Mathematical analysis of the cumulative effect of novel ternary crossover operator and mutation on probability of survival of a schema

The concept of schema plays a vital role in the study of genetic algorithms. The effect of selection, simple crossover and mutation on schemata has already been studied rigorously by several researchers. In this paper a novel ternary crossover operator is introduced and its effects on the probability of survival of a schema are meticulously analyzed. A theorem regarding the effect of novel crossover operator on survival of schemata is proved and based on that the combined effect of novel crossover and mutation on probability of survival of a schema is established mathematically.