如何解决优化具有二元变量的对称 MIP 的 Gurobi 模型 (PuLP)
简而言之；有没有可能更快地解决这个问题？
显然，原始链接解决方案的作者使用SAS在不到一个小时的时间内解决了问题。对我来说，使用 GUROBI 学术许可证在我的笔记本电脑上花了 3 个半小时。
我正在尝试进行整数线性规划。对于我的第一个项目，我想复制解决“8 soldiers lining up for the morning assembly”问题的结果。简而言之，它归结为：
设 P 是 8 个符号的所有排列的集合。让二元决策变量 xₐ 表示置换 a∈P 是否出现在解决方案中。对于 8⋅7⋅6=336 个三元组 t∈T 中的每一个，让 Pₜ⊂P 是包含该三元组的排列子集。问题是最大化：
The (sum of xₐ over all a∈P),subject to (sum of all xₐ across all a∈Pₜ)
我在通用代码中定义了排列（对于 N 个符号和 M-let，然后对于三元组，N=8 和 M=3。）
procedure SetPropertiesForPages(InputOptionWP: TInputOptionWizardPage; TextWP: TOutputMsgWizardPage; SelectDirWP: TInputDirWizardPage; InputQueryWP: TInputQueryWizardPage; Mode: String; AWordWrap: Boolean; AWidth,AHeight,ALeft,ATop: Integer);
begin
case Lowercase(Mode) of
'text':
begin
biLeftSideImage := CreateBitmapImage(TextWP,ExpandConstant('{tmp}\LefthandsideImg.bmp'),True,0);
with TextWP do
begin
MsgLabel.WordWrap := AWordWrap;
MsgLabel.Width := AWidth;
MsgLabel.Height := AHeight;
MsgLabel.Left := ALeft;
end;
end;
'inputoption1':
begin
biLeftSideImage := CreateBitmapImage(InputOptionWP,0);
with InputOptionWP do
begin
SubCaptionLabel.WordWrap := AWordWrap;
SubCaptionLabel.Width := AWidth;
SubCaptionLabel.Left := ALeft;
SubCaptionLabel.Top := ATop;
CheckListBox.Width := AWidth;
CheckListBox.Height := AHeight;
CheckListBox.Left := ALeft;
CheckListBox.Top := ATop + SubCaptionLabel.Height + ScaleY(20);
end;
end;
'inputoption2':
begin
biLeftSideImage := CreateBitmapImage(InputOptionWP,0);
with InputOptionWP do
begin
SubCaptionLabel.WordWrap := AWordWrap;
SubCaptionLabel.Width := AWidth;
SubCaptionLabel.Height := 6 * AHeight + ScaleY(5);
SubCaptionLabel.Left := ALeft;
SubCaptionLabel.Top := ATop;
CheckListBox.Width := AWidth;
CheckListBox.Height := AHeight + ScaleY(40);
CheckListBox.Left := ALeft;
CheckListBox.Top := ATop + SubCaptionLabel.Height + ScaleY(5);
end;
end;
'selectdir':
begin
biLeftSideImage := CreateBitmapImage(SelectDirWP,0);
with SelectDirWP do
begin
Edits[0].ReadOnly := True;
Edits[1].ReadOnly := True;
Edits[0].Left := ALeft;
Edits[1].Left := ALeft;
Edits[0].Width := AWidth - ScaleX(70);
Edits[1].Width := AWidth - ScaleX(70);
Buttons[0].Left := Edits[0].Left + Edits[0].Width + ScaleX(10);
Buttons[1].Left := Edits[1].Left + Edits[1].Width + ScaleX(10);
PromptLabels[0].Left := ALeft;
PromptLabels[1].Left := ALeft;
SubCaptionLabel.WordWrap := AWordWrap;
SubCaptionLabel.Width := AWidth;
SubCaptionLabel.Left := ALeft;
SubCaptionLabel.Top := ATop;
end;
end;
'inputquery':
begin
biLeftSideImage := CreateBitmapImage(InputQueryWP,0);
with InputQueryWP do
begin
Edits[0].Left := ALeft;
Edits[0].Width := AWidth - ScaleX(75);
PromptLabels[0].Left := ALeft;
SubCaptionLabel.WordWrap := AWordWrap;
SubCaptionLabel.Width := AWidth;
SubCaptionLabel.Height := AHeight;
SubCaptionLabel.Left := ALeft;
SubCaptionLabel.Top := ATop;
end;
end;
end;
end;
然后用这个来定义模型（有 8 小时的时间限制）
from sympy.utilities.iterables import permutations
from sympy import factorial
N,M = 8,3
P = ''.join([str(_) for _ in range(N)])
T = {''.join(p):set() for p in permutations(P,M)}
I,J = {},{}
for i,p in enumerate(permutations(P)):
permutation = ''.join(p)
I[permutation],J[i] = i,permutation
for j in range(N-M+1):
T[permutation[j:j+M]].add(permutation)
upper_bound = len(T)//(N-M+1)
print(f"Total of {N}!={factorial(N)} permutations and {len(T)} {M}-subpermutations are ready.")
