[Scip] SCIP v3.2.0 Hanging on Problem

[Benjamin Müller]

Dear Jonathan,

the problem is that the LP relaxation of this problem is unbounded and 
SCIP has some troubles to find a bounded (linear) one. It would 
definitely help if you give your variables some artificial bounds. I 
tried to replace infinity by M (=1000) and solved the problem in 2s and 
got as solution


objective value:                   -0.250000756970904
t_xvar0                             0.793669420214128   (obj:0)
t_xvar1                             0.707148562806428   (obj:0)
t_xvar2                             0.529706057231088   (obj:0)
t_xvar3                             0.840921294489214   (obj:0)
t_nlobj                            -0.250000756970904   (obj:1)
nlreform0                            0.62991145338235   (obj:0)
nlreform1sp                         0.499941002617224   (obj:0)
nlreform2                            0.66741358081024   (obj:0)
nlreform3                           0.374581225460006   (obj:0)

which is far away from M for each variable. Maybe you find some 
artificial bounds which are fine for your purposes.


Best regards,

Benny


On 07/02/2015 02:31 AM, Jonathan Currie wrote:
> Hi All,
>
> The attached problem hangs (well, fails to make any reasonable progress) in my latest build of SCIP v3.2 with default settings. Original problem:
>
> Min     -x(1)*x(2)*x(3)*x(4)
> s.t.    x(1)^3 + x(2)^2 - 1 == 0
>            x(1)^2*x(4) - x(3) == 0
>            x(4)^2 - x(2) == 0
>
> Any ideas?
>
> Thanks,
> Jonathan
>
> SCIP: Solving Constraint Integer Programs [v3.2.0, Built Jul  2 2015, VS2013]
>    - SoPlex [v220] (ZIB Academic License)
>    - Ipopt  [v3.12.3] (Eclipse Public License)
>    - CppAD  [v20140000.3] (Eclipse Public License)
>
> presolving:
> (round 1, fast)       0 del vars, 0 del conss, 0 add conss, 1 chg bounds, 0 chg sides, 0 chg coeffs, 1 upgd conss, 0 impls, 0 clqs
> (round 2, fast)       0 del vars, 0 del conss, 0 add conss, 2 chg bounds, 0 chg sides, 0 chg coeffs, 1 upgd conss, 0 impls, 0 clqs
> (round 3, fast)       0 del vars, 0 del conss, 4 add conss, 2 chg bounds, 0 chg sides, 0 chg coeffs, 1 upgd conss, 0 impls, 0 clqs
> (round 4, fast)       0 del vars, 0 del conss, 4 add conss, 3 chg bounds, 0 chg sides, 0 chg coeffs, 7 upgd conss, 0 impls, 0 clqs
> (round 5, fast)       0 del vars, 0 del conss, 4 add conss, 4 chg bounds, 0 chg sides, 0 chg coeffs, 8 upgd conss, 0 impls, 0 clqs
> presolving (6 rounds: 6 fast, 1 medium, 1 exhaustive):
>   0 deleted vars, 0 deleted constraints, 4 added constraints, 4 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients
>   0 implications, 0 cliques
> presolved problem has 9 variables (0 bin, 0 int, 0 impl, 9 cont) and 8 constraints
>        2 constraints of type <abspower>
>        6 constraints of type <quadratic>
> Presolving Time: 0.00
>
>   time | node  | left  |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr|  dualbound   | primalbound  |  gap
>    0.0s|     1 |     0 |     0 |     - | 219k|   0 |   - |   9 |   8 |   9 |  10 |   0 |   0 |   0 |      --      |      --      |    Inf
>
> ******************************************************************************
> 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
> ******************************************************************************
>
>    0.1s|     1 |     0 |     2 |     - | 223k|   0 |   - |   9 |   8 |   9 |  11 |   1 |   0 |   0 |      --      |      --      |    Inf
> (node 1) LP relaxation is unbounded (LP 1)
> q 0.1s|     1 |     0 |    15 |     - | 225k|   0 |   - |   9 |   8 |   9 |  11 |   1 |   0 |   0 |      --      |0.000000e+000 |    Inf
>    0.1s|     1 |     0 |    15 |     - | 225k|   0 |   - |   9 |   8 |   9 |  11 |   1 |   0 |   0 |      --      |0.000000e+000 |    Inf
> (node 1) LP relaxation is unbounded (LP 4)
>    0.1s|     1 |     2 |    15 |     - | 224k|   0 |   - |   9 |   8 |   9 |  11 |   1 |   0 |   0 |      --      |0.000000e+000 |    Inf
> y 0.1s|     2 |     1 |    15 |  13.0 | 224k|   1 |   - |   9 |   8 |   0 |   0 |   1 |   0 |   0 |      --      |-2.500000e-001 |    Inf
>    0.2s|   100 |    77 |    40 |   0.4 | 254k|  77 |   - |   9 |   8 |   9 |   0 |  26 |   0 |   0 |      --      |-2.500000e-001 |    Inf
>    0.2s|   200 |    45 |    40 |   0.2 | 259k| 112 |   - |   9 |   8 |   0 |   0 |  26 |   0 |   0 |      --      |-2.500000e-001 |    Inf
>    0.3s|   300 |    65 |    40 |   0.1 | 273k| 171 |   - |   9 |   8 |   9 |   0 |  26 |   0 |   0 |      --      |-2.500000e-001 |    Inf
>    0.3s|   400 |   153 |   555 |   1.4 | 372k| 255 |   0 |   9 |   8 |   9 |  79 | 574 |   0 |   0 |      --      |-2.500000e-001 |    Inf
>
> SCIP Status        : solving was interrupted [time limit reached]
> Solving Time (sec) : 1000.00
> Solving Nodes      : 415
> Primal Bound       : -2.50000000000035e-001 (2 solutions)
> Dual Bound         : -1.00000000000000e+020
> Gap                : infinite
>
>
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-- 
______________________________
Benjamin Müller
Zuse Institute Berlin
Takustr. 7, 14195 Berlin
benjamin.mueller at zib.de
+49 30 841 85-195

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