  Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a
point can be partitioned into the incomparable, the dominated and dominating
region. The ratio between the size of the incomparable region, and the
dominated (and dominating) region decreases proportionally to $1/2^{m-1}$,
i.e., the volume of the Pareto dominating orthant as compared to all other
volumes. Due to this reason, it gets increasingly unlikely that dominating
points can be found by random, isotropic mutations. As a remedy to stagnation
of search in many objective optimization, in this paper, we suggest to enhance
the Pareto dominance order by involving an obtuse convex dominance cone in the
convergence phase of an evolutionary optimization algorithm. We propose
edge-rotated cones as generalizations of Pareto dominance cones for which the
opening angle can be controlled by a single parameter only. The approach is
integrated in several state-of-the-art multi-objective evolutionary algorithms
(MOEAs) and tested on benchmark problems with four, five, six and eight
objectives. Computational experiments demonstrate the ability of these
edge-rotated cones to improve the performance of MOEAs on many-objective
optimization problems.
