So far, the basic knowledge about setting up the parameters of Evolutionary Algorithms stems from a lot of empirical work and few theoretical results. The standard guidelines for parameters such as crossover rate, mutation probability, and population size as well as the standard settings of the recombination operator and selection mechanism were presented in chapter 2 for the Evolutionary Algorithms. In the case of Evolution Strategies and Evolutionary Programming, the self-adaptation mechanism for strategy parameters solves this parameterization problem in an elegant way, while for Genetic Algorithms no such technique is employed. Chapter 6 served to identify a reasonable choice of the mutation rate, but no theoretically confirmed knowledge about the choice of the crossover rate and the crossover operator is available. With respect to the optimal population size for Genetic Algorithms, Goldberg presented some theoretical arguments based on maximizing the number of schemata processed by the algorithm within fixed time, arriving at an optimal size λ* = 3 for serial implementations and extremely small string length [Gol89b]. However, as indicated in section 2.3.7 and chapter 6, it is by no means clear whether the schema processing point of view is appropriately preferred to the convergence velocity investigations presented in section 2.1.7 and chapter 6. As pointed out several times, we prefer the point of view which concentrates on a convergence velocity analysis. Consequently, the search for useful parameter settings of a Genetic Algorithm constitutes an optimization problem by itself, leading to the idea of using an Evolutionary Algorithm on a higher level to evolve optimal parameter settings of Genetic Algorithms. Due to the existence of two logically different levels in such an approach, it is reasonable to call it a meta-evolutionary algorithm. By concentrating on meta-evolution in this chapter, we will radically deviate from the biological model, where no two-level evolution process is to be observed but the self-adaptation principle can well be identified (as argued in chapter 2). However, there are several reasons why meta-evolution promises to yield some helpful insight into the working principles of Evolutionary Algorithms: First, meta-evolution provides the possibility to test whether the basic heuristic and the theoretical knowledge about parameterizations of Genetic Algorithms is also evolvable by the experimental approach, thus allowing us to confirm the heuristics or to point at alternatives.
On the Self-Structuring Antenna