On the role of an evolutionary solution for the brachistochrone-problem

An evolutionary solution for the approximation of the brachistochrone problem is presented by a specific configuration and operator setup of an evolutionary strategy (ES). To evaluate and compare the quality of the solution, an approximation of the theoretical cycloid-solution is determined by an approximation of n points with similar distance. The outperforming quality of the evolutionary determined shape of the approximated curve between a given starting- and end-point is verified by the time an idealized particle needs. All empirical results are carried out in a Monte Carlo simulation study. The dependency of the quality enhancement of the evolutionary solution on the number of approximating points is analyzed. Further the role of the evolutionary approach is discussed to encourage the usage of evolutionary computation for linear approximating polygons of well solved analytical problems.