77556 - - 0s
0 0 148.77594 0 38 - 148.77594 - - 0s
0 0 148.77621 0 37 - 148.77621 - - 0s
0 0 148.77646 0 38 - 148.77646 - - 0s
0 0 148.77670 0 37 - 148.77670 - - 0s
0 0 148.77716 0 38 - 148.77716 - - 0s
0 0 148.77754 0 39 - 148.77754 - - 0s
0 0 148.77782 0 38 - 148.77782 - - 0s
0 0 148.77817 0 37 - 148.77817 - - 0s
0 0 148.77851 0 38 - 148.77851 - - 0s
0 0 148.77877 0 38 - 148.77877 - - 0s
0 0 148.77914 0 39 - 148.77914 - - 0s
0 0 148.77946 0 38 - 148.77946 - - 0s
0 0 148.77974 0 38 - 148.77974 - - 0s
0 0 148.78006 0 39 - 148.78006 - - 0s
0 0 148.78035 0 39 - 148.78035 - - 0s
0 2 148.78035 0 39 - 148.78035 - - 0s
H 2016 966 170.8892581 154.48708 9.60% 43.3 2s
* 2016 966 62 170.8892581 154.48708 9.60% 43.3 2s
H 2144 871 169.0815732 156.96927 7.16% 46.5 2s
H 2575 689 168.7372464 159.52525 5.46% 59.1 3s
* 2575 689 78 168.7372464 159.52525 5.46% 59.2 3s
H 3449 511 168.7011130 164.12748 2.71% 80.4 4s
* 3449 511 40 168.7011130 164.12748 2.71% 80.4 4s
3893 389 cutoff 39 168.70111 165.45561 1.92% 87.9 5s
H 4430 80 168.3353499 167.16165 0.70% 93.7 5s
* 4430 80 47 168.3353499 167.16165 0.70% 93.8 5s
Explored 4533 nodes (427982 simplex iterations) in 5.84 seconds (10.24 work units)
Thread count was 8 (of 8 available processors)
Solution count 5: 168.335 168.701 168.737 ... 170.889
Optimal solution found (tolerance 1.00e-04)
Warning: max constraint violation (2.9611e-06) exceeds tolerance
Best objective 1.683353499458e+02, best bound 1.683353499458e+02, gap 0.0000%
```
```
Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (mac64[arm])
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 705 rows, 1900 columns and 5244 nonzeros
Model fingerprint: 0x595f6ff7
Model has 76 quadratic constraints
Variable types: 1824 continuous, 76 integer (76 binary)
Coefficient statistics:
Matrix range [2e-04, 8e+02]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 4e+00]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 8e+02]
Presolve removed 79 rows and 79 columns
Presolve time: 0.00s
Presolved: 626 rows, 1821 columns, 5088 nonzeros
Presolved model has 76 quadratic constraint(s)
Variable types: 1747 continuous, 74 integer (74 binary)
Root relaxation: objective 6.933877e+01, 1052 iterations, 0.02 seconds (0.02 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 69.33877 0 61 - 69.33877 - - 0s
0 0 87.63983 0 70 - 87.63983 - - 0s
H 0 0 184.0764321 87.63983 52.4% - 0s
0 0 102.49449 0 65 184.07643 102.49449 44.3% - 0s
0 0 129.41586 0 51 184.07643 129.41586 29.7% - 0s
0 0 129.41586 0 41 184.07643 129.41586 29.7% - 0s
0 0 129.41586 0 41 184.07643 129.41586 29.7% - 0s
0 0 134.89613 0 38 184.07643 134.89613 26.7% - 0s
0 0 134.89613 0 37 184.07643 134.89613 26.7% - 0s
0 0 135.37013 0 35 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 35 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 33 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 33 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 33 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 33 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 34 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 34 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 35 184.07643 135.37013 26.5% - 0s
0 0 135.37013 0 35 184.07643 135.37013 26.5% - 0s
H 0 0 181.5623361 135.37013 25.4% - 0s
0 2 135.98735 0 32 181.56234 135.98735 25.1% - 0s
H 165 164 180.5565747 143.27211 20.6% 87.6 0s
H 252 209 176.3322100 143.46022 18.6% 91.4 0s
* 252 209 34 176.3322100 143.46022 18.6% 91.4 0s
H 303 246 175.4532924 143.46022 18.2% 95.2 0s
H 613 351 175.4025846 149.82524 14.6% 122 2s
H 627 343 173.6163707 149.82524 13.7% 123 2s
H 645 328 173.6163691 149.82524 13.7% 123 2s
H 901 379 171.9163253 152.47649 11.3% 138 3s
H 912 376 169.9321906 152.47649 10.3% 138 3s
H 1004 380 169.7996062 152.47649 10.2% 139 3s
H 1033 376 169.7995896 153.03147 9.88% 140 3s
H 1060 363 169.7995679 153.03147 9.88% 142 3s
H 1126 373 168.7372464 153.03147 9.31% 145 4s
* 1126 373 69 168.7372464 153.03147 9.31% 145 4s
1480 445 161.86578 31 24 168.73725 155.53567 7.82% 156 5s
H 3005 476 168.3353499 164.27962 2.41% 184 8s
3514 232 cutoff 44 168.33535 165.67672 1.58% 189 10s
Explored 3941 nodes (741947 simplex iterations) in 10.89 seconds (21.47 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: 168.335 168.737 169.8 ... 180.557
Optimal solution found (tolerance 1.00e-04)
Best objective 1.683353499458e+02, best bound 1.683353499458e+02, gap 0.0000%
```
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