[Scip] Solution found, constraint not fulfilled

[Stefan Vigerske]

Hi,

This is normal. Constraints have to be satisfied only within some 
tolerance, which is 1e-6 by default. See the numerics/feastol parameter.

Stefan

On 05/25/2014 08:02 PM, Ramón Casero Cañas wrote:
> Dear all,
>
> I have found a couple of cases where I provide a problem with constraints
> to SCIP, I set the solution limit to 1, optimize, SCIP finds a solution,
> but at least one of the constraints is not fulfilled.
>
> I'm not too sure whether this is a finite precision problem (maybe I'm
> doing something wrong). I have attached a model and solution to illustrate
> the issue.
>
> **********************************************************************************
> SCIP version 3.1.0, Linux 64 bit
> SCIP> read /tmp/model-tpd4cbba1c_26fc_4b5c_81bf_0dcdffc1ec38.pip
>
> read problem </tmp/model-tpd4cbba1c_26fc_4b5c_81bf_0dcdffc1ec38.pip>
> ============
>
> original problem has 61 variables (0 bin, 0 int, 0 impl, 61 cont) and 161
> constraints
> SCIP> set limits solutions 1
> limits/solutions = 1
> SCIP> optimize
> ...
>    2.7s|     1 |     0 | 32399 |     - |2495k|   0 |   0 | 139 | 205 | 139
> |1731 |1697 |   0 |   0 |-2.187679e+04 |-2.003787e+04 |   9.18%
>    2.7s|     1 |     1 | 32399 |     - |2495k|   0 |   0 | 139 | 205 | 139
> |1731 |1697 |   0 |   0 |-2.187679e+04 |-2.003787e+04 |   9.18%
>
> SCIP Status        : solving was interrupted [solution limit reached]
> Solving Time (sec) : 2.67
> Solving Nodes      : 1
> Primal Bound       : -2.00378746938832e+04 (1 solutions)
> Dual Bound         : -2.18767884307964e+04
> Gap                : 9.18 %
>
> SCIP> checksol
>
> check best solution
> solution is feasible in original problem
> **********************************************************************************
>
> However, if we look at constraint 17:
>
>   c17: -0.166666666666667 x197 y204 z202 + 0.166666666666667 x204 y197 z202
> + 0.166666666666667 x197 y202 z204 + -0.166666666666667 x202 y197 z204 +
> -0.166666666666667 x204 y202 z197 + 0.166666666666667 x202 y204 z197 >=
> 4.51681931542477e-08
>
> The values provided by the solution are:
>
> x197 =                               0.371685887161333;
> y197  =                              -1.53809757847603;
> z197   =                             -1.32501091239681;
>
> x202  =                             0.0972528846406156;
> y202  =                              -1.24399107862034;
> z202  =                              -1.64395150486303;
>
> x204 =                              -0.371685854531146;
> y204  =                               1.53809760270505;
> z204   =                              1.32501089342457;
>
>
> If we put these values into the constraint above, we get
>
> 7.723300589346227e-09 >= 4.51681931542477e-08
>
> which is false. I have found another case with a similar problem where the
> left hand side of the inequality comes as a small negative number (~ -1e-8).
>
> Is this kind of "constraint almost fulfilled" behaviour to be expected? Am
> I missing something?
>
> Best regards,
>
> Ramon.
>
>
>
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