Page 96 - 49A Field Guide to Genetic Programming

82 9 Multi-objective Genetic Programming

The pygmies and civil servants approach proposed in (Ryan, 1994, 1996)
combines the separation typical of Pareto-based approaches with biased
search operators. In this system two lists are built, one where individu-
als are ranked based on fitness and the other where individuals are ranked
based on a linear combination of fitness and size (i.e., a parsimonious fit-
ness function). During crossover, the algorithm draws one parent from the
first list and the other from the second list. This can be seen as a form of
disassortative mating aimed at maintain diversity in the population. An-
other example of this kind is (Zhang and Rockett, 2005) where crossover
was modified so that an offspring is retained only if it dominates either of
its parents.
Furthermore, as discussed in Sections 5.2 and 11.3.2, there are several
mutation operators with a direct or indirect bias towards smaller programs.
This provides a pressure towards the evolution of more parsimonious solu-
tions throughout a run.
As with the staged fitness functions discussed in the previous section,
it is also possible to activate operators with a known bias towards smaller
programs only when the main objective — say a 100% correct solution — has
been achieved. This was tested in (Pujol, 1999; Pujol and Poli, 1997), where
GP was used to evolve neural networks. After a 100% correct solution was
found, one hidden node of each network in the population was replaced by
a terminal, and the evolution process was resumed. This pruning procedure
was repeated until the specified number of generations had been reached.