print(f"Upper bound: {upper_bound}.")
注意事项：
- 由于对称性，我添加了
from pulp import LpMaximize,LpProblem,LpStatus,lpSum,LpVariable,GUROBI x = {i: LpVariable(name=f"x{i}",cat="Binary") for i in range(factorial(N))} model = LpProblem(name=f"{N}_soldiers_{M}_puzzle",sense=LpMaximize) for i,t in enumerate(T.keys()): model += (lpSum([x[I[p]] for p in T[t]]) <= 1,f"constrain{i}") model += (x[0] == 1,"WLOG") objective = lpSum([x[i] for i in range(factorial(N))]) model += (objective <= upper_bound,"upper_bound") model += objective print("\nStarting GUROBI solver...") status = model.solve(solver=GUROBI(msg=True,timeLimit=60*60*8,LogToConsole=0))。但是，我不知道如何进一步利用对称性。 - 我添加了
model += (x[0] == 1,"WLOG")条件，但它似乎没有任何区别。
显然，原始链接解决方案的作者使用 SAS 在不到一个小时的时间内解决了问题。
对我来说，在我的笔记本电脑上使用这个 GUROBI 模型需要花费数小时甚至更多时间。我们可以优化它以更快吗？或者是否有其他一些 PuLP 可以使用的求解器在这个模型上效果更好？ （在 GLPK 一夜之间未能解决之后，我改用了学术 gurobi 许可证。）
我最新的日志文件（为了字符限制不得不缩短它）：
"upper_bound"它似乎很快就能找到 55 的解决方案，但要找到最佳的 56 解决方案却要花很长时间。最终，在 3 个半小时后，我得到了一个解决方案：
Gurobi Optimizer version 9.1.1 build v9.1.1rc0 (win64)
Thread count: 4 physical cores,4 logical processors,using up to 4 threads
Optimize a model with 338 rows,40320 columns and 282241 nonzeros
Model fingerprint: 0xa0617a52
Variable types: 0 continuous,40320 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00,1e+00]
Objective range [1e+00,1e+00]
Bounds range [1e+00,1e+00]
RHS range [1e+00,6e+01]
Found heuristic solution: objective 43.0000000
Presolve removed 7 rows and 3624 columns
Presolve time: 0.88s
Presolved: 331 rows,36696 columns,256872 nonzeros
Variable types: 0 continuous,36696 integer (36696 binary)
Starting sifting (using dual simplex for sub-problems)...
