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## [Bug-glpk] Wrong result with MIP presolver - NO PRIMAL FEASIBLE SOLUTION

 From: Heinrich Schuchardt Subject: [Bug-glpk] Wrong result with MIP presolver - NO PRIMAL FEASIBLE SOLUTION Date: Thu, 1 Jan 2015 10:47:48 +0100

```Hello Andrew,

for the appended model I get the following results with glpk 4.55 on Linux
64bit:

\$ glpsol  -m test.mod
...
Preprocessing...
PROBLEM HAS NO PRIMAL FEASIBLE SOLUTION

\$ glpsol --nointopt -m test.mod
...
+356119: mip =   0.000000000e+00 >=     tree is empty   0.0% (0; 3059)
INTEGER OPTIMAL SOLUTION FOUND
Time used:   161.6 secs

The presolver should not influence reported feasiblity.

Best regards

Heinrich Schuchardt

# Number of nodes
param n := 14;
# Connectivity
param c := 4;
# Maximum distance
param d := 2;
# Decay factor;
param f := (c + 1) ^ 2;
# nodes
set V := {1 .. n};
# connections
var x{V,V} binary;
# signal
var s{V,V};
# signal flow
var sf{V,V,V};

s.t. symmetry{i in V, j in V : i < j} :
x[i,j] = x[j,i];

s.t. flowin{i in V} :
sum{j in V: i != j} x[j,i] = c;

s.t. flowout{i in V} :
sum{j in V: i != j} x[i,j] = c;

s.t. diagonal{i in V} :
x[i,i] = 0;

s.t. decay{i in V, j in V} :
s[i,j] = if (i == j)
then f ^ d
else sum{k in V : i != k} sf[k, i, j] / f;

s.t. signalflow{i in V, j in V, k in V} :
sf[i,j,k] <= x[i,j] * f ^ d;

s.t. signalsource{i in V, j in V, k in V} :
sf[i,j,k] <= s[i,k];

s.t. signal{i in V, j in V} :
s[i,j] >= 1;

solve;

for {i in V} {
printf "\n %2d: ", i;
printf {j in V} "%d", x[i,j];
}
printf "\n";

printf "\ns";
for {i in V} {
printf "\n %2d: ", i;
printf {j in V} " %3d", s[j,i];
}
printf "\n";

printf "\nsf[?,?,1]";
for {i in V} {
printf "\n %2d: ", i;
printf {j in V} " %3d", sf[i,j,1];
}
printf "\n";

end;

```

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