Evolution and Optimum Seeking

388 Appendix B
EPSILO (one dimensional Holds parameters that a ect the attainable accuracy of
real array of approximation. The lowest possible values are machinelength
4) dependent.
EPSILO(1) Lower bound to step sizes, absolute.
EPSILO(2) Lower bound to step sizes relative tovalues of variables
(not implemented in this program).
EPSILO(3) Limit to absolute value of objective function di erences
for convergence test.
EPSILO(4) As EPSILO(3) but relative.
DELTAS (real) Factor used in step-size change. All standard deviations
(=step sizes) S(I) are multiplied by a common
random number EXP(GAUSSN(DELTAS)), where
GAUSSN(DELTAS) is a normally distributed random
number with zero mean and standard deviation DELTAS.
EXP(DELTAS) 1.0.
DELTAI (real) As for DELTAS, but each S(I) is multiplied by its own
random factor EXP(GAUSSN(DELTAI)).
EXP(DELTAI) 1.0. The S(I) retain their initial values
if DELTAS = 0.0 and DELTAI = 0.0. The variables
can be scaled only by recombination (IREKOM > 1) if
DELTAI = 0.0.
The following rules are suggested to provide the most
rapid convergence for sphere models:
DELTAS = C/SQRT(2.0 N).
DELTAI = C/(SQRT(2.0 N/SQRT(NS)).
The constant C can increase sublinearly with NACHKO,
but it must be reduced as IELTER increases. The empirical
value C = 1.0 has been found applicable for IELTER
= 10, NACHKO = 100, and BKOMMA = .TRUE., which
is a (10 , 100) evolution strategy.
DELTAP (real) Standard deviation in random variation of the position
angles P(I) for the mutation ellipsoid.
DELTAP > 0.0 if BKORRL = .TRUE. Data in radians.
A suitable value has been found to be DELTAP = 5.0
0.01745 (5 degrees) in certain cases.
N (integer) Number of parameters N > 0.
M (integer) Number of constraints M 0.
NS (integer) Field length in array Sornumber of distinct step-size
parameters that can be used, 1 NS N. The mutation
ellipse becomes a hypersphere for NS = 1. All the principal
axes of the ellipsoid may be di erent for NS = N,
whereas 1