Question

优化多项式时，我得到最大深度级别错误。在下面的输出中，我注意到LP迭代似乎停止了。为什么要在很多变量上剪切分支而不再调用LP求解器？我用Ipopt运行它。

我无法尝试增加最大深度级别，因为#defined为65535，我不想重建scip。

下面是我的输入文件和输出。

$cat mytest.pip
Maximize
obj:5 x1^1*x2^1*x3^1*x7^1*x8^1*x18^1*x19^2 + 3 x1^1*x2^1*x3^1*x10^1*x13^1*x15^1*x19^2 - 6 x1^1*x4^1*x11^1*x15^1*x18^2*x19^2 + 8 x2^3*x4^1*x8^1*x11^1*x14^2 + 9 x2^1*x3^1*x9^1*x11^1*x13^1*x17^2*x18^1 - 3 x4^1*x8^1*x12^1*x14^1*x17^1*x18^2*x20^1 + 1 x5^3*x6^2*x9^1*x18^1*x20^1 - 6 x5^2*x8^1*x16^4*x17^1 + 10 x6^1*x8^1*x15^3*x16^2*x19^1 + 10 x9^1*x12^1*x14^1*x15^1*x16^2*x19^2
Bounds
1 <= x1 <= 150
1 <= x2 <= 150
1 <= x3 <= 150
1 <= x4 <= 150
1 <= x5 <= 150
1 <= x6 <= 150
1 <= x7 <= 150
1 <= x8 <= 150
1 <= x9 <= 150
1 <= x10 <= 150
1 <= x11 <= 150
1 <= x12 <= 150
1 <= x13 <= 150
1 <= x14 <= 150
1 <= x15 <= 150
1 <= x16 <= 150
1 <= x17 <= 150
1 <= x18 <= 150
1 <= x19 <= 150
1 <= x20 <= 150
Integers
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
x17
x18
x19
x20
End


$ ./scip -f  mytest.pip
SCIP version 3.1.0 [precision: 8 byte] [memory: block] [mode: optimized] [LP solver: SoPlex 2.0.0] [GitHash: 577ee45]
Copyright (c) 2002-2014 Konrad-Zuse-Zentrum fuer Informationstechnik Berlin (ZIB)

External codes: 
  Readline 6.3         GNU library for command line editing (gnu.org/s/readline)
  SoPlex 2.0.0         Linear Programming Solver developed at Zuse Institute Berlin (soplex.zib.de) [GitHash: 568f354]
  cppad-20140000.1     Algorithmic Differentiation of C++ algorithms developed by B. Bell (www.coin-or.org/CppAD)
  ZLIB 1.2.8           General purpose compression library by J. Gailly and M. Adler (zlib.net)
  GMP 5.1.3            GNU Multiple Precision Arithmetic Library developed by T. Granlund (gmplib.org)
  ZIMPL 3.3.2          Zuse Institute Mathematical Programming Language developed by T. Koch (zimpl.zib.de)
  Ipopt 3.11.9         Interior Point Optimizer developed by A. Waechter et.al. (www.coin-or.org/Ipopt)

user parameter file <scip.set> not found - using default parameters

read problem <mytest.pip>
============

original problem has 21 variables (0 bin, 20 int, 0 impl, 1 cont) and 1 constraints

solve problem
=============

feasible solution found by trivial heuristic after 0.0 seconds, objective value 1.000000e+05
presolving:
(round 1) 0 del vars, 0 del conss, 0 add conss, 1 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 2) 0 del vars, 0 del conss, 0 add conss, 2 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 3) 0 del vars, 0 del conss, 55 add conss, 2 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 4) 0 del vars, 0 del conss, 55 add conss, 2 chg bounds, 0 chg sides, 0 chg coeffs, 56 upgd conss, 0 impls, 0 clqs
(round 5) 3 del vars, 3 del conss, 55 add conss, 73 chg bounds, 0 chg sides, 0 chg coeffs, 56 upgd conss, 0 impls, 0 clqs
(round 6) 3 del vars, 3 del conss, 55 add conss, 102 chg bounds, 0 chg sides, 0 chg coeffs, 57 upgd conss, 0 impls, 0 clqs
(round 7) 3 del vars, 3 del conss, 55 add conss, 107 chg bounds, 0 chg sides, 0 chg coeffs, 57 upgd conss, 0 impls, 0 clqs
presolving (8 rounds):
 3 deleted vars, 3 deleted constraints, 55 added constraints, 107 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients
 0 implications, 0 cliques
presolved problem has 73 variables (0 bin, 20 int, 52 impl, 1 cont) and 53 constraints
     12 constraints of type <abspower>
     41 constraints of type <quadratic>
Presolving Time: 0.04

