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中国科学院软件研究所
  
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贺毅朝,王熙照,刘坤起,王彦祺.差分演化的收敛性分析与算法改进.软件学报,2010,21(5):875-885
差分演化的收敛性分析与算法改进
Convergent Analysis and Algorithmic Improvement of Differential Evolution
投稿时间:2008-05-01  修订日期:2008-10-07
DOI:
中文关键词:  差分演化  渐近收敛性  压缩映射  随机算子  进化模式
英文关键词:differential evolution  asymptotic convergence  contraction mapping  random operator  evolutionstrategy
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)
作者单位
贺毅朝 石家庄经济学院 信息工程学院,河北 石家庄 050031 
王熙照 河北大学 数学与计算机学院,河北 保定 071002 
刘坤起 石家庄经济学院 信息工程学院,河北 石家庄 050031 中国地质大学 计算机学院,湖北 武汉 430074 
王彦祺 石家庄经济学院 信息工程学院,河北 石家庄 050031 
摘要点击次数: 5458
全文下载次数: 7120
中文摘要:
      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.
英文摘要:
      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.
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