Result violates the constraints. Why and how can I know?

[맹기완]

I am new to AMPL. I am trying to solve an MINLP problem using Couenne.

I tried to solve my problem by looking at the manual and writing mod file, and it generated some results, but the result does not make sense.

I wonder (1) what I have done wrong, and (2) how I can know that the solution is invalid (because it seemed like it was generating results okay).

Below is my mod file.

var n0 >= 2 <= 111 integer;
var x0 >= 1 <= 110 integer;
var n1 >= 2 <= 3 integer;
var x1 >= 1 <= 2 integer;
minimize obj: (111/x0)*(3/x1);
subject to c1: 28416*x0 + 4*x1 <= 262144;
subject to c2: x0*n0 == 111;
subject to c3: x1*n1 == 3;

I am not sure if this is allowed, but I wanted x0 and x1 to be an integer whose integer multiple is 111 and 3, respectively (i.e., x0 in {1, 3, 37, 111} and x1 in {1,3}), hence introduced n0 and n1 and put c2 and c3.

And below is the output log from AMPL. Seemed like something was working, but it wasn't.
==================================
ampl: model wrong2.mod
ampl: option solver couenne;
ampl: solve;
Couenne 0.5.7 -- an Open-Source solver for Mixed Integer Nonlinear Optimization
Mailing list: cou...@list.coin-or.org
Instructions: http://www.coin-or.org/Couenne
couenne:
ANALYSIS TEST: NLP0012I
              Num      Status      Obj             It       time                 Location
NLP0014I             1         OPT 8.9999999       17 0.008
Couenne: new cutoff value 9.0000000000e+00 (0.016 seconds)
Loaded instance "/tmp/at7601.nl"
Constraints:            2
Variables:              4 (4 integer)
Auxiliaries:            6 (2 integer)

Coin0506I Presolve 0 (-2) rows, 0 (-10) columns and 0 (-4) elements
Clp0000I Optimal - objective value 9
Clp0032I Optimal objective 9 - 0 iterations time 0.002, Presolve 0.00
Clp0000I Optimal - objective value 9
Cbc0012I Integer solution of 9 found by Couenne Rounding NLP after 0 iterations and 0 nodes (0.00 seconds)
NLP Heuristic: NLP0014I             2         OPT 9        0 0
no solution.
Cbc0001I Search completed - best objective 9, took 0 iterations and 0 nodes (0.00 seconds)
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
Clp0000I Optimal - objective value 9
        "Finished"

Linearization cuts added at root node:          2
Linearization cuts added in total:              2  (separation time: 0s)
Total solve time:                               0s (0s in branch-and-bound)
Lower bound:                                    9
Upper bound:                                    9  (gap: 0.00%)
Branch-and-bound nodes:                         0

couenne: Optimal
ampl: display x0
ampl? ;
x0 = 37

ampl: display x1;
x1 = 1

ampl: display obj.result;
obj.result = solved

====================================

As you can see, the solution of x0=37, x1=1 does not meet the constraint c1 ( 28416*x0 + 4*x1 <= 262144; ).

However, (1) I am not sure why it is wrong (is my .mod file flawed?), and (2) how I should know if the result is valid or not (it says obj.result == solved!).
Any help or pointers would be highly appreciated.

Thank you!

[AMPL Google Group]

It appears that AMPL's presolve phase is dropping the constraint c1 without properly tightening the bound on variable x0. This problem was not observed previously because it occurs only in unusual cases. We are working to confirm this and to make any needed fixes.

Meanwhile, you can work around the problem by changing AMPL's presolve option to 1. (It is 10 by default.) You can do this by giving the command "option presolve 1;" before the first solve of your AMPL session.

--
Robert Fourer
am...@googlegroups.com

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