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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

We introduce a surrogate-based black-box optimization method, termed Polynomial-model-based optimization (PMBO). The algorithm alternates polynomial approximation with Bayesian optimization steps, using Gaussian processes to model the error…

Optimization and Control · Mathematics 2024-03-13 Janina Schreiber , Pau Batlle , Damar Wicaksono , Michael Hecht

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

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 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

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

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

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

This study modifies the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm for multi-modal optimization problems. The enhancements focus on addressing the challenges of multiple global minima, improving the algorithm's…

Neural and Evolutionary Computing · Computer Science 2024-07-02 Wathsala Karunarathne , Indu Bala , Dikshit Chauhan , Matthew Roughan , Lewis Mitchell

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

Surrogate modeling has become a valuable technique for black-box optimization tasks with expensive evaluation of the objective function. In this paper, we investigate the relationship between the predictive accuracy of surrogate models and…

Neural and Evolutionary Computing · Computer Science 2022-10-04 Zbyněk Pitra , Jan Koza , Jiří Tumpach , Martin Holeňa

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

One method to solve expensive black-box optimization problems is to use a surrogate model that approximates the objective based on previous observed evaluations. The surrogate, which is cheaper to evaluate, is optimized instead to find an…

Optimization and Control · Mathematics 2021-05-28 Rickard Karlsson , Laurens Bliek , Sicco Verwer , Mathijs de Weerdt

Chemical plant design and optimisation have proven challenging due to the complexity of these real-world systems. The resulting complexity translates into high computational costs for these systems' mathematical formulations and simulation…

Neural and Evolutionary Computing · Computer Science 2022-04-28 Liezl Stander , Matthew Woolway , Terence L. Van Zyl

Recently, optimization has become an emerging tool for neuroscientists to study neural code. In the visual system, neurons respond to images with graded and noisy responses. Image patterns eliciting highest responses are diagnostic of the…

Neural and Evolutionary Computing · Computer Science 2022-04-15 Binxu Wang , Carlos R. Ponce

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

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

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

In this study, we consider a continuous min--max optimization problem $\min_{x \in \mathbb{X} \max_{y \in \mathbb{Y}}}f(x,y)$ whose objective function is a black-box. We propose a novel approach to minimize the worst-case objective function…

Neural and Evolutionary Computing · Computer Science 2023-03-29 Atsuhiro Miyagi , Yoshiki Miyauchi , Atsuo Maki , Kazuto Fukuchi , Jun Sakuma , Youhei Akimoto

Black-box optimization problems, which are common in many real-world applications, require optimization through input-output interactions without access to internal workings. This often leads to significant computational resources being…

Neural and Evolutionary Computing · Computer Science 2024-03-25 Hao Hao , Xiaoqun Zhang , Aimin Zhou