[Scip] Solution found, constraint not fulfilled

[Ramón Casero Cañas]

Hi Stefan,

Thanks!

Best regards,

Ramon.


On 25 May 2014 21:25, Stefan Vigerske <stefan at math.hu-berlin.de> wrote:

> 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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>>
>>
>


-- 
Dr. Ramón Casero Cañas

Institute of Biomedical Engineering
Department of Engineering Science, University of Oxford
Old Road Campus Research Building, Headington
Oxford
OX3 7DQ
UK

tlf         +44 (0) 1865 617716
twitter   @Ramon_Casero
web      http://www.cs.ox.ac.uk/people/Ramon.CaseroCanas/
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