This paper establishes a framework for formal comparisons of several leading optimization algorithms, establishing guidance to practitioners for when to use or not use a particular method. The focus in this paper is five general algorithm forms: random search, simultaneous perturbation stochastic approximation, simulated annealing, evolutionary strategies, and genetic algorithms. We summarize the available theoretical results on rates of convergence for the five algorithm forms and then use the theoretical results to draw some preliminary conclusions on the relative efficiency. Our aim is to sort out some of the competing claims of efficiency and to suggest a structure for comparison that is more general and transferable than the usual problem-specific numerical studies.
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