Re: [Help-glpk] operand preceding == has invalid type

[Andrew Makhorin]

> I am new to linear programming and I am having difficulty formulating the
> objective function. glpsol is able to find a solution with a null (0)
> objective function, but cannot process this objective function:
> 
> minimize objective_function:
>   sum{(i11,j11,k11,i12,j12,k12) in LogicalLink,
>       (i21,j21) in PhysicalSwitch, k21 in 1..24,
>       (i22,j22) in PhysicalSwitch, k22 in 1..24:
>        x[i12,j12,k12,i22,j22,k22] + x[i11,j11,k11,i21,j21,k21] == 2}
>          sqrt(
>             (x_offset[i21,j21,k21] - x_offset[i22,j22,k22])**2 +
>             (y_offset[i21,j21,k21] - y_offset[i22,j22,k22])**2
>           );
> 
> I'm trying to map a logical network onto a physical network. Logical
> switches with M ports are mapped to physical switches with N ports (N >= M).
> A logical switch port is mapped to a physical switch port. The constraints
> by themselves give a feasible solution, but I wanted to add an optimization
> function to minimize the total length of physical cable. I'm attaching to
> complete MathProg program below.

Glpk is intended for lp/mip only and therefore does not allow quadratic
objectives like in your instance. You can approximate your objective by
a piecewise linear function using a standard technique; since your
objective is convex, no binary variables are needed. Another way is to
use a quadratic programming package.