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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

This paper explores the theoretical basis of the covariance matrix adaptation evolution strategy (CMA-ES) from the information geometry viewpoint. To establish a theoretical foundation for the CMA-ES, we focus on a geometric structure of a…

Neural and Evolutionary Computing · Computer Science 2012-06-06 Youhei Akimoto , Yuichi Nagata , Isao Ono , Shigenobu Kobayashi

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

Evolutionary optimization algorithms often face defects and limitations that complicate the evolution processes or even prevent them from reaching the global optimum. A notable constraint pertains to the considerable quantity of function…

Neural and Evolutionary Computing · Computer Science 2025-05-23 Farshid Farhadi Khouzani , Abdolreza Mirzaei , Paul La Plante , Laxmi Gewali

The covariance matrix adaptation evolution strategy (CMA-ES) is a stochastic search algorithm using a multivariate normal distribution for continuous black-box optimization. In addition to strong empirical results, part of the CMA-ES can be…

Neural and Evolutionary Computing · Computer Science 2024-08-12 Ryoki Hamano , Shinichi Shirakawa , Masahiro Nomura

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

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

Water distribution system design is a challenging optimisation problem with a high number of search dimensions and constraints. In this way, Evolutionary Algorithms (EAs) have been widely applied to optimise WDS to minimise cost subject…

Neural and Evolutionary Computing · Computer Science 2019-09-12 Mehdi Neshat , Bradley Alexander , Angus Simpson

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

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

In this paper, we propose a novel meta-learning method in a reinforcement learning setting, based on evolution strategies (ES), exploration in parameter space and deterministic policy gradients. ES methods are easy to parallelize, which is…

Machine Learning · Computer Science 2019-05-09 Yiming Shen , Kehan Yang , Yufeng Yuan , Simon Cheng Liu

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

This paper proposes RCMAES, a novel variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for CEC benchmark optimization. RCMAES integrates a dimension-dependent nonlinear population-size reduction strategy with an…

Neural and Evolutionary Computing · Computer Science 2026-05-01 Khoirul Faiq Muzakka , Sören Möller , Martin Finsterbusch

One of the most challenging types of ill-posedness in global optimization is the presence of insensitivity regions in design parameter space, so the identification of their shape will be crucial, if ill-posedness is irrecoverable. Such…

Neural and Evolutionary Computing · Computer Science 2019-05-20 Jakub Sawicki , Maciej Smołka , Marcin Łoś , Robert Schaefer

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

An evolution strategy (ES) variant based on a simplification of a natural evolution strategy recently attracted attention because it performs surprisingly well in challenging deep reinforcement learning domains. It searches for neural…

Neural and Evolutionary Computing · Computer Science 2018-05-03 Joel Lehman , Jay Chen , Jeff Clune , Kenneth O. Stanley

The performance of deep neural networks, such as Deep Belief Networks formed by Restricted Boltzmann Machines (RBMs), strongly depends on their training, which is the process of adjusting their parameters. This process can be posed as an…

Neural and Evolutionary Computing · Computer Science 2019-07-16 S. Ivvan Valdez , Alfonso Rojas-Domínguez

The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for…

Neural and Evolutionary Computing · Computer Science 2025-04-11 Jacob de Nobel , Diederick Vermetten , Hao Wang , Anna V. Kononova , Günter Rudolph , 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

In this work we show that Evolution Strategies (ES) are a viable method for learning non-differentiable parameters of large supervised models. ES are black-box optimization algorithms that estimate distributions of model parameters; however…

Neural and Evolutionary Computing · Computer Science 2019-06-10 Karel Lenc , Erich Elsen , Tom Schaul , Karen Simonyan