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

摘要: 本文介绍了基于遗传算法解决最速降线问题的方法。我们使用算法精确地解出了无阻力、无初速度的最速降线。在此基础上推广，算出了考虑粘滞阻力或摩擦阻力的最速降线。并将计算结果与文献中的结果进行了比较，对唯一不一致的计算结果进行了详细的分析，证明了我们计算结果的正确性。结果显示，随着阻力的增大，最速降线将持续变直。

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.