Re: [Help-glpk] Meaning of the integer problem columns console output

[Andrew Makhorin]

> What is the meaning of the columns in the output by console of a
> integer problem?

> Example:

> Integer optimization begins...
> Objective function is integral
>       ?                                                         ?
> +    56: mip =     not found yet <=              +inf        (1; 0)
> +   243: mip =   2.287300000e+04 <=   2.458500000e+04   7.5% (96; 0)

+nnn: mip = xxx <rho> yyy gap (ppp; qqq)

nnn is the simplex iteration count

xxx is the objective value for a best known integer feasible solution
(incumbent value). It is a lower (minimization) or upper (maximization)
bound for the optimal objective value.

<rho> is either '>=' (minimization) or '<=' (maximization)

yyy is a global upper (minimization) or lower (maximization) bound
for the optimal objective value.

gap is the relative gap, in percents, computed as
   |xxx - yyy| / (|xxx| + 1e-15) * 100%
If it is greater than 999.9%, it is not printed

ppp is the number of subproblems in the active list

qqq is the number of subproblems which have been fathomed and
therewore were removed from the branch-and-bound tree

For example, the line

+   243: mip =   2.287300000e+04 <=   2.458500000e+04   7.5% (96; 0)

means that 243 simplex iteration were made, and the exact optimal
value of the objective function is in the range (22873, 24585).
If you would stop the search right now, the relative error between
the best known solution found so far (i.e. 22873) and the exact
optimal solution (which is unknown yet) would be not greater than
7.5%.