Obtaining Brachistochrone Curve with Metaheuristic Algorithms

Abstract

Brachistochrone means “shortest time” in Ancient Greek. This curve defines the path a bead travels only with gravitational force between point A and a lower point B not directly under, in least amount of time. In this article, with the help of Snell's Law and the Fermat's principle, different metaheuristic algorithms are used to obtain Brachistochrone curve and compared with each other. Fermat's Principle states that wave chooses the shortest travel path when passing between different mediums. Snell's Law indicates the refraction angle of the wave on the surface of the media correlates to the intrinsic quality of the medium. As for metaheuristic algorithms, Genetic Algorithm (GA), Harmony Search (HS), Artificial Bee Colony (ABC) and Differential Evolution (DE) are used.