Evolutionary Computation : A Unified Approach

6.4. REPRODUCTION-ONLY MODELS 157
16
14
12
Blend recombination (0.5) and 1/10 Gaussian mutation (2.0)
Blend recombination (0.5) and 2/10 Gaussian mutation (2.0)
Blend recombination (0.5) and 5/10 Gaussian mutation (2.0)
Blend recombination (0.5) and 10/10 Gaussian mutation (2.0)
Population Dispersion
10
8
6
4
2
0
0 20 40 60 80 100
Generations
Figure 6.28: Population dispersion for simple 2-parent blending recombination and Gaussian
mutation.
A more detailed analysis of these real-valued mutation and recombination operators has
traditionally been done in the context of function optimization. As a consequence, this more
detailed analyses is presented later in this chapter in section 6.9.1.
Fixed-Length Integer-Valued Linear Genomes
Integer-valued genes can be conveniently viewed as a special case of discrete-valued genes if
they are restricted to a finite set of values, or as a special case of real-valued genes if they
can take on an infinite number of values. As such, most of the population-dynamics analysis
of discrete and real-valued representations is easily extended to the integer-valued case. For
example, it is not hard to imagine a discrete (binomial) analog to Gaussian mutation, or
blending recombination operators restricted to integer values. Consequently, there is little
additional analysis that is required at the application-independent level.
Fixed-Size Nonlinear Genomes
There are many application domains in which the natural phenotypic representation of the
objects to be evolved is a nonlinear fixed-size structure. Examples include matrices describing
solutions to transportation problems, and graph structures with a fixed number of nodes
representing finite-state machines or artificial neural networks. Since each such structure
can be “linearized”, it is generally quite straightforward to map these problem domains onto
an internal fixed-length linear genome, and then use the corresponding mutation and recombination
operators. This has the advantage of being able to reuse a significant portion of
existing mature software, but also raises some issues for the EA practitioner. For example,
there is often more than one way to linearize a structure. In the case of matrices, one could