连续负梯度方向获得共轭方向的六寻优化方法

doi:10.3778/j.issn.1673-9418.1806049

计算机科学与探索 ›› 2019, Vol. 13 ›› Issue (9): 1604-1612.DOI: 10.3778/j.issn.1673-9418.1806049

连续负梯度方向获得共轭方向的六寻优化方法

尹晓丽，孙凤，李春明

1.中国石油大学（华东）机电工程学院，山东青岛 266580

2.中国石油大学（华东）中国石油大学胜利学院，山东东营 257061

出版日期:2019-09-01 发布日期:2019-09-06

Six Search Optimization Method on Obtaining Conjugate Direction After Continuous Negative Gradient Directions

YIN Xiaoli, SUN Feng, LI Chunming

1.Institute of Mechanical and Electrical Engineering, China University of Petroleum (East China), Qingdao, Shandong 266580, China
2.Shengli College, China University of Petroleum (East China), Dongying, Shandong 257061, China

Online:2019-09-01 Published:2019-09-06

摘要/Abstract

摘要： 连续两次沿负梯度方向寻优可获得共轭方向，对于一般二次目标函数，从两个角度对该现象进行了理论证明。鉴于为诸多研究领域优化问题的解决提供更多更有效的优化方法，将其推广于一般目标函数，提出了基于辅助方向的共轭方向法、三寻法和六寻法。连续三次沿负梯度方向寻优，然后沿所获得的两个共轭方向分别寻优，最后沿上述两个最优点连线进行第六次寻优，从而完成一轮寻优。给出了六寻法和用于三维优化问题的模块化一维盲人探路法C语言计算程序，并用解析法验证了程序的正确性。以一般的二次三维目标函数和Rosenbrock目标函数为例，验证了六寻法的有效性。其寻优效果比负梯度方向法好，两个算例的计算量分别减小28.70%、54.25%。六寻法可用于求解目标函数梯度可求的多维无约束优化问题。

关键词: 优化算法, 六寻法, 共轭方向, 负梯度方向, 多维优化问题

Abstract: The conjugate direction can be obtained by two successive searches along the negative gradient direction. For the general quadratic objective function, the phenomenon is theoretically proven from two angles. In order to provide more and more effective optimization methods for the optimization of many research fields, it is generalized to the general objective function, and the conjugate direction method based on auxiliary direction, three search method and six search method are proposed. After three times of searching along the negative gradient direction, the two conjugate directions are optimized respectively. Finally, the sixth optimization is carried out along the two optimal points conection above. Thus a round of optimization is completed. The C language computer program of six search method and modular one-dimension blind pathfinding mehod for three-dimension optimal problem is given. The correctness of the program is verified by an analytical example. Taking a general quadratic three-dimensional function and a Rosenbrock function as examples, the effectiveness of the six search optimization method is verified. The optimization effect of six search method is better than that of the negative gradient direction method. The calculation amount of two examples are reduced by 28.70% and 54.25% respectively. The six search method can be used to solve multidimensional unconstrained optimization problems with derivable objective function.

Key words: optimization algorithm, six search method, conjugate direction, negative gradient direction, multi-dimension optimal problem

尹晓丽，孙凤，李春明. 连续负梯度方向获得共轭方向的六寻优化方法[J]. 计算机科学与探索, 2019, 13(9): 1604-1612.

YIN Xiaoli, SUN Feng, LI Chunming. Six Search Optimization Method on Obtaining Conjugate Direction After Continuous Negative Gradient Directions[J]. Journal of Frontiers of Computer Science and Technology, 2019, 13(9): 1604-1612.

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连续负梯度方向获得共轭方向的六寻优化方法

Six Search Optimization Method on Obtaining Conjugate Direction After Continuous Negative Gradient Directions

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