Nelder-Mead Based Algorithms for Noisy Functions

Optimization of noisy objective functions involves the process of searching for increasingly better solutions, perhaps the optimal one, while performing function evaluations that are influenced by some uncertainty. Different types of real-world problems fall into this category and, over time, several algorithms have been proposed to solve them efficiently. One of them is the recent Robust Parameter Searcher (RPS), which uses the Nelder Mead Simplex algorithm with some additional operators that perform multiple evaluations of a tentative solution and compare solutions based on a statistical test. This work further explores some possibilities of new operators, and carries out a computational experiment to analyse the effectiveness of different algorithm versions. The experimental results indicate that the RPS version whose single solution reevaluation limit grows non-linearly and whose comparison operator is based on statistical testing was efficient as a good alternative in dealing with noisy optimization problems with real variables and box-type constraints.