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  • CN 31-1691/TQ

基于降维的全局优化近似解法

陈丹丹 王薇 徐以汎

陈丹丹, 王薇, 徐以汎. 基于降维的全局优化近似解法[J]. 华东理工大学学报(自然科学版), 2019, 45(6): 995-1000. doi: 10.14135/j.cnki.1006-3080.2018071700
引用本文: 陈丹丹, 王薇, 徐以汎. 基于降维的全局优化近似解法[J]. 华东理工大学学报(自然科学版), 2019, 45(6): 995-1000. doi: 10.14135/j.cnki.1006-3080.2018071700
CHEN Dandan, WANG Wei, XU Yifan. Approximate Solution of Global Optimization Problem Based on Dimensionality Reduction[J]. Journal of East China University of Science and Technology, 2019, 45(6): 995-1000. doi: 10.14135/j.cnki.1006-3080.2018071700
Citation: CHEN Dandan, WANG Wei, XU Yifan. Approximate Solution of Global Optimization Problem Based on Dimensionality Reduction[J]. Journal of East China University of Science and Technology, 2019, 45(6): 995-1000. doi: 10.14135/j.cnki.1006-3080.2018071700

基于降维的全局优化近似解法

doi: 10.14135/j.cnki.1006-3080.2018071700
基金项目: 国家自然科学基金(NO. 71531005)
详细信息
    作者简介:

    陈丹丹(1994-),女,安徽芜湖人,硕士生,研究方向为最优化。E-mail:18818262015@163.com

    通讯作者:

    王 薇,E-mail:wangwei@ecust.edu.cn

  • 中图分类号: O221.2

Approximate Solution of Global Optimization Problem Based on Dimensionality Reduction

  • 摘要: 将降维应用到全局优化问题的求解中,提出了一个基于降维的全局优化近似算法,用以求解带箱约束的非线性全局优化问题。首先在区间[0, π]上构造一个新的降维公式,给出基于该降维变换曲线的α-致密度,再从降维曲线长度对该近似算法的计算量进行估计并给予证明,给出理论算法,最后给出了数值实验结果以说明算法的有效性。

     

  • 图  1  算例1目标函数值随着迭代次数的变化情况

    Figure  1.  Value change of Test 1’s objective function with number of iterations

    表  1  函数的数值实验结果

    Table  1.   Numerical results of the function

    Example${\theta ^ * }$minGlobal min
    11.883 780.000 014 120
    21.572 00–0.199 992 11–0.2
    30.792 070.004 134 190
    41.537 41–0.591 313 44–0.6
    50.994 46–0.988 568 68–1
    60.947 43–0.965 497 70–1
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出版历程
  • 收稿日期:  2018-07-20
  • 网络出版日期:  2019-10-12
  • 刊出日期:  2019-12-01

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