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第5卷第3期 智能系统学报 Vol.5 No.3 2010年6月 CAAI Transactions on Intelligent Systems Jun.2010 doi:10.3969/i.issn.1673-4785.2010.03.008 结合变尺度法的改进类电磁机制算法 印峰,王耀南,杨易旻,曹文明 (湖南大学电气与信息工程学院,湖南长沙410082)》 摘要:标准类电磁机制算法处理连续函数优化问题时存在最优参数选取和收敛速度问题.数值实验研究表明类电 磁算法不具备初值敏感性,并在搜索后期算法收敛速度缓慢甚至可能出现停滞.数值实验分析指出粒子之间达成动 态力平衡状态是造成算法停滞的可能原因之一,提出一种解决策略是摒弃EM算法后期搜素过程,结合变尺度法对 EM算法前期搜索到的近似最优值进行二次优化.该混合计算方法将二者的优势相结合,实验结果表明新方法在保 证计算实时性的同时,取得了较高的计算精度.最后,对EM算法本身构造提出一些改进意见,并初步建立用于连续 函数优化的EM算法计算框架,为后续更深入的研究EM算法提供参考. 关键词:连续函数优化;类电磁算法;变尺度法;二次优化 中图分类号:TP301.6文献标识码:A文章编号:16734785(2010)03025406 An improved electromagnetism-like mechanism algorithm combined with the DFP method YIN Feng,WANG Yao-nan,YANG Yi-min,CAO Wen-ming (College of Electrical and Information Engineering,Hunan University,Changsha 410082,China) Abstract:When optimizing a continuous function using a standard electromagnetism-like mechanism (EM),there are known problems,including selection of optimal parameters and convergence speed.Numerical simulations indi- cate that EM is not sensitive to initial values,but algorithm convergence is slow and may even stagnate in the latter part of a search.One of the possible causes for stagnation is the equilibrium of dynamic forces between particles.In order to improve the performance of the EM,instead of the latter search process,a quadratic optimization method was proposed.When combined with the Davidon-Fletcher-Powell (DFP)method,it optimized the approximate op- timal results obtained by a pre-search with the EM algorithm.This hybrid method fully exploits the strengths of the EM method and the DFP method.Experimental results showed it to be more efficient and precise.Finally,some improvements were made to the construction of the EM and a framework for the EM method was established that al- lows continuous function optimization.These results provide a reference for more in-depth study of the EM algo- rithm. Keywords:continuous function optimization;electromagnetism-like algorithm;Davidon-Fletcher-Powell method; quadratic optimization 在求解函数优化问题过程中,如果待优化问题想[12].近年来,Birbil等学者受电磁学中带电粒子 的目标函数较为复杂,或其一、二阶信息难以获取间“排斥-吸引”力的启发,提出一种新的用于求解 时,一般传统的优化方法不再适合求解这类问题.而 含有界变量约束问题的全局收敛算法—类电磁算 启发式的随机搜索方法是求解此类全局优化问题的 法3],通过选取15个函数组成的综合测试函数集对 有效途径之一,至今已得到广泛应用的模拟退火算 EM(electromagnetism-like mechanism)算法性能进 法、遗传算法及蚁群算法等都采用了随机搜索的思 行了测试,并与经典优化方法进行了比较,测试结果 表明EM算法可收敛到问题的最优解,并且显示出 收稿日期:2009-12-15. 更好的优化性能.文献[4]进一步从理论上证明了 基金项目:国家科技支撑计划资助项目(2008BAF36B01):国家“863” 计划资助项目(2008AA04Z214). EM算法依分布全局收敛于问题的ε-最优解.目前, 通信作者:印峰.E-mail:yinfeng83@126.com EM算法在函数优化、神经网络训练、TSP以及项目
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