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This paper addresses the development of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving optimization problems with linear constraints. The proposed algorithm is referred to as Linear Constraint CMSA-ES…

Neural and Evolutionary Computing · Computer Science 2018-09-24 Patrick Spettel , Hans-Georg Beyer , Michael Hellwig

Various variants of the well known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) have been proposed recently, which improve the empirical performance of the original algorithm by structural modifications. However, in practice it…

Neural and Evolutionary Computing · Computer Science 2018-08-20 Sander van Rijn , Hao Wang , Matthijs van Leeuwen , Thomas Bäck

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

Neural and Evolutionary Computing · Computer Science 2024-09-30 Masahiro Nomura , Youhei Akimoto , Isao Ono

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

The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g.,…

Neural and Evolutionary Computing · Computer Science 2025-06-04 Catalin-Viorel Dinu , Yash J. Patel , Xavier Bonet-Monroig , Hao Wang

Despite the state-of-the-art performance of the covariance matrix adaptation evolution strategy (CMA-ES), high-dimensional black-box optimization problems are challenging tasks. Such problems often involve a property called low effective…

Neural and Evolutionary Computing · Computer Science 2024-12-03 Kento Uchida , Teppei Yamaguchi , Shinichi Shirakawa

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

In this paper we investigate the convergence properties of a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Our study is based on the recent theoretical foundation that the pure rank-mu update CMA-ES performs the…

Artificial Intelligence · Computer Science 2017-06-20 Youhei Akimoto

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

Bilinear Matrix Inequalities (BMIs) are fundamental to control system design but are notoriously difficult to solve due to their nonconvexity. This study addresses BMI-based control optimization problems by adapting and integrating advanced…

Systems and Control · Electrical Eng. & Systems 2026-01-14 Syue-Cian Lin , Wei-Yu Chiu , Chien-Feng Wu

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

We present the results of a comprehensive study of optimization algorithms for the calibration of quantum devices. As part of our ongoing efforts to automate bring-up, tune-up, and system identification procedures, we investigate a broad…

Quantum Physics · Physics 2026-04-14 Kevin Pack , Shai Machnes , Frank K. Wilhelm

We introduce an acceleration for covariance matrix adaptation evolution strategies (CMA-ES) by means of adaptive diagonal decoding (dd-CMA). This diagonal acceleration endows the default CMA-ES with the advantages of separable CMA-ES…

Neural and Evolutionary Computing · Computer Science 2019-05-16 Youhei Akimoto , Nikolaus Hansen

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a popular method to deal with nonconvex and/or stochastic optimization problems when the gradient information is not available. Being based on the CMA-ES, the recently proposed…

Neural and Evolutionary Computing · Computer Science 2017-05-19 Ilya Loshchilov , Tobias Glasmachers , Hans-Georg Beyer

Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the…

Neural and Evolutionary Computing · Computer Science 2021-05-12 Yangjie Mei , Hao Wang

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

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

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is one of the most successful examples of a derandomized evolution strategy. However, it still relies on randomly sampling offspring, which can be done via a uniform distribution…

Neural and Evolutionary Computing · Computer Science 2024-09-25 Jacob de Nobel , Diederick Vermetten , Thomas H. W. Bäck , Anna V. Kononova

The covariance matrix adaptation evolution strategy (CMA-ES) is an efficient continuous black-box optimization method. The CMA-ES possesses many attractive features, including invariance properties and a well-tuned default hyperparameter…

Neural and Evolutionary Computing · Computer Science 2023-05-02 Yohei Watanabe , Kento Uchida , Ryoki Hamano , Shota Saito , Masahiro Nomura , Shinichi Shirakawa

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
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