具有间断扩散性质的线性约束全局优化随机算法

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  • 1. 华东理工大学数学系, 上海 200237;
    2. 复旦大学管理学院, 上海 200433

收稿日期: 2019-06-19

  网络出版日期: 2020-03-09

基金资助

国家自然科学基金(No.71531005)

An stochastic algorithm for global optimization with linear constraints based on intermittent diffusion

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  • 1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;
    2. School of Management, Fudan University, Shanghai 200433, China

Received date: 2019-06-19

  Online published: 2020-03-09

摘要

研究带线性约束的非凸全局优化问题,在有效集算法的基础上提出了一个具有间断扩散性质的随机微分方程算法,讨论了算法的理论性质和收敛性,证明了算法以概率收敛到问题的全局最优解,最后列出了数值实验效果.

本文引用格式

陈永, 王薇, 徐以汎 . 具有间断扩散性质的线性约束全局优化随机算法[J]. 运筹学学报, 2020 , 24(1) : 88 -100 . DOI: 10.15960/j.cnki.issn.1007-6093.2020.01.007

Abstract

In this paper, the nonconvex global optimization problem with linear constraints is studied. Based on the effective set algorithm, a stochastic differential equation algorithm with stochastic diffusion properties is proposed. The theoretical properties and convergence of the algorithm are discussed. It is proved that the algorithm converges to the global optimal solution of the problem with probability 1. Finally, the numerical experiment results are listed.

参考文献

[1] 万昭曼, 胡朝明.线上零售商销售策略差异性分析及策略组合优化模型[J]. 经济数学, 2018, (3):37-40.
[2] 刘文丽, 万中. 消费者预防在线销售掺假行为的博弈模型及最优策略[J]. 经济数学, 2018, 35(02):23-28.
[3] Zhang Jing, Liu Jingjing, Wan Zhong. Optimizing transportation network of recovering endof-life vehicles by compromising program in polymorphic uncertain environment[J]. Journal of Advanced Transportation, 2019, 24:Article ID3894064.
[4] Zhu G Y, Zhang W B. Optimal foraging algorithm for global optimization[J]. Applied Soft Computing, 2017, 51:294-313.
[5] Garg H. A hybrid PSO-GA algorithm for constrained optimization problems[J]. Applied Mathematics and Computation, 2016, 274:292-305.
[6] Aluffi-Pentini F, Parisi V, Zirilli F. Global optimization and stochastic differential equations[J]. Journal of optimization theory and applications, 1985, 47(1):1-16.
[7] Wang W, Xu Y F. Transformed functions for global optimization with linear constraints[J]. Pacific Journal of Optimization, 2010, 6(3):641-651.
[8] Zhang L S, Ng C K, Li D, et al. A new filled function method for global optimization[J]. Journal of Global optimization, 2004, 28(1):17-43.
[9] Chiang Tzuu-Shuh, Hwang Chii-Ruey, Sheu Shuenn Jyi. Diffusion for global optimization in Rn[J]. SIAM Journal on Control and Optimization, 1987, 25(3):737-753.
[10] Parpas Panos, Rustem Berç, Pistikopoulos Efstratios N. Linearly constrained global optimization and stochastic differential equations[J]. Journal of Global Optimization, 2006, 36(2):191-217.
[11] Yuan Honglin, Gu Xiaoyi, Lai Rongjie, et al. Global optimization with orthogonality constraints via stochastic diffusion on manifold[J]. 2017, arXiv:1707.02126.
[12] Chow Shui Nee, Yang Tzi Sheng, Zhou Hao Min. Global optimizations by intermittent diffusion[M]//Chaos, CNN, Memristors and Beyond:A Festschrift for Leon Chua With DVD-ROM, Composed by Eleonora Bilotta, New York:World Scientific, 2013, 466-479.
[13] 王力. 鞅与随机微分方程[M]. 北京:科学出版社, 2015.
[14] 伊藤清. 随机过程[M]. 北京:人民邮电出版社, 2010.
[15] Schuss Zeev. Theory and Applications of Stochastic Processes:an Analytical Approach[M]. New York:Springer, 2009.
[16] Arnold Anton, Markowich Peter, Toscani Giuseppe, et al. On convex sobolev inequalities and the rate of convergence to equilibrium for fokker-planck type equations[J]. Communications in Partial Differential Equations, 2001, 26(1-2):43-100.
[17] Markowich Peter A, Villani Cédric. On the trend to equilibrium for the fokker-planck equation:an interplay between physics and functional analysis[J]. Physics and Functional Analysis, Matematica Contemporanea, 2000, 19:1-29.
[18] Barkai E. Fractional fokker-planck equation, solution, and application[J]. Physical Review E, 2001, 63(4):046118.
[19] Holley Richard, Stroock Daniel. Logarithmic sobolev inequalities and stochastic ising models[J]. Journal of statistical physics, 1987, 46(5):1159-1194.
[20] 张慧雯, 王薇, 李民, 等. 基于梯度投影的广义滤子填充函数方法[J]. 数学杂志, 2019, 39(01):32-44.
[21] Michalewicz Z. Genetic Algorithms + Data Structures=Evolution Programs[M]. Beijing:Science Press, 2000:1-128.
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