Schema survival rates and heuristic search in genetic algorithms

Genetic algorithms are a relatively new paradigm for search in artificial intelligence. It is shown that, for certain kinds of search problems, called permutation problems, the ordinary rule for intermixing the genes between two organisms leads to longer search chains than are necessary. A schema is a partially completed organism. Its order is the number of fixed components and its length is the distance between its first and last fixed component. A scheme is compact if its length and order are nearly equal. It is shown that the survival rate of a compact schema is directly proportional to the quality of the solution after a fixed number of iterations. The ordinary gene intermixing method called a crossover rule, separates the parents of a new organism at almost the precise point at which the compact scheme survival rate is at a minimum. A variation of the crossover rule is proposed that takes advantage of the knowledge of survival rates on the quality of the solution