In this paper, we introduce a new effective matrix adaptation evolution
strategy (MADFO) for noisy derivative-free optimization problems. Like
every MAES solver, MADFO consists of three phases: mutation, selection
and recombination. MADFO improves the mutation phase by generating
good step sizes, neither too small nor too large, that increase the
probability of selecting mutation points with small inexact function
values in the selection phase. In the recombination phase, recombination
points with low inexact function values (best points) are found
by a new randomized non-monotone line search method. If no new
best point is found, heuristic points may be accepted as new best
points. We compare MADFO with state-of-the-art DFO solvers on noisy
test problems obtained by adding various kinds and levels of noise
to all unconstrained CUTEst test problems with dimensions n ≤ 20,
and find that MADFO has the highest number of solved problems.