CONVERGENCE RATES FOR A CLASS OF EVOLUTIONARY ALGORITHMS WITH ELITIST STRATEGY

This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies.

Elitism-based immune genetic algorithm and its application to optimization of complex multi-modal functions

A novel immune genetic algorithm with the elitist selection and elitist crossover was proposed, which is called the immune genetic algorithm with the elitism （IGAE）. In IGAE, the new methods for computing antibody similarity, expected reproduction probability, and clonal selection probability were given. IGAE has three features. The first is that the similarities of two antibodies in structure and quality are all defined in the form of percentage, which helps to describe the similarity of two antibodies more accurately and to reduce the computational burden effectively. The second is that with the elitist selection and elitist crossover strategy IGAE is able to find the globally optimal solution of a given problem. The third is that the formula of expected reproduction probability of antibody can be adjusted through a parameter r, which helps to balance the population diversity and the convergence speed of IGAE so that IGAE can find the globally optimal solution of a given problem more rapidly. Two different complex multi-modal functions were selected to test the validity of IGAE. The experimental results show that IGAE can find the globally maximum/minimum values of the two functions rapidly. The experimental results also confirm that IGAE is of better performance in convergence speed, solution variation behavior, and computational efficiency compared with the canonical genetic algorithm with the elitism and the immune genetic algorithm with the information entropy and elitism.

Adaptive template filter method for image processing based on immune genetic algorithm

To preserve the original signal as much as possible and filter random noises as many as possible in image processing,a threshold optimization-based adaptive template filtering algorithm was proposed.Unlike conventional filters whose template shapes and coefficients were fixed,multi-templates were defined and the right template for each pixel could be matched adaptively based on local image characteristics in the proposed method.The superiority of this method was verified by former results concerning the matching experiment of actual image with the comparison of conventional filtering methods.The adaptive search ability of immune genetic algorithm with the elitist selection and elitist crossover(IGAE) was used to optimize threshold t of the transformation function,and then combined with wavelet transformation to estimate noise variance.Multi-experiments were performed to test the validity of IGAE.The results show that the filtered result of t obtained by IGAE is superior to that of t obtained by other methods,IGAE has a faster convergence speed and a higher computational efficiency compared with the canonical genetic algorithm with the elitism and the immune algorithm with the information entropy and elitism by multi-experiments.