关键词: 差分进化算法, 进化规划算法, 双种群, 混沌重组策略, 非均匀变异

Abstract: The Standard Differential Evolution（SDE） algorithm has the advantages of simplicity, few control parameters required, and easily be used, but has the disadvantage of premature convergence and relatively slow rate for hard optimization problems. The improved DE algorithm, namely Bi-Group Differential Evolutionary Programming（BGDEP）, is presented to overcome some drawbacks of the SDE algorithm. The proposed BGDEP algorithm divides the entire population into double subgroups which utilize DE/rand/1/bin and DE/best/2/bin schemes to generate new mutate individuals to evolve next generation in parallel, respectively. In order to interact information between double subgroups, the modified algorithm merges them into one whole population at intervals of δt-periodic generations and divides subsequently this population into new double subgroups by using chaotic recombination operators. In every generation of co-evolution process of bi-group, the best individual in double subgroups is evolved by evolutionary programming with non-uniform mutation operators. Due to the above co-evolution, the proposed algorithm performs significantly fast and robust convergence, and performs a global exploratory search. 4 benchmark 30-dimensional functions in hard optimization fields are utilized to test comparatively performances of the new BGDEP algorithm and the experimental results show that this approach outperforms other 4 algorithms, such as SDEs（i.e., DE/rand/1/bin and DE/best/2/bin strategies），Bi-Group Differential Evolution（BGDE） and Evolutionary Programming with Non-Uniform Mutation（NUMEP），etc.，in terms of solution accuracy，robustness，convergence speed and global exploring ability.

Key words: differential evolution, evolutionary programming, bi-group, chaotic recombination strategy, non-uniform mutation