计算机科学 ›› 2020, Vol. 47 ›› Issue (6A): 54-57.doi: 10.11896/JsJkx.191000179
张玉琴, 张建亮, 冯向东
ZHANG Yu-qin, ZHANG Jian-liang and FENG Xiang-dong
摘要: 填充函数法是求解无约束全局优化问题的重要方法,其核心工作在于构建具有良好性质、形式简单而且容易求解极小值的填充函数。基于填充函数的定义,针对无约束的全局优化问题的目标函数满足条件的基础上,构建了一个无参数的填充函数。此函数形式简单,便于计算。针对此填充函数,首先,在满足合适的假设条件下,研究并证明了填充函数的某些性质;其次,在遵照这些相关性质的基础上,设计了适合此填充函数的算法,该填充函数算法主要包含极小化过程与填充过程,这两个过程循环交替进行,直至满足终止条件;最后,利用经典算例,进行了算例实验并与其他文献结果比较。结果显示,不仅此填充函数可行,算法有效;而且计算结果准确,计算迭代次数较少。
中图分类号:
[1] GE R P.A filled function method forfinding a global minimizer of a function of several variables.Math.Prog.,1990,46:191-204. [2] LIU X.The impelling function method applied to global optimization .Applied Mathematics and Computation,2004,151:745-754. [3] ZHANG L S,N G C K,LID.A new filled function method for global optimization.Journal of Global Optimization,2004,28:17-43. [4] SHANG Y L,PU D G,JIANG A P.Finding global minimizer with one parameter filled function on unconstrained global optimization.Applied Mathematics and Computation,2007,191:176-182. [5] YANG Y J,SHANG Y L.A new filled function method for unconstrained global optimization.Applied Mathematics and Computation,2006,173:501-512. [6] LIANG Y M,ZHANG L S,LI M M,et al.A filled function method for global optimization.Journal of Computational and Applied Mathematics,2007,205:16-31. [7] WANG C J,YANG Y J,LI J.A new filled function method for unconstrained global optimization.Journal of Computational and Applied Mathematics,2009,225:68-79. [8] HE S X,CHENG W L.A filled function algorithm for unconstrained global optimization problems.Journal of ZheJiang University (Science Edition),2011,38(2):144-149. [9] LIANG Y M,LI M M,CHI D X.A Filled Fucnction Method with One Parameter for Global Optimization.Operations Research Transactions,2009,13(4):102-108. [10] CAI Z Z,YE Z Q.New Continuously Differentiable Filled Function with One Parameter.Computer Science,2016,43(8):204-206. [11] LI B,LU D J.A Parameter-free filled function method for global optimization.Journal of Mathematics,2014,34(4):773-778. [12] WANG P,LI B,WANG P.Parameter-free Filled Function Method for the Global Optimization Problems.Journal of Qingdao University of Science and Technology(Natural Science Edition),2008,29(6):553-556. [13] MAO J,YANG Y J.A Filled Function Method Without Parameter.Communication on Applied Mathematics and Computation,2010,24(1):35-44. [14] ROCKAFELLAR R T.Convex Analysis.Prentice Hall, 1970. [15] LIN Y J,YANG Y J.Filled function method for nonlinear equations.Journal of Computational and Applied Mathematics,2010,234(3):695-702. [16] GAO L F,LIU X W,The Global Optimization Algorithm Based on Chaos Optimization and Filled Function.Operations Research and Management Science,2009,18(2):25-29. [17] GAO Y L,WU P P.A New Parmeter-free Filled Function Algorithm for Nonlinear Integer Programming.Journal of Computational Mathematics,2017,39(3):321-327. [18] SHI L T,CHEN W.A Filled-filter Function Algorithm for Solving Unconstrained Integer Programming.Communications on Applied Mathematics and Computation,2018,32(2):331-342. |
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