# orthogonal_distance

Get subset of Pareto front based on distance

**Specification**

*Alias:*None*Arguments:*REALLIST*Default:*0.01 for all objectives

**Description**

Note that MOGA and SOGA create additional output files during
execution. “finaldata.dat” is a file that holds the final set of
Pareto optimal solutions after any post-processing is complete.
“discards.dat” holds solutions that were discarded from the population
during the course of evolution. It can often be useful to plot
objective function values from these files to visually see the Pareto
front and ensure that finaldata.dat solutions dominate discards.dat
solutions. The solutions are written to these output files in the
format “Input1…InputN..Output1…OutputM”. If MOGA is used in a
hybrid optimization meta-iteration (which requires one optimal
solution from each individual optimization method to be passed to the
subsequent optimization method as its starting point), the solution in
the Pareto set closest to the “utopia” point is given as the best
solution. This solution is also reported in the Dakota output. This
“best” solution in the Pareto set has minimum distance from the utopia
point. The utopia point is defined as the point of extreme (best)
values for each objective function. For example, if the Pareto front
is bounded by (1,100) and (90,2), then (1,2) is the utopia point.
There will be a point in the Pareto set that has minimum L2-norm
distance to this point, for example (10,10) may be such a point. In
SOGA, the solution that minimizes the single objective function is
returned as the best solution. If moga is used in meta-iteration
which may require passing multiple solutions to the next level (such
as the `surrogate_based_global`

or `hybrid`

methods), the
`orthogonal_distance`

postprocessor type may be used to specify the
distances between each solution value to winnow down the solutions in
the full Pareto front to a subset which will be passed to the next
iteration.