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Benchmarking Global Optimizers

Working Paper 801 | Published December 15, 2023

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Antoine Arnoud International Monetary Fund
Fatih Guvenen Consultant
Benchmarking Global Optimizers


We benchmark six global optimization algorithms by comparing their performance on challenging multidimensional test functions as well as on a method of simulated moments estimation of a panel data model of earnings dynamics. Five of the algorithms are from the popular NLopt open-source library: (i) Controlled Random Search with local mutation (CRS), (ii) Improved Stochastic Ranking Evolution Strategy (ISRES), (iii) Multi-Level Single-Linkage (MLSL), (iv) Stochastic Global Optimization (StoGo), and (v) Evolutionary Strategy with Cauchy distribution (ESCH). The sixth algorithm is TikTak, which is a multistart global optimization algorithm used in some recent economic applications. For completeness, we add three popular local algorithms to the comparison—the Nelder-Mead downhill simplex algorithm, the Derivative-Free Nonlinear Least Squares (DFNLS) algorithm, and a popular variant of the Davidon-Fletcher-Powell (DFPMIN) algorithm. To give a detailed comparison of algorithms, we use benchmarking tools recently developed in the optimization literature. We find that the success rate of many optimizers varies dramatically with the characteristics of each problem and the computational budget that is available. Overall, TikTak is the strongest performer both on the test functions and the economic application. The next-best performing optimizers are StoGo for the test functions and MLSL and ISRES for the economic application.