A Formal Design Model for Genetic Algorithms Operators and its Encoding in PVS

Abstract

Genetic Algorithms (GA) are bio-inspired algorithms that are now used in safety critical systems, robotics, artificial intelligence and bioinformatics, etc. A formal semantic model for GA is needed that can provide a framework for the modeling, reasoning and verification of GA based systems. On the other hand, Unifying Theories of Programming (UTP) offers formal semantic foundations for programming as well as specification languages. UTP is used in this paper to formalize a family of crossover and mutation operators of GA, where operators are defined as design models. UTP design models also allow the establishment of refinement and equivalence relations between GA operators by introducing implication between predicates. As an example, the equivalence relation between operators is proved with the PVS proof assistant.