[Coin-discuss] OsiCpx optimality for MIPs

[Jonathan Eckstein]

0 is not a good tolerance, but .01% (4 digits) is a surprisingly loose 
tolerance!  I think such a tolerance could cut most of the tree out of 
some of the old MIPLIB 3 problems.  If the absolute tolerance can 
override the relative one even if both the gap and incumbent are 
non-zero, that is also surprising.

Generally, I think the default MIP tolerance should be in the same 
ballpark as the LP tolerance.  Setting a MIP tolerance smaller than the 
LP tolerance isn't advisable.

   -- Jonathan


Matthew Saltzman wrote:
> On Fri, 28 Jan 2005, Brady Hunsaker wrote:
> 
>> I just ran into a quirk with OsiCpx solving a MIP.  CPLEX 9.0 has 
>> default gap parameters so that it stops the branch-and-bound process 
>> if the gap gets within 0.01% or an absolute value of 0.000001.
>>
>> This caused the solution process to stop, but 
>> OsiCpx->isProvenOptimal() returned false, because CPLEX returns a 
>> separate return code (CPXMIP_OPTIMAL_TOL) for this situation.
>>
>> I believe this should be corrected.  I can see two possible solutions:
>> 1. Reply true to isProvenOptimal() if CPXMIP_OPTIMAL_TOL is returned, 
>> even though this is technically incorrect.
>> 2. Explicitly set the gap parameters to 0 in branchAndBound().
>>
>> I'm using the first solution right now, but I'd like to hear any other 
>> opinions, especially from OsiCpx maintainers.
>>
>> Brady
> 
> 
> My first reaction is in favor of solution 1.
> 
> (1) Overriding tolerances that users may have reason to set is a bad idea.
> 
> (2) Most users probably would accept that a solution that's within 
> tolerance is optimal "for all practical purposes".  If a user wants a 
> guarantee of optimality, he can set CPXMIP_OPTIMAL_TOL to zero himself.
> 
> Is this a small enough example to pass around for testing?  I wonder how 
> other solver/SI combinations handle this issue.
>