Self-Adaptation - Self-Adaptive Heuristics for Evolutionary Computation - page 36

Table 3.1. Experimental comparison of an ES with a fixed step size on the 2-
dimensional sphere function and the self-adaptive step size control (SA-ES) on a 30-
dimension sphere function. The SA-ES shows outstanding results in comparison to the
ES with constant step sizes.

Experimental settings
Population model (15,100)

standard, n σ = N , τ 0 =( √ 2 n ) − 1 and τ =( 2 √ n ) − 1 Mutation type

intermediate, ρ =2 Crossover type

Selection type comma

Initialization [-100;100]

Termination 1000 generations

best worst mean dev
ES σ =0 . 1 2.77E-05 2.55E-03 9.72E-04 0.00058
ES σ =0 . 001 3.57E-08 1.11E+02 1.20E+01 25.30838
SA-ES 2.92E-56 3.71E-50 3.36E-51 8.27E-51

1e+010

SA-ES on 30-dim sphere
ES with sigma=0.1 on 2-dim sphere
ES with sigma=0.001 on 2-dim sphere

1

1e-010

1e-020

1e-030

1e-040

1e-050

1e-060

0 200 400 600 800 1000

generations

Fig. 3.5. Plot of typical runs of the variants ES with constant mutation strength ( σ =
0 . 1and σ =0 . 001) and the self-adaptive ES on the sphere function. The approximation
abilities of the self-adaptive process are outstanding in comparison to the ES with
constant step sizes. The approximation abilities of a SA-ES on the 2-dimensional sphere
function - not displayed here - go beyond the accuracy of the data structure after a
few hundred generations.