[SCIP] question on a warning

[Marc Pfetsch]

Hi James,

the message is issued if a primal solution is found that has a better 
objective value (smaller if you are minimizing) than the previously 
computed dual bound. This should not happen, because the dual bound then 
is wrong and this usually indicates a problem - at least a numerical one.

Best

Marc

On 01/08/2023 18:03, James Cussens wrote:
> Hi all,
> 
> I am getting the following warning:
> 
>    time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows 
> |cuts |sepa|confs|strbr|  dualbound   | primalbound  |  gap   | compl.
>    0.0s|     1 |     0 |    39 |     - |  1118k |   0 |  20 |  36 |  63 
> |  30 | 31 |   1 |   0 |-1.804449e+02 | 0.000000e+00*|    Inf | unknown
>    0.0s|     1 |     0 |    40 |     - |  1118k |   0 |  20 |  36 |  64 
> |  31 | 32 |   1 |   0 |-1.802198e+02 | 0.000000e+00*|    Inf | unknown
>    0.0s|     1 |     0 |    41 |     - |  1124k |   0 |  20 |  36 |  65 
> |  32 | 33 |   1 |   0 |-1.801160e+02 | 0.000000e+00*|    Inf | unknown
>    0.1s|     1 |     2 |    41 |     - |  1128k |   0 |  20 |  36 |  65 
> |  32 | 34 |   1 |  15 |-1.800907e+02 | 0.000000e+00*|    Inf | unknown
> r 0.1s|    15 |    14 |    57 |   1.1 |rounding|  14 |  20 |  36 |  65 | 
>   33 |  0 |   1 |  42 |-1.758398e+02 |-1.151438e+01 |1427.13%| unknown
> r 0.1s|    16 |    15 |    65 |   1.6 |rounding|  15 |  20 |  36 |  65 | 
>   33 |  0 |   1 |  45 |-1.758398e+02 |-1.604484e+01 | 995.93%| unknown
> * 0.1s|    17 |    14 |    66 |   1.6 |    LP  |  16 |  20 |  36 |  65 | 
>   33 |  1 |   1 |  45 |-1.758398e+02 |-2.039660e+01 | 762.10%| unknown
> r 0.1s|    24 |    17 |    78 |   1.6 |rounding|  16 |  20 |  36 |  66 | 
>   35 |  0 |   1 |  50 |-1.758398e+02 |-2.640592e+01 | 565.91%| unknown
> * 0.1s|    34 |    21 |    95 |   1.6 |    LP  |  17 |  20 |  36 |  69 | 
>   39 |  1 |   1 |  54 |-1.758398e+02 |-2.719577e+01 | 546.57%| unknown
> * 0.1s|    37 |    22 |    99 |   1.6 |    LP  |  18 |  20 |  36 |  70 | 
>   40 |  1 |   1 |  54 |-1.758398e+02 |-6.270300e+01 | 180.43%| unknown
> r 0.2s|    57 |    30 |   144 |   1.8 |rounding|  18 |  20 |  36 |  72 | 
>   54 |  1 |   1 |  61 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
>    0.2s|   100 |    63 |   235 |   2.0 |  1345k |  18 |  20 |  36 |  69 
> |  73 |  2 |   1 |  69 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
>    0.3s|   200 |   159 |   480 |   2.2 |  1845k |  18 |  20 |  36 |  71 
> | 149 |  2 |   1 |  71 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
> WARNING: Dual bound 69.0721 is larger than the objective of the primal 
> solution 68.1511. The solution might not be optimal.
>    0.5s|   300 |   253 |   758 |   2.4 |  2248k |  18 |  20 |  36 |  76 
> | 226 |  1 |   1 |  71 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
>    0.6s|   400 |   351 |  1029 |   2.5 |  2670k |  18 |  20 |  36 |  73 
> | 312 |  1 |   1 |  71 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
>   time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows 
> |cuts |sepa|confs|strbr|  dualbound   | primalbound  |  gap   | compl.
>    0.7s|   500 |   443 |  1254 |   2.4 |  2799k |  18 |  20 |  36 |  70 
> | 367 |  1 |   1 |  71 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
>    0.8s|   600 |   537 |  1467 |   2.4 |  3062k |  18 |  20 |  36 |  70 
> | 411 |  1 |   3 |  71 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
>    1.0s|   700 |   633 |  1696 |   2.4 |  3247k |  18 |  20 |  36 |  70 
> | 470 |  1 |   3 |  71 |-1.758398e+02 |-6.485425e+01 | 171.13%| unknown
> 
> SCIP Status        : solving was interrupted [time limit reached]
> 
> The solutions I am getting are fine and I have no obvious errors, but I 
> am curious as to what might have generated the warning. Perhaps it comes 
> from some subscip run by a heuristic since the dual bound the warning 
> mentions (69.0721) is some distance from that of the main problem ( 
> -1.758398e+02). Can anyone explain what might be happening here; perhaps 
> this indicates some problem I have not yet noticed.
> 
> James
> 
> James Cussens
> Room MVB 3.26
> Dept of Computer Science, University of Bristol
> Phone: +44 (0)117 455 8723
> https://jcussens.github.io/ <https://jcussens.github.io/>
> Funded PhDs available in Bristol in the following areas: Data Science 
> <http://www.bristol.ac.uk/cdt/compass/>, Interactive AI 
> <http://www.bristol.ac.uk/cdt/interactive-ai/>, Cyber Security 
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> <http://www.bristol.ac.uk/cdt/digital-health/>.
> 
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