[Couenne] Bug in adjust of branching intervals?

[Pietro Belotti]

Francois,

this should be fixed now.

>> I think there is indeed a bug. However, the solution you propose might 
>> introduce another bug, especially if brpt is equal to one of the 
>> bounds. I am going to commit the following (hopefully comprehensive) 
>> code:
>>
>> [...]
>
> The above is incorrect. The condition if(firstBranch_) should be
>
> if(!branchIndex_) {
>
> firstBranch_ indicates the direction of preferred branching, it has the 
> same value in all branches. The above code adjusts the branching point 
> in both branches, resulting in one integer value being excluded from 
> both.

I'm now using branchIndex_, thanks for pointing that out.

> In addition, due to rounding error, replacing
>
> brpt -= 1.; (resp. brpt += 1.;)
>
> by brpt -= 0.99999; (resp. brpt += 0.99999;)
>
> avoids the disappearance of some integer values in both branches. Maybe 
> the value delta = 0.99999 should be related to the tolerance used in 
> isInteger().

Given the further rounding performed by bound tightening and branching 
itself, I believe a (1. - COUENNE_EPS) should suffice.

> If isInteger(a)==true with closest integer value b, then we 
> must have (a-delta) > b-1 and (a+delta < b+1).
>
> Also, just below,
>
> else if (u - brpt > .5) {if  (way) brpt += 1.;}
> else if (brpt - l > .5) {if (!way) brpt -= 1.;}
>
> the value 1. should also be replace by delta.

Done.

> Finally some thoughts should be devoted to the case
>
>  if ((brpt < l) || (brpt > u))
>    brpt = 0.5 * (l+u);
>
> If the violation of the bounds is small and (l+u) is huge, it might be
> better to alter brpt slighlty than taking the midpoint. Also, if the
> variable is integer and (l+u) is a multiple of 2, the two branches will
> share a value.

The current code eliminates that value and should also take care of large 
bounds (where "large" is now any value whose absolute value is above 1e9).

Pietro