---
# System prepended metadata

title: Untitled

---

## 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%

```