基于改进粒子群算法的重力坝断面优化研究

Improved PSO based optimal design of gravity dam section

【目的】将改进粒子群算法用于重力坝断面的优化计算,为重力坝的优化设计提供支持。【方法】针对传统粒子群算法(PSO)中线性递减的惯性权重极易导致算法陷入局部极值的不足,提出一种改进的粒子群算法(Improved PSO),该算法利用三角函数的相关性质改进惯性权重(w)随时间的动态变化模式,以使惯性权重值在算法的初期保持较大取值,然后逐渐递减而在算法的末期保持较小取值,从而提高粒子群算法的全局搜索能力,增强算法的收敛性能。编制基于改进粒子群算法的重力坝断面优化设计计算程序,对某水利枢纽工程的非溢流重力坝断面进行优化计算分析,并与遗传算法和标准粒子群算法的计算结果进行比较。【结果】采用改进粒子群算法得到的非溢流重力坝的最优断面面积为5 147.3 m^2,而采用标准粒子群算法(SPSO)得到的非溢流重力坝的最优断面面积为5 416.5m^2,前者较后者减小9.45%,极大地提高了经济性;采用改进的粒子群算法得到最优解需要计算15步,而采用标准粒子群算法得到最优解需要计算22步,粒子群算法收敛速度提高了31.8%。通过2种算法计算结果的对比,表明改进的粒子群算法不仅能得到更好的优化结果,而且保持了较快的收敛速度。【结论】改进粒子群算法可以用于大型水利工程结构的优化计算与设计。

【Objective】This study applied the improved particle swarm optimization algorithm（PSO）to optimization of gravity dam section to provide support for the optimization design of gravity dam.【Method】Aiming at the fact that general PSO algorithms have the disadvantages of falling into local extremum caused by linear decreasing inertia weight,an improved PSO was proposed.The improved PSO uses the related properties of the trigonometric function to improve the dynamic changes of inertia weight along with time.It makes inertia weight maintain a large value in the initial stage,which decreases gradually and maintained a small value at the end.Thus,the global search capability and convergence performance were improved.A calculation program of gravity dam section optimal design based on the improved PSO was compiled and a non-overflow gravity dam section optimal design of a water conservancy project was calculated.The calculation results were compared with the results of GA and SPSO.【Result】The optimal result ofgravity dam section based on the improved PSO was A（X）=5 147.3m^2,while that based on SPSO was A（X）=5 416.5m^2.The 9.45% decrease greatly improved the economy.The steps needed to obtain optimal solution were reduced by 31.8%from 22 steps of SPSO to 15 steps.The proposed improved PSO algorithm obtained better optimal results with less steps.【Conclusion】Structure optimization calculation and design of large-scale water conservancy project can be achieved by the improved PSO algorithm.