Survival and Construction Theory for One-Point Crossover

As a fundamental operator in genetic algorithms (GAs), crossover may not only make an existing schema survived, but also construct a new one from other existing schemata. Unfortunately, the traditional schema theorem (Holland 1975) does not take into account the positive effects of a schema construction through crossover operation. Thus, they can not well characterize the evolution of a schema. In this paper we first propose a new ternary representation, through which the survival and construction of a schema can be easily distinguished. Subsequently, we discuss the survival theory and construction one for one-point crossover. It deepens and generalizes the existing results on schema theorems