On Foundations of Evolutionary Computation

Abstract

There are different models of evolutionary computations: genetic algorithms, genetic programming, etc. This chapter presents mathematical foundations of evolutionary computation based on the concept of evolutionary automaton. Different classes of evolutionary automata (evolutionary finite automata, evolutionary Turing machines and evolutionary inductive Turing machines) are introduced and studied. It is demonstrated that evolutionary algorithms are more expressive than conventional recursive algorithms, such as Turing machines. Universal evolutionary algorithms and automata are constructed. It is proved that classes of evolutionary finite automata, evolutionary Turing machines and evolutionary inductive Turing machines have universal automata. As in the case of conventional automata and Turing machines, universal evolutionary algorithms and automata provide means to study many important problems in the area of evolutionary computation, such as complexity, completeness, optimality and search decidability of evolutionary algorithms, as well as such natural phenomena as cooperation and competition. Expressiveness and generality of the introduced classes of evolutionary automata are investigated.