Abstract: Schema theorems are important theoretical results in genetic algorithms. However, the general schema theorems only discuss the probability of the survival of schemas, but do not discuss the probability of the construction of schemas. In this paper we discuss the schema theorems affected by both the survival and the construction of schemas. First, some basic concepts including the subschema, the complementary-schema, the survival and the construction of schema are introduced, and then the schema theorems affected by both the survival and the construction of schemas are proposed. They are generalizations and extensions of the existing schema theorems.

Key words: genetic algorithm, schema theorem, uniform recombination