I am getting a max depth level error when optimizing a polynomial. In the output below, I noticed that the LP iterations seem to stop. Why would scip branch on a lot of variables and never call the LP solver again? I am running it with Ipopt.
I cannot try to increase the max depth level because it is #defined to be 65535, and I do not want to rebuild scip.
Below is my input file and output.
$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
first of all thanks for submitting this problem. We have identified two major problems.
Your model seams to be numerically unstable because after some iterations some variable bounds are set to something with the magnitude of 1^{13} before and 1^{-4} behind the comma. In floating point arithmetic there are 15-16 significant signs. Thats why using 'ceil' and 'floor' functions may produce unpredictable results. Currently we are not sure how to handle this, but we are working on it. At this point, you can try to change the precisions by changing the parameters for the numerics, e.g.,
After some iterations the variable bounds are in the magnitude of 1^{13}. In particular, SCIP branches in each iteration on the same variable and the lower bound increase by exactly one. In other words, SCIP performs probably a depth-first-search and since the range of your integral variables x_{i} is 150, the range of the variables that are introduced to replace the products in your polynomial increase to 11390625000000. Obviously, SCIP runs into the depth limit. Moreover, due to the numerical troubles mentioned above, SCIP does not recognize bound changes after branching on some variables in one of the nodes. If SCIP selects this node the LP does not need to be solved again.
If you have improved your model feel free to post it again or send us an email to the SCIP mailing-list.
Kind regards,
Jakob