基于改进单纯形法的杆塔优化规划
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摘要
输电线路的杆塔规划问题是一个由简单不等式约束的多维、非线性最优化问题,且不能保证其目标函数连续或可导,故传统的算法如穷举法、试凑法、解析法等求解均有较大局限性。为了解决上述问题,采用改进单纯形算法结合外点法罚函数求解此类问题,结果表明,算法辅以将约束条件作为指数罚函数的外点法构造增广目标函数,可以方便地处理各项约束条件的限制,计算效率高,鲁棒性强,程序实现简单。同时,文中采用的算法对于可能出现的局部最优解可以根据工程经验加以判别和剔除,适用性强。
Pole and tower planning of trasmission line is a non-liner and multi-dimensional optimization problem which maybe has an discontinous or underivable objective function,so it is difficult to be resolved by traditional methods such as exhaustive method,trial-and-error method or analytical method. To solve these problems,Nelder-Mead simplex method and exterior point penalty function are used in combination to resolve pole and tower planning problem. The results show that the algorithm,supplemented by the external point method which takes the constraint condition as exponential penalty function to construct the augmented objective function,can easily deal with the constraints of various constraints.This algorithm is efficient 、and robust.It is easy to be programed,while,the possible local optimum should be excluded by engineering experience,so this algorithm has strong applicability.
Pole and tower planning of trasmission line is a non-liner and multi-dimensional optimization problem which maybe has an discontinous or underivable objective function,so it is difficult to be resolved by traditional methods such as exhaustive method,trial-and-error method or analytical method. To solve these problems,Nelder-Mead simplex method and exterior point penalty function are used in combination to resolve pole and tower planning problem. The results show that the algorithm,supplemented by the external point method which takes the constraint condition as exponential penalty function to construct the augmented objective function,can easily deal with the constraints of various constraints.This algorithm is efficient 、and robust.It is easy to be programed,while,the possible local optimum should be excluded by engineering experience,so this algorithm has strong applicability.
引文
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[13]陈美珠.关于线性连续系统的三种分析方法[J].江苏电机工程,1997,16(4):61-62.CHEN Meizhu. Three analysis methods for linear continuous systems[J]. Jiangsu Electrical Engineering,1997,16(4):61-62.
[14]薛静芳.线性规划的单纯形算法研究及应用[D].辽宁:大连海事大学,2013.XUE Jingfang. Research and application of simplex algorithm for linear programming[D]. Liaoning:Dalian Maritime University,2013.
[15]WANG P C,SHOUP T E. Parameter sensitivity study of the Nelder-Mead simplex method[J]. Advances in Engineering Software,2011,42(7):529-533.
[16]张勇,巩敦卫,张婉秋.一种基于单纯形法的改进微粒群优化算法及其收敛性分析[J].自动化学报,2009,35(3):289-298.ZHANG Yong,GONG Dunwei,ZHANG Wanqiu. An improved particle swarm optimization algorithm based on simplex method and its convergence analysis[J]. Journal of Automation,2009,35(3):289-298.
[17]OURIA A,TOUFIGH M M. Application of Nelder-Mead simplex method for unconfined seepage problems[J]. Applied Mathematical Modelling,2009,33(9):3589-3598.
[18]燕子宗,费浦生,万仲平.线性规划的单纯形法及其发展[J].计算数学,2007,29(1):1-14.YAN Zizong,FEI Pusheng,WAN Zhongping. Simplex method of linear programming and its development[J]. Computational Mathematics,2007,29(1):1-14.
[2]黄兴,田雷,杨洋,等.基于点估计法的杆塔结构平均可靠度分析[J].电力工程技术,2018,37(2):127-131.HUANG Xing,TIAN Lei,YANG Yang,et al. Analysis of the average reliability of tower structures based on point estimation method[J]. Electric Engineering Technology,2018,37(2):127-131.
[3]施亮.特高压交流同塔双回输电线路杆塔规划研究[D].北京:华北电力大学,2013.SHI Liang. Study on the planning of double circuit transmission line of uhv alternating current tower[D]. Beijing:North China Electric Power University,2013.
