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A hallmark of intelligence is the ability to exhibit a wide range of effective behaviors. Inspired by this principle, Quality-Diversity algorithms, such as MAP-Elites, are evolutionary methods designed to generate a set of diverse and…

Neural and Evolutionary Computing · Computer Science 2024-10-07 Maxence Faldor , Félix Chalumeau , Manon Flageat , Antoine Cully

Quality Diversity (QD) algorithms such as MAP-Elites are a class of optimisation techniques that attempt to find many high performing points that all behave differently according to a user-defined behavioural metric. In this paper we…

Optimization and Control · Mathematics 2023-07-20 Paul Kent , Adam Gaier , Jean-Baptiste Mouret , Juergen Branke

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

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

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

This paper introduces a user-driven evolutionary algorithm based on Quality Diversity (QD) search. During a design session, the user iteratively selects among presented alternatives and their selections affect the upcoming results. We aim…

Neural and Evolutionary Computing · Computer Science 2023-04-10 Konstantinos Sfikas , Antonios Liapis , Georgios N. Yannakakis

Quality-Diversity optimization comprises a family of evolutionary algorithms aimed at generating a collection of diverse and high-performing solutions. MAP-Elites (ME), a notable example, is used effectively in fields like evolutionary…

Neural and Evolutionary Computing · Computer Science 2025-02-03 Konstantinos Mitsides , Maxence Faldor , Antoine Cully

Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing…

Computational Engineering, Finance, and Science · Computer Science 2026-03-19 Fabian Key , Lukas Freinberger , Mayu Muramatsu , Norbert Hosters

We propose a novel constraint-handling technique for the covariance matrix adaptation evolution strategy (CMA-ES). The proposed technique is aimed at solving explicitly constrained black-box continuous optimization problems, in which the…

Neural and Evolutionary Computing · Computer Science 2022-05-11 Naoki Sakamoto , Youhei Akimoto

Evolutionary search via the quality-diversity (QD) paradigm can discover highly performing solutions in different behavioural niches, showing considerable potential in complex real-world scenarios such as evolutionary robotics. Yet most QD…

Neural and Evolutionary Computing · Computer Science 2024-04-10 Roberto Gallotta , Antonios Liapis , Georgios N. Yannakakis

Diversity optimization seeks to discover a set of solutions that elicit diverse features. Prior work has proposed Novelty Search (NS), which, given a current set of solutions, seeks to expand the set by finding points in areas of low…

Machine Learning · Computer Science 2024-05-31 David H. Lee , Anishalakshmi V. Palaparthi , Matthew C. Fontaine , Bryon Tjanaka , Stefanos Nikolaidis

Designing optimal soft modular robots is difficult, due to non-trivial interactions between morphology and controller. Evolutionary algorithms (EAs), combined with physical simulators, represent a valid tool to overcome this issue. In this…

Robotics · Computer Science 2021-04-27 Enrico Zardini , Davide Zappetti , Davide Zambrano , Giovanni Iacca , Dario Floreano

We present the first application of MAP-Elites, a quality-diversity algorithm, to trade execution. Rather than searching for a single optimal policy, MAP-Elites generates a diverse portfolio of regime-specialist strategies indexed by…

Trading and Market Microstructure · Quantitative Finance 2026-02-02 Robert de Witt , Mikko S. Pakkanen

Navigating deceptive domains has often been a challenge in machine learning due to search algorithms getting stuck at sub-optimal local optima. Many algorithms have been proposed to navigate these domains by explicitly maintaining diversity…

Neural and Evolutionary Computing · Computer Science 2023-11-07 Ryan Boldi , Li Ding , Lee Spector

Quality-Diversity algorithms search for large collections of diverse and high-performing solutions, rather than just for a single solution like typical optimisation methods. They are specially adapted for multi-modal problems that can be…

Neural and Evolutionary Computing · Computer Science 2021-05-04 Leo Cazenille

Quality-Diversity optimisation algorithms enable the evolution of collections of both high-performing and diverse solutions. These collections offer the possibility to quickly adapt and switch from one solution to another in case it is not…

Neural and Evolutionary Computing · Computer Science 2023-04-26 Manon Flageat , Antoine Cully

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 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

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

A fascinating aspect of nature lies in its ability to produce a collection of organisms that are all high-performing in their niche. Quality-Diversity (QD) methods are evolutionary algorithms inspired by this observation, that obtained…

Neural and Evolutionary Computing · Computer Science 2023-09-11 Felix Chalumeau , Thomas Pierrot , Valentin Macé , Arthur Flajolet , Karim Beguir , Antoine Cully , Nicolas Perrin-Gilbert