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

摘要： 标准差分进化算法（SDE）具有算法简单，控制参数少，易于实现等优点。但在难优化问题中，算法存在收敛速度较慢和容易早熟等缺陷。为克服此缺点，提出一种改进算法——双种群差分进化规划算法（BGDEP）。该算法将种群划分为两个子群独立进化，分别采用DE/rand/1/bin和DE/best/2/bin版本生成变异个体。每隔δt（取5~10）代，将两个子群合并为一个种群，再应用混沌重组算子将之划分为两个子群，以实现子群间的信息交流。在双种群协同差分进化的同时，应用非均匀变异算子对其最优个体执行进化规划操作，使得算法具有较快的收敛速度和较强的全局寻优能力。为测试BGDEP的性能，给出了4个30维benchmark函数优化问题的对比数值实验。结果表明，BGDEP的求解精度、收敛速度、鲁棒性等性能优于SDE、双种群差分进化（BGDE）和非均匀变异进化规划（NUMEP）等4种算法。

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