[Help-glpk] [Fwd: simplex - mip]

[Andrew Makhorin]

-------- Forwarded Message --------
From: Claudia <address@hidden>
To: address@hidden
Subject: simplex - mip
Date: Wed, 02 Feb 2005 09:18:03 +0100

hello everybody,

I have got a question concerning the coupling of the simplex lp 
relaxation of a mixed integer problem and the brunch and bound solution:

my code looks as follows:

.
.
int solutionStatus = lpx_simplex( lp );
   //sparseVector x = getOptimalX();
   //x.dump();
   lpx_set_int_parm( lp, LPX_K_DUAL, 0 );
   lpx_set_int_parm( lp, LPX_K_PRESOL, 1 );
   lpx_set_int_parm( lp, LPX_K_BRANCH, 0 );
   solutionStatus = lpx_integer( lp );
.
.

I think that I first compute the LP-Relaxation (lpx_simplex) to get a 
good bound for my brunch and bound (lpx_integer).

In my special example the LP-Relaxation already is integer. Why needs 
the brunch and bound some steps to recognize it? :

Size of triangular part = 11
     364: obj =  -1.000000000e+30  infeas =  2.921e+30 (0)
*   389: obj =   5.092437748e+13  infeas =  0.000e+00 (0)
Warning: numerical instability (primal simplex, phase II)
     400: obj =  -1.960385743e+00  infeas =  1.327e+00 (0)
*   403: obj =  -1.580848544e+00  infeas =  5.551e-17 (0)
*   410: obj =  -3.126052553e+00  infeas =  0.000e+00 (0)
OPTIMAL SOLUTION FOUND
Integer optimization begins...
+   410: mip =     not found yet >=              -inf        (1; 0)
+   436: >>>>>  -1.074662258e+00 >=  -3.126052553e+00 190.9% (15; 0)
+   442: >>>>>  -1.541946553e+00 >=  -3.126052553e+00 102.7% (18; 2)
+   443: >>>>>  -3.126052553e+00 >=  -3.126052553e+00   0.0% (16; 6)
+   443: mip =  -3.126052553e+00 >=     tree is empty   0.0% (0; 39)
INTEGER OPTIMAL SOLUTION FOUND
Current lower bound (iteration 6): -3.12605^C

What happens in the first brunch and bound computations? The 
LP-Relaxation of the problem ist solved? but than the computation would 
not need more than one step because the LP-Relaxation is integer.

Could anybody solve my problems?
thanks a lot
claudia stangl