Analysis and parameter selection for an adaptive random search algorithm (Q1780461)

An adaptive random search (ARS) algorithm for solving global optimization problems is investigated. The algorithm aims to find an \(\varepsilon\)-minimizer of the problem. Two versions of the ARS algorithm are studied, the Las Vegas version if the global minimum, \(f^*\), is a priori known, and a Monte Carlo version otherwise. Firstly, a probabilistic model for the number of iterations is developed that are required fo find a \(\varepsilon\)-solution in an \(N\)-parameter system. The model enables to establish a termination criterion to predict the maximum number of samples to achieve an \(\varepsilon\)-solution with the desired confidence. Secondly, a scheme to choose the user-specified parameters is so provided that the algorithm becomes as fast as possible.