The Hyperbell Algorithm for global optimization: A random walk using Cauchy densities

This article presents a new algorithm, called the ''Hyperbell Algorithm'', that searches for the global extrema of numerical functions of numerical variables. The algorithm relies on the principle of a monotone improving random walk whose steps are generated around the current position according to a gradually scaled down Cauchy distribution. The convergence of the algorithm is proven and its rate of convergence is discussed. Its performance is tested on some ''hard'' test functions and compared to that of other recent algorithms and possible variants. An experimental study of complexity is also provided, and simple tuning procedures for applications are proposed.