Benchmarking constrained, multi-objective and surrogate-assisted derivative-free optimization methods

Benchmarking is essential for assessing the effectiveness of optimization algorithms. This is especially true in derivative-free optimization, where target problems are often complex simulations that require extensive time to evaluate.This limits the number of evaluations that can be performed, making it critical to have a good understanding of the potential quality of various algorithms. This paper reviews standard benchmarking methods, including convergence plots, performance profiles, data profiles, and accuracy profiles, widely used to evaluate optimization algorithms. The primary contribution of this work is a formal extension of these benchmarking techniques to three specific contexts: constrained optimization, multi-objective optimization, and surrogate-based optimization. AMS subject classifications: primary 90-05, 90C56; secondary 90C29, 90-10