Biased Mutation for Evolution Strategies - Self-Adaptive Heuristics for Evolutionary Computation - page 54

2

1

x b

1

2

Fig. 4.2. Concept of the BMO in two dimensions: The center of the mutation ellipsoid
is shifted by the bias coecient vector b within the bounds of the step sizes σ

-4 -2 2 4

b

Fig. 4.3. Comparison of standard mutation (solid), directed mutation (dotted) and
biased mutation (dashed) with bias b

The bias coecient vector ξ improves the success rate situation as the success
area increases. The BMO approach is as flexible as correlated and directed mu-
tation, but is less computational expensive than both methods, see section 4.2.4.
In comparison to the directed mutation the computation of the random numbers
of an asymmetric probability density function is usually more computationally
expensive than the computation of Gaussian random numbers. Especially, in
practice the implementation is less complex. Figure 4.3 shows a comparison of
the different probability density functions of the three mentioned approaches. In
the following, we introduce various variants of the standard BMO. In section 4.5
their capabilities are examined experimentally.

4.2.2 Sphere Biased Mutation Operator (sBMO)

We propose the Sphere Biased Mutation Operator (sBMO) as a variant of the
BMO with only one step size analog to the isotropic Gaussian mutation with one