[4]朱轶,张大长,林致添.±800 k V特高压直流输电杆塔结构的动力特性研究[J].江苏电机工程,2008,27(6):11-13.ZHU Yi,ZHANG Dachang,LIN Zhitian. Study on dynamic characteristics of 800 k V ultra-high voltage direct current transmission tower structure[J]. Jiangsu Electric Engineering,2008,27(6):11-13.
[5]李永双,廖宗高,肖洪伟,等.直流UHV线路杆塔规划及经济档距的确定[J].高电压技术,2008,34(6):1121-1125.LI Yongshuang,LIAO Zonggao,XIAO Hongwei,et al. DC UHV line pole tower planning and determination of economic range[J]. High Voltage Engineering,2008,34(6):1121-1125.
[6]李显鑫,郭咏华,唐明贵. 1 000 k V交流双回路单柱组合耐张塔型式规划[J].电网技术,2009(7):1-6.LI Xianxin,GUO Yonghua,TANG minggui. Type planning of1 000 k V ac double circuit single-column combination resistant tower[J]. Grid Technology,2009(7):1-6.
[7]汪勇.新型杆塔规划方法研究及应用[J].陕西水利,2011(1):106-107.WANG Yong. Research and application of new planning methods for poles and towers[J]. Shaanxi Water Conservancy,2011(1):106-107.
[8]李永双,张国良.交流特高压线路杆塔规划及经济档距分析[J].电力建设,2007,28(4):7-10.LI Yongshuang,ZHANG Guoliang. The planning and economic analysis of ac uhv line poles and towers[J]. Electric Power Construction,2007,28(4):7-10.
[9]胡淑兵.±800 k V直流输电线路在平原地区的杆塔规划研究[J].低碳世界,2016(21):42-43.HU Shubing. Study on the planning of poles and towers of 800k V dc transmission lines in plain areas[J]. Low-carbon World,2016(21):42-43.
[10]郑团结,景钦刚.基于海拉瓦-洛斯达技术的输电线路优化设计与应用研究[J].水电能源科学,2007,25(6):133-135.ZHEN Tuanjie,JING Qingang. Study on optimal design and application of transmission lines based on helawa-losta technology[J]. Hydropower Energy Science, 2007, 25(6):133-135.
[11]陈宝林.最优化理论与算法[M].北京:清华大学出版社,2005.CHEN Baolin. Optimization theory and algorithm[M]. Beijing:Tsinghua University Press,2005.
[12]杨志军,周刚,王劲.三沪直流工程±500 k V线路杆塔规划设计[J].电力建设,2008,29(3):18-21.YANG Zhijun,ZHOU Gang,WANG Jin. Planning and design of poles and towers for±500 k V transmission lines in Sanhu DC project[J]. Electric Power Construction,2008,29(3):18-21.
[13]陈美珠.关于线性连续系统的三种分析方法[J].江苏电机工程,1997,16(4):61-62.CHEN Meizhu. Three analysis methods for linear continuous systems[J]. Jiangsu Electrical Engineering,1997,16(4):61-62.
[14]薛静芳.线性规划的单纯形算法研究及应用[D].辽宁:大连海事大学,2013.XUE Jingfang. Research and application of simplex algorithm for linear programming[D]. Liaoning:Dalian Maritime University,2013.
[15]WANG P C,SHOUP T E. Parameter sensitivity study of the Nelder-Mead simplex method[J]. Advances in Engineering Software,2011,42(7):529-533.
[16]张勇,巩敦卫,张婉秋.一种基于单纯形法的改进微粒群优化算法及其收敛性分析[J].自动化学报,2009,35(3):289-298.ZHANG Yong,GONG Dunwei,ZHANG Wanqiu. An improved particle swarm optimization algorithm based on simplex method and its convergence analysis[J]. Journal of Automation,2009,35(3):289-298.
[17]OURIA A,TOUFIGH M M. Application of Nelder-Mead simplex method for unconfined seepage problems[J]. Applied Mathematical Modelling,2009,33(9):3589-3598.
[18]燕子宗,费浦生,万仲平.线性规划的单纯形法及其发展[J].计算数学,2007,29(1):1-14.YAN Zizong,FEI Pusheng,WAN Zhongping. Simplex method of linear programming and its development[J]. Computational Mathematics,2007,29(1):1-14.