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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

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

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 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

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

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

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

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

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

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 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

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

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

In this paper, we propose an efficient approximated rank one update for covariance matrix adaptation evolution strategy (CMA-ES). It makes use of two evolution paths as simple as that of CMA-ES, while avoiding the computational matrix…

Neural and Evolutionary Computing · Computer Science 2017-10-24 Zhenhua Li , Qingfu Zhang

We focus on the challenge of finding a diverse collection of quality solutions on complex continuous domains. While quality diver-sity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are designed to generate…

Machine Learning · Computer Science 2020-05-08 Matthew C. Fontaine , Julian Togelius , Stefanos Nikolaidis , Amy K. Hoover

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

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

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

The covariance matrix adaptation evolution strategy (CMA-ES) is a powerful optimization method for continuous black-box optimization problems. Several noise-handling methods have been proposed to bring out the optimization performance of…

Neural and Evolutionary Computing · Computer Science 2024-05-21 Kento Uchida , Kenta Nishihara , Shinichi Shirakawa

We combine a refined version of two-point step-size adaptation with the covariance matrix adaptation evolution strategy (CMA-ES). Additionally, we suggest polished formulae for the learning rate of the covariance matrix and the…

Neural and Evolutionary Computing · Computer Science 2008-12-18 Nikolaus Hansen
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