Given the ubiquity of non-separable optimization problems in real worlds, in
this paper we analyze and extend the large-scale version of the well-known
cooperative coevolution (CC), a divide-and-conquer optimization framework, on
non-separable functions. First, we reveal empirical reasons of why
decomposition-based methods are preferred or not in practice on some
non-separable large-scale problems, which have not been clearly pointed out in
many previous CC papers. Then, we formalize CC to a continuous game model via
simplification, but without losing its essential property. Different from
previous evolutionary game theory for CC, our new model provides a much simpler
but useful viewpoint to analyze its convergence, since only the pure Nash
equilibrium concept is needed and more general fitness landscapes can be
explicitly considered. Based on convergence analyses, we propose a hierarchical
decomposition strategy for better generalization, as for any decomposition
there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally,
we use powerful distributed computing to accelerate it under the multi-level
learning framework, which combines the fine-tuning ability from decomposition
with the invariance property of CMA-ES. Experiments on a set of
high-dimensional functions validate both its search performance and scalability
(w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores