  Evolutionary processes proved very useful for solving optimization problems.
In this work, we build a formalization of the notion of cooperation and
competition of multiple systems working toward a common optimization goal of
the population using evolutionary computation techniques. It is justified that
evolutionary algorithms are more expressive than conventional recursive
algorithms. Three subclasses of evolutionary algorithms are proposed here:
bounded finite, unbounded finite and infinite types. Some results on
completeness, optimality and search decidability for the above classes are
presented. A natural extension of Evolutionary Turing Machine model developed
in this paper allows one to mathematically represent and study properties of
cooperation and competition in a population of optimized species.
