Evolutionary Optimization in an Algorithmic Setting

TL;DR

This paper formalizes cooperation and competition in evolutionary algorithms, proposing subclasses and analyzing their properties, and introduces an Evolutionary Turing Machine model to study population dynamics.

Contribution

It introduces a formal framework for cooperation and competition in evolutionary algorithms, including subclasses and a new Evolutionary Turing Machine model.

Findings

Evolutionary algorithms are more expressive than recursive algorithms.

Proposed subclasses include bounded finite, unbounded finite, and infinite types.

Results on completeness, optimality, and search decidability.

Abstract

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.