  Artificial Neural Networks (ANN) comprise important symmetry properties,
which can influence the performance of Monte Carlo methods in Neuroevolution.
The problem of the symmetries is also known as the competing conventions
problem or simply as the permutation problem. In the literature, symmetries are
mainly addressed in Genetic Algoritm based approaches. However, investigations
in this direction based on other Evolutionary Algorithms (EA) are rare or
missing. Furthermore, there are different and contradictionary reports on the
efficacy of symmetry breaking. By using a novel viewpoint, we offer a possible
explanation for this issue. As a result, we show that a strategy which is
invariant to the global optimum can only be successfull on certain problems,
whereas it must fail to improve the global convergence on others. We introduce
the \emph{Minimum Global Optimum Proximity} principle as a generalized and
adaptive strategy to symmetry breaking, which depends on the location of the
global optimum. We apply the proposed principle to Differential Evolution (DE)
and Covariance Matrix Adaptation Evolution Strategies (CMA-ES), which are two
popular and conceptually different global optimization methods. Using a wide
range of feedforward ANN problems, we experimentally illustrate significant
improvements in the global search efficiency by the proposed symmetry breaking
technique.
