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
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