An abstract and postscript version of the thesis can be found here. The search space induced by an algorithm can be represented by a graph with vertices representing state and edges representing possible shifts in state. In GAs using finite strings over finite discrete alphabets, these graphs can be simplified so that nodes represent strings, or populations of strings, and edges join strings that can be created one from the other through some genetic operation. The structure of the graphs will depend on the types of operations and on the size of the alphabet. This research identifies isomorphisms between mutation and crossover on arbitrary alphabets, higher order crossover operators that follow naturally, and other extensions of the usual notion of crossover in ordinary GAs.
Preliminary results show in some respects superior properties under certain benign assumptions.
It is observed in various studies that Genetic Algorithms when implemented in parallel give super-linear speed up in solution time. However, elementary theoretical considerations indicate that any parallel algorithm can be simulated by a sequential algorithm with at worst a linear time ratio. Thus, the switch from a single population to multiple populations must yield additional benefits on these problems. This opens questions on the role of recombination and transfer of information between individuals and populations. Initial research is on the correlations one can expect between simple real-valued operators working at the phenotypical level on landscapes with simple features such as ranges of peaks.