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| 基于混沌变量的变步长梯度下降优化算法 | |
| 引用本文： | 姚俊峰,杨献勇,彭小奇,张田,郑顺斌.基于混沌变量的变步长梯度下降优化算法[J].清华大学学报(自然科学版),2003,43(12):1676-1678. |
| 作者姓名： | 姚俊峰 杨献勇 彭小奇 张田 郑顺斌 |
| 作者单位： | 1. 清华大学,热能工程系,北京,100084 2. 中南大学,热工设备仿真与优化研究所,长沙,410083 3. 福建浔兴集团公司,晋江,362246 |
| 基金项目： | 国家教育部科技研究重点项目(02146)，湖南省自然科学基金资助项目(01JJY2110) |
| 摘 要： | 梯度下降法与混沌优化法均具有各自的缺点。该文将二者结合起来,利用混沌运动的遍历性,将混沌因子引入到变步长中,对梯度下降法进行改进。首先利用混沌变量来初始化步长大小,并随着搜索过程向最优点靠近,逐渐调整混沌变量,从而使步长的变化也不断变小,以使最优点附近步长波动平稳,避免了梯度下降法拉锯现象的产生。通过3个典型算例,用该算法和梯度下降法以及其他2种算法进行了优化计算对比。结果表明,采用该算法的迭代次数减少了45%以上。 |
| 关 键 词： | 最佳控制 混沌 变步长 梯度下降法 优化 |
| 文章编号： | 1000-0054(2003)12-1676-03 |
| 修稿时间： | 2003年5月19日 |
Decreasing gradient optimization algorithm with variable step length based on chaotic variables |
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| YAO Junfeng,YANG Xianyong,PENG Xiaoqi,ZHANG Tian,ZHENG Shunbing.Decreasing gradient optimization algorithm with variable step length based on chaotic variables[J].Journal of Tsinghua University(Science and Technology),2003,43(12):1676-1678. | |
| Authors: | YAO Junfeng YANG Xianyong PENG Xiaoqi ZHANG Tian ZHENG Shunbing |
| Institution: | YAO Junfeng~1,YANG Xianyong~1,PENG Xiaoqi~2,ZHANG Tian~3,ZHENG Shunbing~3 |
| Abstract: | The decreasing gradient algorithm and chaos algorithm both have shortcomings for optimization problems. This paper presents a new algorithm which combines the 2 algorithms to produce a greatly improved decreasing gradient algorithm by introducing chaos variables into the variable step length to take advantage of the randomness of the chaotic movements. The step length was initialized using chaotic variables which were adjusted step by step as the search procedure reached the best point, so that the step length fluctuated smoothly and avoided oscillations which often arise in the decreasing gradient algorithm. The number of iterations was reduced by at least 45% compared with the other 2 algorithms mentioned above using 3 typical numerical examples. |
| Keywords: | optimal control chaos variable step length decreasing gradient algorithm optimization |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |