Research On Compact Genetic Algorithm In Continuous Domain

The genetic algorithm is a stochastic search and optimization method inspired by the biological evolution phenomenon, first proposed by Dr. Holland in 1970. This algorithm is widely used in aspects such as image coding and decoding, machine learning, biological information and wireless sensor network. However, the genetic algorithm has some inner defects which have prevent its further application. These inner defects including the slow convergence speed, the high demand of memory and the difficulty in ensure of stop criteria. Many paper proposed the probability based evolution algorithms to further improve the general genetic algorithm and the CGA (compact genetic algorithm) is a kind of successful probability based algorithm. CGA uses probability vector to store the information of the whole generation rather than record every individual, cross over and mutation in general genetic algorithm for evolution are replaced by updating on the probability vector, thus CGA requires much lower memory cost and this is the key point making its successful.Recent researches on CGA are mostly in discrete domain and the inner theory of CGA is applicable only to discrete encoded problems. In this paper we establish the basic theory on how to adopt CGA to continuous domain. We give the new probability representation, the new updating rules on probability and the initialization of the algorithm which compose the key structure of the new algorithm, mathematical analysis and numerical simulation are presented to support our theory; We adopt elitism selection to improve the new algorithm further, we propose different kinds of elitism selection strategy, compare their performance and analysis the life cycle of the elitism; we study the evolution model of our algorithm and deduced some relation between cCGA and ES; research on the selection density of our algorithm is given and the speedup model of elitism is proposed. Also, we extend some theory in discrete CGA to continuous CGA and outline the unified conclusion. In this paper, each point is supported by strict analysis and large amount of numerical experiment. The combination of theory and experiment make our algorithm reliability and scalability.