[Couenne] Lower/Upper bounds variables

[Pietro Belotti]

Hi Luca,

that's a bit more complicated. The lower bound is the minimum (for a
minimization problem), across all open branch-and-bound nodes, of the
objective function value of optimal solution of the relaxation at the
node. There is no option to obtain that since an LP solution of a BB
node is quite useless at the end of a solve, so you'll have to modify
the source code to read the LP solution after the resolve() call
within CouenneSolverInterface::resolve(), see
CouenneSolverInterface.c. Keep in mind that there is at least one call
to this for every branch-and-bound node.

Pietro

On Thu, Jun 4, 2015 at 3:22 PM, Luca Mencarelli
<mencarelli at lix.polytechnique.fr> wrote:
> Dear Pietro,
>
> Thanks for the answer. Yes, I agree with you. Maybe I didn't explain
> myself well,
> but the point is that I will like to retrieve the values corresponding to
> -283,
> since I'm developing a feasibility recovering heuristic based on the DUAL
> bound.
>
> Best,
> Luca
>
> --
> Luca Mencarelli
> PhD Candidate at LIX, Ecole Polytechnique
> 91128 Palaiseau CEDEX, France
> Office: 2072 (Bâtiment Alan Turing, second floor)
> LIX e-mail address: mencarelli at lix.polytechnique.fr
> INRIA e-mail address:  luca.mencarelli at inria.fr
>
>
>> Dear Luca,
>>
>> I tried the following AMPL script:
>>
>> model nonlinear_w_cont.mod
>> data mnck_instance_0.dat
>> write gdis;
>> option solver couenne;
>> solve;
>> display sigmoid_p;
>>
>> The output I get from the script shows a DUAL bound of -283 and a
>> PRiMAL bound of -214 when stopping couenne after 20 seconds. The dual
>> bound does not refer to a solution as it is simply a lower bound on
>> the optimal solution. The primal bound instead refers to a feasible
>> solution. Indeed when printing the only variables appearing in the
>> objective, their sum seems roughly equal to 214.
>>
>> Since Couenne generally refers to minimization problems, the lower
>> bound is the dual bound and the upper bound the primal one. in the
>> case of a maximization (which you correctly reformulate as a min
>> problem) the upper bound is a dual and the lower bound is a primal
>> bound. Hence Couenne reports the solution found that refers to the
>> primal bound.
>>
>> When re-running Couenne on the dis.nl saved by the script, the same
>> thing happens, then the dis.sol file contains, from lines 39 onward,
>> the same solution found by the script, which again sums up to about
>> 214. I'm running stable/0.4, but it really seems like I can't
>> reproduce your problem. What solution are you getting?
>>
>> Regards,
>> Pietro
>>
>>
>>
>>
>>
>> On Wed, Jun 3, 2015 at 5:23 PM, Luca Mencarelli
>> <mencarelli at lix.polytechnique.fr> wrote:
>>> Dear Pietro,
>>>
>>> I've done other experiments with the code, but I cannot retrieve
>>> the values of the decision variables corresponding to the Upper Bound
>>> provided by Couenne.
>>>
>>> Thanks very much. Best regards,
>>> Luca
>>>
>>>> Dear Pietro,
>>>>
>>>> I attach the model and the output files. I get an upper_bound =
>>>> -210.89,
>>>> while the upper bound provided by Couenne (version 0.4.8) is -286.95.
>>>> The original problem is a maximization one.
>>>>
>>>> Thanks again. Best,
>>>> Luca
>>>>
>>>> --
>>>> Luca Mencarelli
>>>> PhD Candidate at LIX, Ecole Polytechnique
>>>> 91128 Palaiseau CEDEX, France
>>>> Office: 2072 (Bâtiment Alan Turing, second floor)
>>>> LIX e-mail address: mencarelli at lix.polytechnique.fr
>>>> INRIA e-mail address:  luca.mencarelli at inria.fr
>>>>
>>>>
>>>>
>>>>> Hi Luca,
>>>>>
>>>>> this should not happen, it might be a bug. Can you send me the model
>>>>> (a .nl file should suffice)? I suspect the constant term of the
>>>>> objective function might be ignored. Also, what version of Couenne are
>>>>> you using?
>>>>>
>>>>> Pietro
>>>>>
>>>>> On Mon, May 18, 2015 at 4:55 PM, Luca Mencarelli
>>>>> <mencarelli at lix.polytechnique.fr> wrote:
>>>>>> Dear Pietro,
>>>>>>
>>>>>> First of thanks very much for the answer. However in the .sol file I
>>>>>> found
>>>>>> the same values as the one I obtain via the display command. But when
>>>>>> I
>>>>>> recompute
>>>>>> the objective function with these values, it is less than the upper
>>>>>> bound
>>>>>> provided
>>>>>> by Couenne.
>>>>>>
>>>>>> Best,
>>>>>> Luca
>>>>>>
>>>>>> --
>>>>>>
>>>>>> Luca Mencarelli
>>>>>> PhD Candidate at LIX, Ecole Polytechnique
>>>>>> 91128 Palaiseau CEDEX, France
>>>>>> Office: 2072 (Bâtiment Alan Turing, second floor)
>>>>>> LIX e-mail address: mencarelli at lix.polytechnique.fr
>>>>>> INRIA e-mail address:  luca.mencarelli at inria.fr
>>>>>>
>>>>>>
>>>>>>
>>>>>>> Hi Luca,
>>>>>>>
>>>>>>> when Couenne stops before closing the gap, the best feasible MINLP
>>>>>>> solution found (if any) is saved in a file with the same name as the
>>>>>>> input file but with extension .sol (which is the format read by
>>>>>>> AMPL).
>>>>>>> So the answer is yes for the upper bound if at least one solution is
>>>>>>> found.
>>>>>>>
>>>>>>> However, this does not make much sense for the lower bound, given
>>>>>>> that
>>>>>>> it's obtained by a relaxation of the MINLP (and would hence be
>>>>>>> infeasible) and is related to the whole branch-and-bound search tree
>>>>>>> rather than a specific subproblem. Hence no solution is available
>>>>>>> for
>>>>>>> the lower bound.
>>>>>>>
>>>>>>> Hope this helps,
>>>>>>> Pietro
>>>>>>>
>>>>>>>
>>>>>>> On Mon, May 18, 2015 at 11:05 AM, Luca Mencarelli
>>>>>>> <mencarelli at lix.polytechnique.fr> wrote:
>>>>>>>> Hi,
>>>>>>>>
>>>>>>>> If Couenne did not succeed in solving a problem to optimality, it's
>>>>>>>> possible to
>>>>>>>> retrieve the values of the decision variables corresponding to the
>>>>>>>> lower
>>>>>>>> and to
>>>>>>>> the upper bounds provided by the solver?
>>>>>>>>
>>>>>>>> Thanks. Best,
>>>>>>>> Luca
>>>>>>>>
>>>>>>>> --
>>>>>>>> Luca Mencarelli
>>>>>>>> PhD Candidate at LIX, Ecole Polytechnique
>>>>>>>> 91128 Palaiseau CEDEX, France
>>>>>>>> Office: 2072 (Bâtiment Alan Turing, second floor)
>>>>>>>> E-mail address: mencarelli at lix.polytechnique.fr
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
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>>>>>>>
>>>>>>
>>>>>>
>>>>>
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>>
>
>