8 An Introduction to Many-Objective Evolutionary Optimization
281
Fig. 8.10 GD is calculated as
distance from each
non-dominated points (blue
star) to the closest reference
point (red circle)
Fig. 8.11 The
non-dominated points are not
well spread, but the GD
measure is good (small value)
GD is calculated as the average (usually Euclidean) distance of all nondominated points to its closest reference point. Regularly, the reference points are
spread all over the real Pareto front (see Fig. 8.10).
It should be noted that the reference points in GD serve different purposes
compared to the reference point in hypervolume measurement. In hypervolume
measurement, the reference point has quite a bad quality in terms of convergence to
the real Pareto front; hence, it is only used as a limit of how far away the edges of
the hypervolume are. In GD, the reference points are actually target points, placed
on the Pareto front.
A small GD implies that all non-dominated points (i.e., the map of our best
solutions in the objective space) are located near the real Pareto front which is
what we want to achieve. However, a small GD does not imply the non-dominated
points are well spread because it could be that all the points are gathered (converged)
around a single reference point (see Fig. 8.11).
281
Fig. 8.10 GD is calculated as
distance from each
non-dominated points (blue
star) to the closest reference
point (red circle)
Fig. 8.11 The
non-dominated points are not
well spread, but the GD
measure is good (small value)
GD is calculated as the average (usually Euclidean) distance of all nondominated points to its closest reference point. Regularly, the reference points are
spread all over the real Pareto front (see Fig. 8.10).
It should be noted that the reference points in GD serve different purposes
compared to the reference point in hypervolume measurement. In hypervolume
measurement, the reference point has quite a bad quality in terms of convergence to
the real Pareto front; hence, it is only used as a limit of how far away the edges of
the hypervolume are. In GD, the reference points are actually target points, placed
on the Pareto front.
A small GD implies that all non-dominated points (i.e., the map of our best
solutions in the objective space) are located near the real Pareto front which is
what we want to achieve. However, a small GD does not imply the non-dominated
points are well spread because it could be that all the points are gathered (converged)
around a single reference point (see Fig. 8.11).