| 摘要: |
| 为了分析差分演化(differential evolution,简称DE)的收敛性并改善其算法性能,首先将差分算子
(differential operator,简称DO)定义为解空间到解空间的笛卡尔积的一种随机映射,利用随机泛函理论中的随机压缩
映射原理证明了DE 的渐近收敛性;然后,在“拟物拟人算法”的启发下,通过对DE 各进化模式的共性特征与性能差
异的分析,提出了一种具有多进化模式协作的差分演化算法(differential evolution with multi-strategy cooperatingevolution,简称MEDE),分析了它所具有的隐含特性,并在多模式差分算子(multi-strategy differential operator,简称
MDO)定义的基础上证明了它的渐进收敛性.对5 个经典测试函数的仿真计算结果表明,与原始的DE,DEfirDE 和
DEfirSPX 等算法相比,MEDE 算法在求解质量、适应性和鲁棒性方面均具有较明显的优势,非常适于求解复杂高维
函数的数值最优化问题. |
| 关键词: 差分演化 渐近收敛性 压缩映射 随机算子 进化模式 |
| DOI： |
| 分类号: |
| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60473045, 60471022 (国家自然科学基金); theHebei Provincial Natural Science Foundation of China under Grant No.F2008000635 (河北省自然科学基金) |
|
| Convergent Analysis and Algorithmic Improvement of Differential Evolution |
|
HE Yi-Chao,WANG Xi-Zhao,LIU Kun-Qi,WANG Yan-Qi
|
| Abstract: |
| To analyze the convergence of differential evolution (DE) and enhance its capability and stability, this
paper first defines a differential operator (DO) as a random mapping from the solution space to the Cartesian
product of solution space, and proves the asymptotic convergence of DE based on the random contraction mapping
theorem in random functional analysis theory. Then, inspired by “quasi-physical personification algorithm”, this
paper proposes an improved differential evolution with multi-strategy cooperating evolution (MEDE) is addressed
based on the fact that each evolution strategy of DE has common peculiarity but different characteristics. Its
asymptotic convergence is given with the definition of multi-strategy differential operator (MDO), and the
connotative peculiarity of MEDE is analyzed. Compared with the original DE, DEfirDE and DEfirSPX, the
simulation results on 5 classical benchmark functions show that MEDE has obvious advantages in the convergence
rate, solution-quality and adaptability. It is suitable for solving complex high-dimension numeral optimization
To analyze the convergence of differential evolution (DE) and enhance its capability and stability, this
paper first defines a differential operator (DO) as a random mapping from the solution space to the Cartesian
product of solution space, and proves the asymptotic convergence of DE based on the random contraction mapping
theorem in random functional analysis theory. Then, inspired by “quasi-physical personification algorithm”, this
paper proposes an improved differential evolution with multi-strategy cooperating evolution (MEDE) is addressed
based on the fact that each evolution strategy of DE has common peculiarity but different characteristics. Its
asymptotic convergence is given with the definition of multi-strategy differential operator (MDO), and the
connotative peculiarity of MEDE is analyzed. Compared with the original DE, DEfirDE and DEfirSPX, the
simulation results on 5 classical benchmark functions show that MEDE has obvious advantages in the convergence
rate, solution-quality and adaptability. It is suitable for solving complex high-dimension numeral optimization
problems. |
| Key words: differential evolution asymptotic convergence contraction mapping random operator evolutionstrategy |
