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In many practical optimization problems, the derivatives of the functions to be optimized are unavailable or unreliable. Such optimization problems are solved using derivative-free optimization techniques. One of the state-of-the-art…

Neural and Evolutionary Computing · Computer Science 2018-05-30 Najeeb Khan

This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex…

Machine Learning · Computer Science 2023-03-13 Nikolaus Hansen

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost…

Neural and Evolutionary Computing · Computer Science 2014-06-12 Ilya Loshchilov , Marc Schoenauer , Michèle Sebag , Nikolaus Hansen

Proportional integral derivative (PID) controllers are important and widely used tools in system control. Tuning of the controller gains is a laborious task, especially for complex systems such as combustion engines. To minimize the time of…

Systems and Control · Computer Science 2017-06-07 Katerina Henclova

Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a highly effective optimization technique. A primary challenge when applying CMA-ES in high dimensionality is sampling from a multivariate normal distribution with an arbitrary…

Neural and Evolutionary Computing · Computer Science 2026-01-05 Jarosław Arabas , Adam Stelmaszczyk , Eryk Warchulski , Dariusz Jagodziński , Rafał Biedrzycki

We propose a computationally efficient limited memory Covariance Matrix Adaptation Evolution Strategy for large scale optimization, which we call the LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for numerical…

Neural and Evolutionary Computing · Computer Science 2014-04-23 Ilya Loshchilov

This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a…

Neural and Evolutionary Computing · Computer Science 2022-03-25 Xiaoyu He , Zibin Zheng , Yuren Zhou

In this study, we consider simulation-based worst-case optimization problems with continuous design variables and a finite scenario set. To reduce the number of simulations required and increase the number of restarts for better local…

Neural and Evolutionary Computing · Computer Science 2022-12-01 Atsuhiro Miyagi , Kazuto Fukuchi , Jun Sakuma , Youhei Akimoto

This paper investigates the control of an ML component within the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) devoted to black-box optimization. The known CMA-ES weakness is its sample complexity, the number of evaluations of…

Machine Learning · Computer Science 2013-08-20 Ilya Loshchilov , Marc Schoenauer , Michèle Sebag

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving black-box continuous optimization problems. One practically useful aspect of the CMA-ES is that it can be used without…

Neural and Evolutionary Computing · Computer Science 2023-09-15 Masahiro Nomura , Youhei Akimoto , Isao Ono

The covariance matrix adaptive evolution strategy (CMA-ES) has been widely used in the field of 2D/3D registration in recent years. This optimization method exhibits exceptional robustness and usability for complex surgical scenarios.…

Image and Video Processing · Electrical Eng. & Systems 2024-05-17 Zhirun Zhang , Minheng Chen

Discrete and mixed-variable optimization problems have appeared in several real-world applications. Most of the research on mixed-variable optimization considers a mixture of integer and continuous variables, and several integer handlings…

Optimization and Control · Mathematics 2024-08-26 Kento Uchida , Ryoki Hamano , Masahiro Nomura , Shota Saito , Shinichi Shirakawa

Bilevel optimization is a field of significant theoretical and practical interest, yet solving such optimization problems remains challenging. Evolutionary methods have been employed to address these problems in the black-box setting;…

Neural and Evolutionary Computing · Computer Science 2026-04-06 Marc Ong , Youhei Akimoto

Hyperparameters of deep neural networks are often optimized by grid search, random search or Bayesian optimization. As an alternative, we propose to use the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is known for its…

Neural and Evolutionary Computing · Computer Science 2016-04-26 Ilya Loshchilov , Frank Hutter

Rather than obtaining a single good solution for a given optimization problem, users often seek alternative design choices, because the best-found solution may perform poorly with respect to additional objectives or constraints that are…

Neural and Evolutionary Computing · Computer Science 2025-08-06 Maria Laura Santoni , Christoph Dürr , Carola Doerr , Mike Preuss , Elena Raponi

Multimodal optimization requires both exploration and exploitation. Exploration identifies promising attraction basins, while exploitation finds the best solutions within these basins. The balance between exploration and exploitation can be…

Neural and Evolutionary Computing · Computer Science 2025-06-03 Chandula Fernando , Kushani De Silva

The interest in accelerating black-box optimizers has resulted in several surrogate model-assisted version of the Covariance Matrix Adaptation Evolution Strategy, a state-of-the-art continuous black-box optimizer. The version called…

Neural and Evolutionary Computing · Computer Science 2017-10-02 Jakub Repicky , Lukas Bajer , Zbynek Pitra , Martin Holena

Modern machine learning uses more and more advanced optimization techniques to find optimal hyper parameters. Whenever the objective function is non-convex, non continuous and with potentially multiple local minima, standard gradient…

Machine Learning · Computer Science 2019-02-13 Eric Benhamou , Jamal Atif , Rida Laraki

Bayesian Optimization (BO) is an effective method for finding the global optimum of expensive black-box functions. However, it is well known that applying BO to high-dimensional optimization problems is challenging. To address this issue, a…

Machine Learning · Statistics 2024-02-06 Lam Ngo , Huong Ha , Jeffrey Chan , Vu Nguyen , Hongyu Zhang

Evolution Strategies such as CMA-ES (covariance matrix adaptation evolution strategy) and NES (natural evolution strategy) have been widely used in machine learning applications, where an objective function is optimized without using its…

Optimization and Control · Mathematics 2019-10-28 Haishan Ye , Tong Zhang