Research On Schemata Theorem And Emergence Of Evolutionary Computation And Applications

Evolutionary computation is a random heuristic stochastic search algorithm which simulates biological evolution and modern genetics. As a novel interdisciplinary field, evolutionary computation has an expansive foreground. At the same time, evolutionary computation need to improve its theory foundations. The understanding of evolutionary computation's mechanisms and principles will not only help people analyze the dynamic behavior of an evolutionary population and convergence of an algorithm but also assist people to design a new algorithm or improve the old ones. The main contents are as following:1. We depict separately the frameworks of evolution strategy, evolutionary programming, genetic algorithms and genetic programming firstly. And then a framework of evolutionary computation is given. Some mathematical descriptions of evolutionary computation are introduced by using different mathematical methods.2. A unified representation of evolutionary computation is formulated on the basis of analyzing the evolutionary operators of evolution strategy, evolutionary programming, genetic algorithms and genetic programming one by one. Appropriate schema is defined as a new concept, and building blocks conception is extended to all fields in evolutionary computation. For different selection mechanism of evolutionary computation, we study schemata evolution and obtain exact schemata theorem based on approximate schemata theorem, then coarse-grain schemata theorem is derived from a fine-gain one. On the other hand, we study the schemata form invariance, and get a result of schemata theorem of variable-length evolutionary computation. So, the schemata theorem is extended to all evolutionary computation fields. Finally, we analyze the building blocks hypothesis on experiment problems, and obtain a good outcome. These prove that the building blocks are ubiquitous in evolutionary computation.3. The definitions of emergence and chaos are introduced to evolutionary computation. And then, On the basis of evolutionary computation's experiment results, we analyze the emergence in evolutionary computation from experiment and theory. The evolutionary operators are defined as a mapping from one discrete topological space into another one, and evolutionary computation is equivalent to a composite function of shift map. We apply Dynamical Systems as a tool to do it. The paper demonstrates that the genetic algorithm with finite population is chaotic in Devaney. Hence, the scope of topological entropy in Bowen is presented. And we explain the relation of emergence and chaos in evolutionary computation. 4. We give an analysis of cohort genetic algorithm in theory, and a proof of algorithm convergence is presented. And we point out, this is a key factor of cohort genetic algorithm for finding a balance between escaping from premature convergence and making the power schemata of high evolutionary ability having enough time in the population. Then, we apply cohort genetic algorithm to optimize multimodal problems. With different parameters, experimental are implemented, and the results show proper parameters control in cohort genetic algorithm is important to its performance.