 time | node  | left  |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr|  dualbound   | primalbound  |  gap   
  0.1s|     1 |     0 |    47 |     - | 447k|   0 |   1 |  73 |  53 |  73 | 190 |   0 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.1s|     1 |     0 |    48 |     - | 480k|   0 |   1 |  73 |  54 |  73 | 191 |   1 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|     1 |     0 |    49 |     - | 481k|   0 |   1 |  73 |  54 |  73 | 192 |   2 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|     1 |     0 |    50 |     - | 483k|   0 |   1 |  73 |  54 |  73 | 193 |   3 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|     1 |     0 |    51 |     - | 484k|   0 |   1 |  73 |  54 |  73 | 194 |   4 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|     1 |     0 |    52 |     - | 486k|   0 |   1 |  73 |  54 |  73 | 195 |   5 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|     1 |     0 |    53 |     - | 487k|   0 |   1 |  73 |  54 |  73 | 196 |   6 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|     1 |     2 |   171 |     - | 502k|   0 |   1 |  73 |  54 |  73 | 196 |   6 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|   100 |   101 |   479 |   4.3 | 566k|  98 |   0 |  73 |  54 |  73 | 164 | 139 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.2s|   200 |   201 |   774 |   3.6 | 669k| 198 |   0 |  73 |  54 |  73 | 237 | 241 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

  0.5s|   300 |   301 |  1070 |   3.4 | 831k| 271 |   0 |  73 |  54 |  73 |  86 | 410 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.6s|   400 |   402 |  1077 |   2.6 | 884k| 271 |   0 |  73 |  54 |  73 |  87 | 412 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.6s|   500 |   502 |  1077 |   2.1 | 929k| 271 |   0 |  73 |  54 |  73 |  87 | 412 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.6s|   600 |   602 |  1077 |   1.7 | 973k| 326 |   0 |  73 |  54 |  73 |  87 | 412 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
  0.6s|   700 |   702 |  1077 |   1.5 |1020k| 426 |   0 |  73 |  54 |  73 |  87 | 412 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
...
  9.4s| 65800 | 65802 |  1079 |   0.0 |  30M|  65k|   0 |  73 |  54 |  73 |  87 | 412 |   0 |   0 | 1.178930e+19 | 1.000000e+05 |  Large 
[src/scip/tree.c:777] ERROR: maximal depth level exceeded
[src/scip/tree.c:969] ERROR: Error <-16> in function call
[src/scip/tree.c:5268] ERROR: Error <-16> in function call
[src/scip/tree.c:5514] ERROR: Error <-16> in function call
[src/scip/scip.c:30672] ERROR: Error <-16> in function call
[src/scip/branch_pscost.c:610] ERROR: Error <-16> in function call
[src/scip/branch.c:1581] ERROR: Error <-16> in function call
[src/scip/branch.c:2503] ERROR: Error <-16> in function call
[src/scip/solve.c:3863] ERROR: Error <-16> in function call
[src/scip/solve.c:4312] ERROR: Error <-16> in function call
[src/scip/scip.c:13633] ERROR: Error <-16> in function call
[src/scip/scipshell.c:98] ERROR: Error <-16> in function call
[src/scip/scipshell.c:284] ERROR: Error <-16> in function call
[src/scip/scipshell.c:332] ERROR: Error <-16> in function call
SCIP Error (-16): maximal branching depth level exceeded

Answer 1

首先感谢您提交此问题。我们发现了两个主要问题。

你的模型接缝在数值上是不稳定的，因为在一些迭代之后，一些变量边界被设置为大小为1 ^ {13}之前和1 ^ { - 4}之后的逗号。在浮点运算中，有15-16个显着的符号。这就是为什么使用'ceil'和'floor'功能可能会产生不可预测的结果。目前我们还不确定如何处理这个问题，但我们正在努力解决这个问题。此时，您可以尝试通过更改数字的参数来更改精度，例如，
```
numerics/epsilon    and     numerics/hugeval.
```
经过一些迭代后，变量边界的大小为1 ^ {13}。特别是，SCIP在每次迭代中对同一个变量进行分支，下限只增加一个。换句话说，SCIP可能执行深度优先搜索，并且由于积分变量x_ {i}的范围是150，因此用于替换多项式中的乘积的变量范围增加到11390625000000.显然，SCIP遇到了深度限制。此外，由于上述数字问题，SCIP在其中一个节点中的某些变量上分支后不识别绑定变化。如果SCIP选择此节点，则不需要再次解决LP。

如果您的模型有所改进，请随时再次发布或发送电子邮件至SCIP邮件列表。

亲切的问候，

氏

scip超出最大深度级别

1 个答案: