[Couenne] Wrong optimum

[Pietro Belotti]

Dear Pedro,

in principle, Couenne should find the optimal solution with value zero. 
However, sometimes Couenne does find a solution with the right value (zero 
in this case), but it can't convince Cbc (the underlying branch-and-bound 
algorithm) of that, and Cbc retains the wrong solution (5.44 in this case) 
as the best one.

Moreover, Couenne uses 0 as a cutoff to eliminate portions of the feasible 
set (through bound reduction) and terminates quickly, with Cbc, 
unfortunately, outputting the wrong solution as optimal.

I have made some changes (namely, introducing a looser tolerance) to both 
Couenne/trunk and Couenne/stable/0.3, and was able to compute the optimal 
solution. Please let me know if you are using stable/0.2 or stable/0.1 
instead. I do plan to merge those changes into the older versions too, 
just not too soon.

Hope this helps.

Best,
Pietro

--
Pietro Belotti
Dept. of Mathematical Sciences
Clemson University
email: pbelott at clemson.edu
phone: 864-656-6765
www:   myweb.clemson.edu/~pbelott

On Fri, 22 Oct 2010, Joao Pedro Pedroso wrote:

> Dear Pietro,
>
> I am using Couenne for solving the AMPL model below.  The optimum is
> y = x = profit = 0; however Couenne reports:
>
>   couenne: Optimal
>   y = 1
>   x = 13.335
>   h = 0
>   q = 13.335
>   profit = -5.54444
>
> Is there any assumption on the models that can be solved by Couenne?
>
> Thanks,
>
> Pedro
> --
> var y binary;                # setup
> var x >= 0;                  # production
> var q >= 0;                  # put in market
> var p >= 0;                  # price
> var h >= 0;                  # inventory
>
> maximize profit:
>  (q * p - (50 * y + 5 * h));
>
> subject to
>  BOM:        0 + x = q + h;
>  Demand:     p = 10 - .25 * (q + 13.33);
>  Fixed:      x <= y * 20;
>  # Init:               y = 0;
>
> option halt_on_ampl_error yes;
> option solver couenne;
>
> solve;
>
> display y, x, h, q, profit;
>
>