Iter Pivots Primal Obj Dual Obj Time
0 0 infinity -4.7000000e+02 1s
1 306 1.9619997e+09 -1.8714284e+02 1s
2 1956 -3.2453701e+01 -9.5576700e+01 1s
3 4263 -3.7141380e+01 -6.0449129e+01 2s
4 6546 -5.3519665e+01 -5.9851524e+01 2s
5 8510 -5.5832220e+01 -5.8952552e+01 3s
Sifting complete
Root relaxation: objective 5.600000e+01,10313 iterations,1.97 seconds
Total elapsed time = 17.14s
Total elapsed time = 24.25s
Total elapsed time = 48.86s
Total elapsed time = 53.33s
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 56.00000 0 165 43.00000 56.00000 30.2% - 59s
H 0 0 52.0000000 56.00000 7.69% - 61s
H 0 0 54.0000000 56.00000 3.70% - 100s
0 0 56.00000 0 298 54.00000 56.00000 3.70% - 102s
0 0 56.00000 0 140 54.00000 56.00000 3.70% - 214s
H 0 0 55.0000000 56.00000 1.82% - 246s
0 0 56.00000 0 161 55.00000 56.00000 1.82% - 247s
0 0 56.00000 0 228 55.00000 56.00000 1.82% - 250s
0 0 56.00000 0 212 55.00000 56.00000 1.82% - 277s
0 0 56.00000 0 285 55.00000 56.00000 1.82% - 329s
0 0 56.00000 0 257 55.00000 56.00000 1.82% - 345s
0 0 56.00000 0 257 55.00000 56.00000 1.82% - 348s
0 2 56.00000 0 253 55.00000 56.00000 1.82% - 364s
2 3 56.00000 1 257 55.00000 56.00000 1.82% 8759 387s
4 4 56.00000 1 147 55.00000 56.00000 1.82% 4380 575s
5 5 56.00000 1 134 55.00000 56.00000 1.82% 3504 743s
6 6 56.00000 1 144 55.00000 56.00000 1.82% 2920 781s
7 6 56.00000 1 254 55.00000 56.00000 1.82% 2503 819s
8 7 56.00000 1 290 55.00000 56.00000 1.82% 2190 841s
9 8 56.00000 1 280 55.00000 56.00000 1.82% 1946 875s
10 8 56.00000 1 294 55.00000 56.00000 1.82% 1752 891s
11 9 56.00000 1 294 55.00000 56.00000 1.82% 1593 899s
12 10 56.00000 1 284 55.00000 56.00000 1.82% 1460 915s
13 10 56.00000 1 317 55.00000 56.00000 1.82% 1348 924s
14 11 56.00000 1 314 55.00000 56.00000 1.82% 1251 950s
15 12 56.00000 1 320 55.00000 56.00000 1.82% 1168 958s
16 12 56.00000 1 331 55.00000 56.00000 1.82% 1095 998s
17 13 56.00000 1 320 55.00000 56.00000 1.82% 1030 1024s
18 14 56.00000 1 320 55.00000 56.00000 1.82% 973 1093s
19 17 56.00000 14 333 55.00000 56.00000 1.82% 16480 1161s
21 21 56.00000 15 333 55.00000 56.00000 1.82% 14954 1234s
25 23 56.00000 16 332 55.00000 56.00000 1.82% 12618 1286s
29 26 56.00000 16 324 55.00000 56.00000 1.82% 10952 1346s
33 29 56.00000 17 333 55.00000 56.00000 1.82% 9669 1372s
37 31 56.00000 17 328 55.00000 56.00000 1.82% 8648 1405s
41 34 56.00000 18 333 55.00000 56.00000 1.82% 7821 1428s
45 37 56.00000 18 327 55.00000 56.00000 1.82% 7150 1579s
49 42 56.00000 19 333 55.00000 56.00000 1.82% 6576 1611s
56 47 56.00000 20 333 55.00000 56.00000 1.82% 5778 1642s
63 78 56.00000 21 334 55.00000 56.00000 1.82% 5160 1733s
95 221 56.00000 23 334 55.00000 56.00000 1.82% 3480 1900s
250 303 56.00000 27 321 55.00000 56.00000 1.82% 1421 2081s
1258 322 56.00000 55 121 55.00000 56.00000 1.82% 602 2118s
2173 333 infeasible 64 55.00000 56.00000 1.82% 548 2144s
2884 385 56.00000 57 131 55.00000 56.00000 1.82% 532 2166s
3596 411 infeasible 58 55.00000 56.00000 1.82% 515 2189s
3968 424 56.00000 43 234 55.00000 56.00000 1.82% 507 2230s
3981 443 56.00000 44 234 55.00000 56.00000 1.82% 506 2267s
