Physics and Computation Genetic Algorithms on Structurally Dynamic Lattices

We introduce a new type of genetic algorithm (GA) modell7, 4] that consists of a lattice, a group of organisms (one to each lattice site) and a set of dynamical rules. These rules govern crossover and mutation of the organisms, as well as alterations in the lattice structure. The lattice and its dynamical rules belong to a class of objects known as topological cellular automataa8, 5] (TCA). In the spirit of Darwinian optimization modelss3], we wish to apply observed features of biological natural selection within a computational framework. In this case, the evolutionary principle of interest is the propensity for animals to choose mates from neighboring groups, but not from their own immediate families. A well-studied example of this is the desire for song-birds to select partners with similar, but not identical songss1]. In this manner, they hope to avoid mating with family members, but at the same time increase their chances of procreating with their ttest neighbors. Because this principle serves in biological systems to increase species tness, we hope that it will provide a sound strategy for computational models as well. We have found commonalities between these geographic-and tness-based procreative connection mechanisms and the link dynamics of topological cellular automata. Like conventional cellular automata, TCA consist of a lattice, a set of site values, and a list of simple rules to determine future site values. They diier from standard automata, however, in the fact that TCA lattice connections are subject to addition or removal, based upon local coupling and decoupling rules. These rules, functions of site values in a given neighborhood, act each time step to alter lattice topology. TCA dynamics have been shown to yield a wide range of behavior, including growth, decay, periodicity and self-organizationn9, 6]. Applications of TCA models are diverse, including studies of phase transformations in physical and chemical systemss10, 11]. Das, Crutchheld, Mitchell and Hansonn2] have observed emergent collective behavior by using a genetic algorithm to evolve cellular automata. In the system that we propose, a hybrid between GA and TCA dynamics, we use TCA rules to evolve a set of GA. We have found the link structure exibility of TCA to aid in the optimization properties of GA. In our model a lattice is rst seeded with single-chromosome organisms of xed length, one per site. Each chromosome is, in turn, composed of a combination of genes, randomly chosen to be zeroes or …