基于遗传算法的最速降线问题求解
The Solution of Brachistochrone Problem Based on the Genetic Algorithm
作者: 陈德锋 , 王江涌 ：汕头大学理学院物理系，广东 汕头; 廖桂颖 ：汕头大学理学院数学系，广东 汕头;
关键词: 遗传算法； 最速降线； 贝塞尔曲线； 粘滞阻力； 摩擦阻力； Genetic Algorithm； Brachistochrone Curve； Bezier Curve； Viscous Resistance； Frictional Resistance
摘要:Abstract: The Brachistochrone problem has been solved by the genetic algorithm method. The calculated results are exactly the same as the analytical solutions under the conditions of no resistance and no initial velocity. Furthermore, this method is extended for considering both the viscous and frictional resistances. The simulated results are compared with the ones in literature. The discrepancy of the only one simulated result is detailedly discussed in order to verify the current simulation result. Finally, the result shows that with the increase of the resistance, the brachistochrone will continually become flatter.
文章引用: 陈德锋 , 廖桂颖 , 王江涌 (2015) 基于遗传算法的最速降线问题求解。 力学研究， 4， 76-88. doi: 10.12677/IJM.2015.44010
参考文献
[1]
Vratanar, B. and Saje, M. (1998) On the Analytical Solution of the Brachistochrone Problem in a Non-Conservative Field. International Journal of Non-Linear Mechanics, 33, 489-505.
http://dx.doi.org/10.1016/S0020-7462(97)00026-7
[2] 周嘉炜, 曹炳阳, 过增元. 具有黏滞阻力时的最速降线[J]. 力学与实践, 2011, 33(3): 11-14.
[3]
Hayen, J.C. (2005) Brachistochrone with Coulomb Friction. International Journal of Non-Linear Mechanics, 40, 1057- 1075.
http://dx.doi.org/10.1016/j.ijnonlinmec.2005.02.004
[4] 尤明庆. 最速降线求解和摩擦力影响的研究[J]. 河南理工大学学报, 2005, 24(1): 83-88.
[5] 周先东, 马翠. 最速降线问题的一种新解法[C]//第一届中国智能计算大会论文集. 庐山: 中国运筹学会, 2007: 59-62.
[6]
Wensrich, C.M. (2004) Evolutionary Solutions to the Brachistochrone Problem with Coulomb Friction. Mechanics Research Communications, 31,151-159.
http://dx.doi.org/10.1016/j.mechrescom.2003.09.005
[7] 陈爱军, 李金宗, 李东东. 一种改进的随机圆检测算法[J]. 光电工程, 2006, 33(12): 91-95.