4000 517 56.00000 48 233 55.00000 56.00000 1.82% 504 2292s
4380 518 56.00000 73 153 55.00000 56.00000 1.82% 497 2378s
4387 565 56.00000 74 153 55.00000 56.00000 1.82% 496 2399s
5294 556 56.00000 56 120 55.00000 56.00000 1.82% 492 2437s
5485 594 56.00000 57 123 55.00000 56.00000 1.82% 491 2460s
5915 712 infeasible 57 55.00000 56.00000 1.82% 489 2484s
6561 721 infeasible 68 55.00000 56.00000 1.82% 483 2507s
7614 756 56.00000 73 139 55.00000 56.00000 1.82% 484 2528s
8751 776 56.00000 41 184 55.00000 56.00000 1.82% 484 2548s
9929 795 56.00000 76 137 55.00000 56.00000 1.82% 486 2569s
11200 833 56.00000 75 154 55.00000 56.00000 1.82% 488 2648s
13684 840 56.00000 69 139 55.00000 56.00000 1.82% 495 2663s
14584 881 56.00000 42 178 55.00000 56.00000 1.82% 496 2678s
14725 945 56.00000 60 167 55.00000 56.00000 1.82% 495 2692s
15603 952 56.00000 84 143 55.00000 56.00000 1.82% 494 2709s
16132 1027 56.00000 62 148 55.00000 56.00000 1.82% 495 2726s
16783 1077 infeasible 92 55.00000 56.00000 1.82% 494 2739s
17705 1055 56.00000 58 128 55.00000 56.00000 1.82% 494 2751s
18547 1034 infeasible 72 55.00000 56.00000 1.82% 495 2763s
19242 1058 infeasible 81 55.00000 56.00000 1.82% 495 2774s
20032 1040 infeasible 95 55.00000 56.00000 1.82% 496 2786s
20772 1048 infeasible 77 55.00000 56.00000 1.82% 497 2797s
21530 1133 56.00000 86 152 55.00000 56.00000 1.82% 498 3287s
23023 1114 56.00000 74 134 55.00000 56.00000 1.82% 498 3304s
23838 1117 56.00000 84 134 55.00000 56.00000 1.82% 499 3317s
24509 1088 infeasible 98 55.00000 56.00000 1.82% 501 3330s
25326 1079 infeasible 78 55.00000 56.00000 1.82% 502 3344s
25999 1058 56.00000 74 135 55.00000 56.00000 1.82% 503 3356s
26666 1050 infeasible 89 55.00000 56.00000 1.82% 504 3367s
27396 1076 56.00000 76 126 55.00000 56.00000 1.82% 506 3445s
28034 1071 56.00000 81 140 55.00000 56.00000 1.82% 506 3458s
28879 1111 56.00000 77 151 55.00000 56.00000 1.82% 506 3470s
29474 1108 56.00000 71 135 55.00000 56.00000 1.82% 506 3485s
30263 1167 infeasible 93 55.00000 56.00000 1.82% 507 3498s
31138 1143 infeasible 90 55.00000 56.00000 1.82% 507 3510s
31960 1144 56.00000 74 142 55.00000 56.00000 1.82% 507 3624s
31967 1090 56.00000 75 142 55.00000 56.00000 1.82% 507 3636s
32569 1064 infeasible 63 55.00000 56.00000 1.82% 508 3648s
33337 1035 infeasible 91 55.00000 56.00000 1.82% 509 3660s
34006 1092 56.00000 67 140 55.00000 56.00000 1.82% 510 3671s
34805 1143 infeasible 72 55.00000 56.00000 1.82% 509 3717s
36468 1176 infeasible 84 55.00000 56.00000 1.82% 509 3730s
36863 1193 56.00000 71 132 55.00000 56.00000 1.82% 509 3745s
37318 1171 56.00000 75 141 55.00000 56.00000 1.82% 509 3760s
37802 1131 infeasible 76 55.00000 56.00000 1.82% 509 3775s
38288 1100 infeasible 74 55.00000 56.00000 1.82% 510 3789s
39133 1060 56.00000 61 121 55.00000 56.00000 1.82% 510 3802s
39967 1095 infeasible 83 55.00000 56.00000 1.82% 511 3814s
40728 1135 56.00000 58 154 55.00000 56.00000 1.82% 511 3827s
41362 1104 56.00000 90 128 55.00000 56.00000 1.82% 511 3841s
41973 1133 56.00000 68 146 55.00000 56.00000 1.82% 512 3854s
42664 1152 56.00000 77 151 55.00000 56.00000 1.82% 512 3867s
43363 1140 infeasible 88 55.00000 56.00000 1.82% 513 3879s
44043 1155 56.00000 81 144 55.00000 56.00000 1.82% 514 3890s
44399 1091 infeasible 79 55.00000 56.00000 1.82% 514 3902s
45077 1159 56.00000 60 151 55.00000 56.00000 1.82% 515 3914s
45801 1168 infeasible 75 55.00000 56.00000 1.82% 516 3956s
47178 1197 56.00000 71 151 55.00000 56.00000 1.82% 517 3982s
47467 1190 infeasible 80 55.00000 56.00000 1.82% 517 3996s
48262 1164 56.00000 81 132 55.00000 56.00000 1.82% 518 4010s
49032 1185 infeasible 88 55.00000 56.00000 1.82% 519 4022s
49785 1214 56.00000 81 151 55.00000 56.00000 1.82% 520 4033s
50534 1157 infeasible 88 55.00000 56.00000 1.82% 520 4045s
51183 1121 infeasible 83 55.00000 56.00000 1.82% 521 4056s
51835 1081 infeasible 91 55.00000 56.00000 1.82% 522 4067s
52241 1075 infeasible 89 55.00000 56.00000 1.82% 522 4079s
52801 1150 infeasible 85 55.00000 56.00000 1.82% 523 4092s
53438 1151 56.00000 60 148 55.00000 56.00000 1.82% 522 4169s
53445 1200 56.00000 61 147 55.00000 56.00000 1.82% 522 4181s
54146 1252 infeasible 89 55.00000 56.00000 1.82% 521 4202s
54758 1247 56.00000 76 125 55.00000 56.00000 1.82% 521 4213s
55573 1297 56.00000 80 139 55.00000 56.00000 1.82% 520 4223s
56237 1302 infeasible 67 55.00000 56.00000 1.82% 520 4264s
57604 1334 56.00000 65 139 55.00000 56.00000 1.82% 519 4275s
58328 1245 56.00000 70 128 55.00000 56.00000 1.82% 519 4284s
58917 1220 infeasible 96 55.00000 56.00000 1.82% 519 4293s
59566 1214 infeasible 106 55.00000 56.00000 1.82% 519 4303s
60048 1328 infeasible 79 55.00000 56.00000 1.82% 519 4331s
60576 1324 infeasible 102 55.00000 56.00000 1.82% 518 4415s
60588 1349 56.00000 87 134 55.00000 56.00000 1.82% 518 4426s
61361 1326 infeasible 88 55.00000 56.00000 1.82% 518 4436s
62074 1326 56.00000 59 148 55.00000 56.00000 1.82% 517 4446s
62640 1411 infeasible 75 55.00000 56.00000 1.82% 518 4457s
63277 1353 infeasible 79 55.00000 56.00000 1.82% 517 4490s
63713 1374 56.00000 72 142 55.00000 56.00000 1.82% 518 4517s
64314 1376 infeasible 100 55.00000 56.00000 1.82% 517 4535s
65036 1482 56.00000 72 144 55.00000 56.00000 1.82% 518 4548s
65766 1463 infeasible 84 55.00000 56.00000 1.82% 517 4561s
66389 1481 infeasible 115 55.00000 56.00000 1.82% 516 4574s
66588 1481 56.00000 77 132 55.00000 56.00000 1.82% 516 4576s
67121 1453 infeasible 88 55.00000 56.00000 1.82% 516 4622s
68467 1463 infeasible 90 55.00000 56.00000 1.82% 517 4633s
68891 1433 infeasible 62 55.00000 56.00000 1.82% 516 4650s
69379 1476 56.00000 63 141 55.00000 56.00000 1.82% 517 4664s
70167 1472 infeasible 77 55.00000 56.00000 1.82% 516 4676s
70907 1401 56.00000 79 135 55.00000 56.00000 1.82% 516 4689s
71564 1360 56.00000 96 139 55.00000 56.00000 1.82% 517 4716s
72197 1355 infeasible 80 55.00000 56.00000 1.82% 517 4738s
72826 1375 56.00000 67 140 55.00000 56.00000 1.82% 518 4755s
73520 1342 56.00000 79 137 55.00000 56.00000 1.82% 517 4820s
73812 1342 infeasible 100 55.00000 56.00000 1.82% 518 4834s
74252 1359 56.00000 57 143 55.00000 56.00000 1.82% 518 4845s
74979 1292 56.00000 60 141 55.00000 56.00000 1.82% 518 4857s
