  In this paper, we propose a new natural evolution strategy for unconstrained
black-box function optimization (BBFO) problems and implicitly constrained BBFO
problems. BBFO problems are known to be difficult because explicit
representations of objective functions are not available. Implicit constraints
make the problems more difficult because whether or not a solution is feasible
is revealed when the solution is evaluated with the objective function.
DX-NES-IC is one of the promising methods for implicitly constrained BBFO
problems. DX-NES-IC has shown better performance than conventional methods on
implicitly constrained benchmark problems. However, DX-NES-IC has a problem in
that the moving speed of the probability distribution is slow on ridge
structure. To address the problem, we propose the Fast Moving Natural Evolution
Strategy (FM-NES) that accelerates the movement of the probability distribution
on ridge structure by introducing the rank-one update into DX-NES-IC. The
rank-one update is utilized in CMA-ES. Since naively introducing the rank-one
update makes the search performance deteriorate on implicitly constrained
problems, we propose a condition of performing the rank-one update. We also
propose to reset the shape of the probability distribution when an infeasible
solution is sampled at the first time. In numerical experiments using
unconstrained and implicitly constrained benchmark problems, FM-NES showed
better performance than DX-NES-IC on problems with ridge structure and almost
the same performance as DX-NES-IC on the others. Furthermore, FM-NES
outperformed xNES, CMA-ES, xNES with the resampling technique, and CMA-ES with
the resampling technique.
