Formal verification of crossover operator in Genetic Algorithms using Prototype Verification System (PVS)

Genetic Algorithms (GA) are commonly used for solving search problems. Modeling of evolutionary systems is another interesting area for GA research. Using Prototype Verification System (PVS), this article presents a method of formal specification and verification for the most rudimentary properties of genetic algorithms. This research formally proves a generalized version of the crossover operator of GA. Starting with a single-point crossover operator and its properties using PVS specification language, it specifies a multi-point crossover operator (along with properties). Operators used in both single-point and multi-point crossover operation are specified and their properties are proved. The exact relation between these operators has also been established. The research also proves the correctness of both the operators using proof assistant PVS.