Biased Mutation for Evolution Strategies - Self-Adaptive Heuristics for Evolutionary Computation - page 72

Table 4.15. Experimental results of the BMO with various populations ratios on the
constrained function g04. Only the population ratio of (50,100) could not achieve good
approximation results because of the weak selection pressure.

(5,100) (15,100) (15,300) (15,500) (50,100) (50,300) (50,500)
best -30665.538 -30665.538 -30665.538 -30665.538 -30552.670 -30665.538 -30665.538
mean -30665.538 -30665.538 -30665.538 -30665.538 -30438.105 -30665.538 -30665.538
dev 0.00069 0.00056 0.00039 0.00039 82.70956 0.00039 0.0

the quality is comparatively worse after 1000 generations. The similar behavior of
the other settings does not allow a recommendation of a specific setting. But fur-
ther tests on other functions showed that (15,100) and (15,300) are good choices.

Interpretation of the BMO in Constrained Domains

The question arises, how the BMO is able to prevent the premature step size
reduction in constrained search domains. Figure 4.10 shows the situation in the
vicinity of the constraint boundary. As we will explain in chapter 7, the success
probability p s for big step sizes σ>d is small, d is the distance of individual x
to the optimum. The mutation ellipsoid is cut off by the constraint boundary.
The experiments show that the BMO produces mutations without decreasing the

infeasible search space

direction
to optimum

b

lines of constant fitness

x+b

feasible search space

Fig. 4.10. The effect of the BMO in the vicinity of the infeasible search region: The
bias is able to increase the success rate p s . Mutations become possible that main-
tain a certain distance to the constraint boundary. A decrease of the step sizes is not
advantageous anymore.