Research On Improved Methods And Convergent Theory Of Artificial Bee Colony Algorithm

Artificial Bee Colony (ABC) algorithm, after more than a decade of research and development, has become an important technology of solving the complex optimization problems for scientific research and engineering practice. As the theory research and application field for ABC algorithm goes deeper and broadens, ABC algorithm has become an increasing important topics in nature-inspired computation field. The advances in theoretical research and application fields of ABC algorithm has been reviewed from the angle of methodology. Some innovations about improved algorithms, algorithm fusion and algorithm applications have been conducted. The improved algorithms have broadened the application fields of ABC algorithm. Meanwhile, The Markov model of bee colony and the convergence about ABC algorithm has been proved. The major researches on ABC algorithm are as follows:1. In order to improve the optimized ability fully and begin with diversity of the colony, the two improved algorithms are proposed by combining the advantages of other evolutionary algorithms and swarm intelligence algorithms, on the basis of a comprehensive analysis of the performance of ABC algorithm:(1) In swarm intelligence optimization algorithms, the rapid reduction of the diversity of population will enable the algorithms trap into local optimum. It is difficult to break local constraints and reach the global optimum. One multi-population scheme has formed using the partitioning strategy based on the fitness values. The Intersect Mutation Artificial Bee Colony algorithm has been proposed by introducing intersect mutation operator among multi-population to improve the diversity and overcome the shortcoming such as trapping into the local optimum in optimizing multimodal functions using standard ABC algorithm.(2) Inspired by the group dynamics, the cognitive ability for an individual (including self-awareness and social-awareness) will have significant impact on the development of the optimized performance.BY combining the self-awareness and social-awareness for every individual in bee colony, one new improved ABC algorithm based on the "Dual cognitive ability" has been proposed which is named Dual Cognitive Abilities Artificial Bee Colony algorithm (DCA-ABC).Specifically, each individual should remember not only their location and the corresponding fitness value which is reflecting the individual’s perception of its own, but also the current global optimal solution in the entire population during the search which is reflecting the individual’s learning communication and social cognition ability. At the same time, in order relieve the "premature" phenomenon, two methods are incorporated into DCA-ABC algorithm:one is to avoid the adhesion phenomena in the same location, a mutually exclusive factor has been introduced to enhance the chance for finding new candidate solutions, the other is that one dynamic adjustment mechanism has been proposed by using the dynamic weighting factor as a function of the number of iterations in the DCA-ABC algorithm. The numerical experiments show that the overall optimization ability has a more significant improvement for the improved algorithm.2. The research on fusion algorithm has been one of the important ways to improve the performance of the algorithm. Differential Evolution algorithm has been widely used in many fields because of its good global optimization ability which is depending on the different mutation strategies to approximate the optimal solution. A set of improved artificial bee colony algorithms based on operator-based DE has been put forward according to the six mutation strategies commonly used in DE algorithm. A comprehensive comparison and convergence of numerical experiments about the improved algorithms which are based on DE operators has been conducted according to some benchmark functions.3. The K-means clustering algorithm is one of the most widely used algorithms because of its simpler principles and easier implementation. A local search technique is used to locate the clustering center in K-means algorithm. The technique depended strongly the choice of the initial cluster centers, resulting in premature convergence and trapping into local optimal. The ABC algorithm and improved algorithms which are proposed and validated by some numerical experiments in this paper have been used to optimize the search process in locating the clustering center and improve the quality of clustering. In the experimental design, several standard test data sets selected from UCI machine learning database has been used to compare, verify and analysis between we proposed and other optimization algorithm.4. Currently, the researches about ABC are usually algorithm improvements and the application based and the analysis of the convergence of the algorithm is relatively weak which is in the preliminary stage. Based on the empirical literatures about the proving of the convergence of ABC algorithm, the conclusion that the population sequence is finite Markov chain model has been made and the population sequence converges with probability1to the global optimal solution set has also been clarified.