具有间断扩散性质的线性约束全局优化随机算法

doi:10.15960/j.cnki.issn.1007-6093.2020.01.007

Abstract

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.

Key words: linear constraint, global optimization, effective set algorithm, stochastic differential equation, diffusion process

CLC Number:

O221.2

CHEN Yong, WANG Wei, XU Yifan. An stochastic algorithm for global optimization with linear constraints based on intermittent diffusion[J]. Operations Research Transactions, 2020, 24(1): 88-100.

References

[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.

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

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