75656 1337 infeasible 67 55.00000 56.00000 1.82% 519 4868s
76357 1384 infeasible 77 55.00000 56.00000 1.82% 519 4885s
77046 1436 56.00000 85 151 55.00000 56.00000 1.82% 519 4903s
77680 1612 infeasible 111 55.00000 56.00000 1.82% 519 4948s
79106 1645 infeasible 85 55.00000 56.00000 1.82% 518 4960s
79699 1660 infeasible 82 55.00000 56.00000 1.82% 518 4971s
80278 1586 infeasible 62 55.00000 56.00000 1.82% 518 4980s
80854 1554 56.00000 68 124 55.00000 56.00000 1.82% 518 5007s
81420 1551 infeasible 67 55.00000 56.00000 1.82% 518 5016s
82081 1479 56.00000 89 141 55.00000 56.00000 1.82% 518 5026s
82657 1603 infeasible 59 55.00000 56.00000 1.82% 519 5035s
83353 1607 infeasible 79 55.00000 56.00000 1.82% 518 5044s
84049 1613 infeasible 69 55.00000 56.00000 1.82% 518 5053s
84709 1565 infeasible 81 55.00000 56.00000 1.82% 518 5062s
85333 1546 infeasible 69 55.00000 56.00000 1.82% 518 5072s
85998 1552 infeasible 89 55.00000 56.00000 1.82% 518 5083s
86658 1650 56.00000 104 139 55.00000 56.00000 1.82% 518 5091s
87162 1655 infeasible 87 55.00000 56.00000 1.82% 517 5100s
87801 1676 infeasible 75 55.00000 56.00000 1.82% 517 5109s
88114 1676 56.00000 91 127 55.00000 56.00000 1.82% 517 5111s
88442 1609 56.00000 86 134 55.00000 56.00000 1.82% 517 5146s
89775 1525 infeasible 91 55.00000 56.00000 1.82% 517 5155s
90351 1522 56.00000 81 141 55.00000 56.00000 1.82% 517 5166s
90882 1518 56.00000 81 124 55.00000 56.00000 1.82% 517 5175s
91464 1540 infeasible 90 55.00000 56.00000 1.82% 518 5184s
92116 1525 56.00000 81 132 55.00000 56.00000 1.82% 517 5193s
92673 1492 infeasible 72 55.00000 56.00000 1.82% 517 5203s
93284 1581 infeasible 81 55.00000 56.00000 1.82% 517 5212s
93969 1584 infeasible 89 55.00000 56.00000 1.82% 517 5221s
94538 1508 56.00000 53 132 55.00000 56.00000 1.82% 517 5231s
95024 1495 56.00000 72 134 55.00000 56.00000 1.82% 517 5240s
95651 1472 infeasible 81 55.00000 56.00000 1.82% 517 5283s
95912 1472 infeasible 84 55.00000 56.00000 1.82% 517 5362s
95920 1448 56.00000 78 135 55.00000 56.00000 1.82% 517 5373s
96484 1435 infeasible 70 55.00000 56.00000 1.82% 517 5383s
97101 1453 56.00000 79 148 55.00000 56.00000 1.82% 517 5395s
97649 1414 56.00000 73 138 55.00000 56.00000 1.82% 517 5405s
98152 1376 56.00000 67 126 55.00000 56.00000 1.82% 518 5415s
98644 1484 56.00000 68 141 55.00000 56.00000 1.82% 518 5427s
99118 1468 56.00000 75 149 55.00000 56.00000 1.82% 518 5461s
100424 1416 infeasible 85 55.00000 56.00000 1.82% 517 5471s
100940 1426 infeasible 67 55.00000 56.00000 1.82% 518 5481s
101520 1435 56.00000 83 124 55.00000 56.00000 1.82% 518 5491s
102149 1388 infeasible 76 55.00000 56.00000 1.82% 517 5572s
102558 1392 56.00000 102 140 55.00000 56.00000 1.82% 518 5585s
103392 1444 infeasible 84 55.00000 56.00000 1.82% 518 5596s
104180 1433 infeasible 77 55.00000 56.00000 1.82% 518 5606s
104927 1478 infeasible 77 55.00000 56.00000 1.82% 517 5617s
105734 1463 56.00000 83 154 55.00000 56.00000 1.82% 517 5627s
106509 1458 56.00000 95 133 55.00000 56.00000 1.82% 517 5638s
107180 1458 56.00000 71 129 55.00000 56.00000 1.82% 517 5647s
