函数周期与遗传算法编码元数.pdf

On Function Period and Coding-Alphabet Cardinality * of Genetic Algorithms Hongqiang Mo 1, Zhong Li 2 , Zongyuan Mao 1, and Xiangyang Li 1 1College of Automation Science and Engineering, South China University of Technology, 510641 Guangzhou, P.R. China, Corresponding author Email: hqiangmo@ 2 Faculty of Electrical and Computer Engineering, FernUniversität in Hagen, 58084 Hagen, Germany Abstract – By introducing a criterion based on order-1 building blocks, a framework is established for comparing different choices of the cardinalities of the coding alphabets of the genetic algorithms (GA’s) applied to single-periodical and multiple-periodical fitness functions. It is shown that the genetic algorithms sample the search spaces simultaneously with multiple sampling periods. Thus, by properly choosing the cardinalities in terms of the periods of the fitness functions, order-1 building blocks can be obtained on the corresponding fixed positions of the strings of the GA’s. Thereafter, in the simulations, survival and domination rates of the order-1 schemata are introduced to compare the performance of the genetic algorithms with different cardinalities of the coding alphabets. The simulation results demonstrate the effectiveness of the framework. Key Words — genetic algorithms, coding, function period, cardinality of coding alphabet 1. Introduction The capacity of the GA’s to simultaneously process a large number of schemata lies in the implicit parallelism, which leads to the success of GA’s in exploring complex fitness [1-4]. To make use of implicit parallelism