沈继红,李加莲,魏斌.光线寻优算法的寻优机理分析[J].数学研究及应用,2012,32(5):530~542
光线寻优算法的寻优机理分析
Optimal Search Mechanism Analysis of Light Ray Optimization Algorithm
投稿时间:2010-12-21  最后修改时间:2012-03-27
DOI:10.3770/j.issn:2095-2651.2012.05.002
中文关键词:  费马原理  智能优化算法  光线寻优  寻优机理.
英文关键词:Fermat's principle  intelligent optimization algorithm  light ray optimization  optimal search mechanism.
基金项目:黑龙江自然科学基金 (Grant No.F200931).
作者单位
沈继红 哈尔滨工程大学理学院, 黑龙江 哈尔滨 150001 
李加莲 哈尔滨工程大学自动化学院, 黑龙江 哈尔滨 150001 
魏斌 哈尔滨工程大学理学院, 黑龙江 哈尔滨 150001 
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中文摘要:
      基于费马原理和光传播过程中的自动寻优机理,提出了一种新型智能优化算法—光线寻优算法,它将光的折射和反射定律与寻优过程结合起来.在该算法中,坐标空间被设想为填充了具有不同折射率的介质区域,然后用网格划分该区域,最后将搜索路径设想为光的传播路径.根据折射定律,搜索方向偏向于使目标函数值减小的方向.当搜索按照折射定律无法进行时将根据折射定律改变搜索方向.在光线寻优算法中,仅用到目标问题的函数值,并且不涉及人为规则,简单容易实现.理论分析和数值实验结果表明算法是可行和有效地.
英文摘要:
      Based on Fermat's principle and the automatic optimization mechanism in the propagation process of light, an optimal searching algorithm named light ray optimization is presented, where the laws of refraction and reflection of light rays are integrated into searching process of optimization. In this algorithm, coordinate space is assumed to be the space that is full of media with different refractivities, then the space is divided by grids, and finally the searching path is assumed to be the propagation path of light rays. With the law of refraction, the search direction is deflected to the direction that makes the value of objective function decrease. With the law of reflection, the search direction is changed, which makes the search continue when it cannot keep going with refraction. Only the function values of objective problems are used and there is no artificial rule in light ray optimization, so it is simple and easy to realize. Theoretical analysis and the results of numerical experiments show that the algorithm is feasible and effective.
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