107942 1416 infeasible 81 55.00000 56.00000 1.82% 516 5657s
108570 1442 56.00000 67 153 55.00000 56.00000 1.82% 517 5667s
109216 1433 56.00000 99 154 55.00000 56.00000 1.82% 517 5718s
109825 1435 56.00000 96 147 55.00000 56.00000 1.82% 517 5729s
110528 1481 infeasible 77 55.00000 56.00000 1.82% 517 5740s
111210 1453 infeasible 83 55.00000 56.00000 1.82% 517 5774s
112332 1477 56.00000 94 125 55.00000 56.00000 1.82% 517 5783s
112948 1500 56.00000 85 131 55.00000 56.00000 1.82% 518 5793s
113569 1560 infeasible 101 55.00000 56.00000 1.82% 518 5803s
114235 1493 infeasible 86 55.00000 56.00000 1.82% 518 5812s
114852 1498 56.00000 87 141 55.00000 56.00000 1.82% 518 5821s
115485 1526 56.00000 85 153 55.00000 56.00000 1.82% 518 5831s
116033 1491 infeasible 105 55.00000 56.00000 1.82% 518 5841s
116606 1448 56.00000 105 146 55.00000 56.00000 1.82% 518 5851s
117175 1417 infeasible 93 55.00000 56.00000 1.82% 518 5861s
117656 1435 56.00000 98 149 55.00000 56.00000 1.82% 519 5871s
118272 1449 infeasible 111 55.00000 56.00000 1.82% 519 5880s
118864 1445 infeasible 78 55.00000 56.00000 1.82% 519 5889s
119478 1422 infeasible 94 55.00000 56.00000 1.82% 519 5899s
120063 1358 56.00000 106 153 55.00000 56.00000 1.82% 520 5908s
120589 1527 56.00000 68 152 55.00000 56.00000 1.82% 520 5918s
121286 1577 infeasible 67 55.00000 56.00000 1.82% 520 5928s
121926 1603 56.00000 83 132 55.00000 56.00000 1.82% 520 5969s
122738 1582 infeasible 96 55.00000 56.00000 1.82% 520 5982s
123534 1579 infeasible 91 55.00000 56.00000 1.82% 520 6067s
123545 1577 infeasible 90 55.00000 56.00000 1.82% 520 6086s
124105 1592 56.00000 103 139 55.00000 56.00000 1.82% 520 6102s
124862 1596 56.00000 81 114 55.00000 56.00000 1.82% 521 6115s
125568 1559 infeasible 86 55.00000 56.00000 1.82% 521 6129s
126209 1545 infeasible 97 55.00000 56.00000 1.82% 521 6141s
126863 1586 56.00000 78 139 55.00000 56.00000 1.82% 521 6157s
127546 1599 56.00000 91 127 55.00000 56.00000 1.82% 521 6174s
128235 1668 56.00000 75 140 55.00000 56.00000 1.82% 522 6188s
128936 1675 56.00000 100 148 55.00000 56.00000 1.82% 521 6201s
129679 1672 infeasible 85 55.00000 56.00000 1.82% 521 6213s
130330 1664 56.00000 99 129 55.00000 56.00000 1.82% 521 6224s
130994 1637 56.00000 85 141 55.00000 56.00000 1.82% 522 6236s
131619 1645 56.00000 77 131 55.00000 56.00000 1.82% 522 6248s
132243 1602 56.00000 88 151 55.00000 56.00000 1.82% 522 6286s
133298 1589 infeasible 107 55.00000 56.00000 1.82% 522 6299s
133665 1698 56.00000 63 152 55.00000 56.00000 1.82% 523 6314s
134174 1716 infeasible 101 55.00000 56.00000 1.82% 522 6331s
134698 1676 infeasible 100 55.00000 56.00000 1.82% 522 6348s
135192 1685 56.00000 85 137 55.00000 56.00000 1.82% 522 6383s
135547 1700 56.00000 85 140 55.00000 56.00000 1.82% 523 6405s
136108 1687 infeasible 117 55.00000 56.00000 1.82% 523 6425s
136667 1655 56.00000 95 147 55.00000 56.00000 1.82% 523 6446s
137191 1629 infeasible 109 55.00000 56.00000 1.82% 523 6465s
138127 1587 infeasible 96 55.00000 56.00000 1.82% 524 6483s
138983 1539 infeasible 114 55.00000 56.00000 1.82% 524 6496s
139796 1556 infeasible 88 55.00000 56.00000 1.82% 524 6509s
140627 1693 56.00000 76 137 55.00000 56.00000 1.82% 525 6524s
141398 1676 56.00000 76 154 55.00000 56.00000 1.82% 524 6540s
142123 1687 56.00000 97 136 55.00000 56.00000 1.82% 525 6557s
142497 1687 infeasible 95 55.00000 56.00000 1.82% 525 6560s
142864 1740 infeasible 101 55.00000 56.00000 1.82% 525 6577s
143641 1705 56.00000 76 140 55.00000 56.00000 1.82% 525 6656s
144440 1654 56.00000 93 137 55.00000 56.00000 1.82% 526 6685s
146083 1610 infeasible 86 55.00000 56.00000 1.82% 526 6707s
146985 1542 infeasible 100 55.00000 56.00000 1.82% 527 6725s
147767 1626 infeasible 99 55.00000 56.00000 1.82% 527 6742s
148401 1731 infeasible 99 55.00000 56.00000 1.82% 527 6759s
149062 1740 56.00000 100 132 55.00000 56.00000 1.82% 527 6776s
149671 1776 56.00000 70 137 55.00000 56.00000 1.82% 527 6792s
150381 1813 infeasible 93 55.00000 56.00000 1.82% 527 6810s
151150 1761 56.00000 81 144 55.00000 56.00000 1.82% 527 6828s
151862 1918 infeasible 95 55.00000 56.00000 1.82% 527 6841s
152733 1896 56.00000 101 128 55.00000 56.00000 1.82% 527 6855s
153535 1814 infeasible 75 55.00000 56.00000 1.82% 527 6867s
154289 1823 infeasible 74 55.00000 56.00000 1.82% 527 6880s
154972 1820 infeasible 102 55.00000 56.00000 1.82% 527 6968s
154980 1820 56.00000 90 133 55.00000 56.00000 1.82% 527 6970s
154983 1787 56.00000 94 132 55.00000 56.00000 1.82% 527 6986s
155598 1755 infeasible 85 55.00000 56.00000 1.82% 527 6999s
156268 1721 infeasible 80 55.00000 56.00000 1.82% 527 7011s
156914 1750 56.00000 55 150 55.00000 56.00000 1.82% 528 7024s
157475 1763 56.00000 78 127 55.00000 56.00000 1.82% 528 7037s
158095 1736 56.00000 49 151 55.00000 56.00000 1.82% 528 7073s
159044 1732 infeasible 69 55.00000 56.00000 1.82% 528 7134s
159056 1777 56.00000 56 142 55.00000 56.00000 1.82% 528 7149s
159753 1802 56.00000 58 123 55.00000 56.00000 1.82% 528 7161s
160442 1843 56.00000 80 138 55.00000 56.00000 1.82% 528 7175s
161141 1826 infeasible 88 55.00000 56.00000 1.82% 528 7187s
161776 1956 56.00000 48 149 55.00000 56.00000 1.82% 528 7199s
162558 1965 infeasible 85 55.00000 56.00000 1.82% 528 7208s
163275 1984 56.00000 90 140 55.00000 56.00000 1.82% 527 7219s
163900 2139 infeasible 71 55.00000 56.00000 1.82% 527 7231s
164601 2194 56.00000 76 137 55.00000 56.00000 1.82% 527 7241s
165360 2189 infeasible 81 55.00000 56.00000 1.82% 527 7252s
这意味着遵循正确的排列
Verifying solution...
status: 1,Optimal
objective: 56.0
{0: 1.0,1117: 1.0,11495: 1.0,11960: 1.0,13117: 1.0,14379: 1.0,14536: 1.0,15015: 1.0,1507: 1.0,15172: 1.0,15324: 1.0,16147: 1.0,16388: 1.0,16729: 1.0,17926: 1.0,18102: 1.0,18440: 1.0,19084: 1.0,20435: 1.0,21488: 1.0,2236: 1.0,22658: 1.0,22905: 1.0,23115: 1.0,23844: 1.0,24149: 1.0,24508: 1.0,24989: 1.0,25259: 1.0,26122: 1.0,26657: 1.0,3065: 1.0,31490: 1.0,31741: 1.0,31841: 1.0,33370: 1.0,34319: 1.0,34381: 1.0,34480: 1.0,34566: 1.0,36400: 1.0,37111: 1.0,37700: 1.0,38281: 1.0,38728: 1.0,39329: 1.0,39982: 1.0,4631: 1.0,5013: 1.0,5234: 1.0,5353: 1.0,6010: 1.0,8296: 1.0,8441: 1.0,8663: 1.0,989: 1.0}
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