Evaluating the CMA Evolution Strategy on Multimodal Test Functions
Nikolaus Hansen and Stefan Kern
Abstract:
In this paper the performance of the CMA evolution strategy with
rank-$\mu$-update and weighted recombination is empirically
investigated on eight multimodal test functions. In particular the
effect of the population size $\lambda$ on the performance is
investigated. Increasing the population size remarkably improves
the performance on six of the eight test functions. The optimal
population size takes a wide range of values, but, with one
exception, scales sub-linearly with the problem dimension. The
global optimum can be located in all but one function. The
performance for locating the global optimum scales between linear
and cubic with the problem dimension. In a comparison to
state-of-the-art global search strategies the CMA evolution strategy
achieves superior performance on multimodal, non-separable test
functions without intricate parameter tuning.
Errata:
Section 3.1, "Additional bounds are implemented...E.g.
f_Schwefel(x) + 10^4 sum_{i=1}^n \theta(|x_i|-500) x_i^2 is minimized..."
the formula must read
f_Schwefel(x) + 10^4 sum_{i=1}^n \theta(|x_i|-500)*(|x_i|-500)^2 is minimized...
Section 3.2: "The starting point x^(0) is sampled uniformly..."
must read "The starting point _w^(0) is sampled uniformly..."
In: Parallel Problem Solving from Nature PPSN VIII, Proceedings, 2004.
http://www.springer.de/comp/lncs/index.html