Some new results for multiple-valued genetic algorithms

The paper describes each of the operations involved in a genetic algorithm: reproduction, mutation, and selection, and discusses each in the language of classical multiple-valued logic. The differences among forms of reproduction that have been used by various researchers are examined and the relative importance of each of the operations in searching for highly fit members of a population is evaluated. The role of mutation in ensuring the completeness of the set of genetic operators is established. A recently proposed form of selection is shown to force convergence of the genetic algorithm, independently of reproduction and mutation. Finally, the theorems developed are applied to practical problems in the use of genetic algorithms.