Evolution and Optimum Seeking

Numerical Comparison of Strategies 213
Table 6.7: Results of all strategies in the second comparison test,
constrained problems
Problem No. ROSE COMP EVOL GRUP REKO
2.29 3 1 4 3 3
2.30 1 5 1 1 1
2.31 3v 3 1 1 1
2.32 3v 3 1 1 1
2.33 3 2 5 4 1
2.34 1 2 3 3 2
2.35 3v 1 4 4 4
2.36 1 1 1 1 1
2.37 3 1 1 1 1
2.38 3v 3 1 1 1
2.39 3 3 4 4 3
2.40 5 5 5 5 5
2.41 5 5 5 5 5
2.42 3 3 2 2 1
2.43 3v 3 2 2 1
2.44 1 5 1 1 1
2.45 3 2 4 2 1
2.46 3 2 3 3 1
2.47 3v 1 1 1 1
2.48 3v 3 1 1 1
2.49 3 2 4 3 1
2.50 3 1 1 1 1
Sum 62 57 55 50 38
The meaning of the symbols is as in Table 6.5 \v" is
used in connection with the Rosenbrock method for
constrained cases: The starting point hadtobe
displaced since it was not feasible for this method.
each case the closest to the objective was again the (10 , 100) evolution strategy with
recombination, but even that result had to be classi ed as \no solution."
On the whole the evolution methods cope with constrained problems no worse than the
Rosenbrock or complex strategies, but they do reveal inadequacies that are not apparent
in unconstrained problems. In particular the 1=5 success rule for adapting the variances
of the mutation step lengths in the (1+1) evolution strategy appears to be unsuitable for
attaining an optimal rate of convergence when several constraints become active.
In problems with active constraints, the tendency of the evolution methods to follow
the average gradient trajectory causes the search to come quickly up against one or more
boundaries of the feasible region. The subsequent migration towards the objective along