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CMA-ES

swMATH ID: 5063
Software Authors: Hansen
Description: CMA-ES stands for Covariance Matrix Adaptation Evolution Strategy. Evolution strategies (ES) are stochastic, derivative-free methods for numerical optimization of non-linear or non-convex continuous optimization problems. They belong to the class of evolutionary algorithms and evolutionary computation. An evolutionary algorithm is broadly based on the principle of biological evolution, namely the repeated interplay of variation (via mutation and recombination) and selection: in each generation (iteration) new individuals (candidate solutions, denoted as x) are generated by variation, usually in a stochastic way, and then some individuals are selected for the next generation based on their fitness or objective function value f(x). Like this, over the generation sequence, individuals with better and better f-values are generated. In an evolution strategy, new candidate solutions are sampled according to a multivariate normal distribution in the mathbb{R}^n. Pairwise dependencies between the variables in this distribution are represented by a covariance matrix. The covariance matrix adaptation (CMA) is a method to update the covariance matrix of this distribution. This is particularly useful, if the function f is ill-conditioned. Adaptation of the covariance matrix amounts to learning a second order model of the underlying objective function similar to the approximation of the inverse Hessian matrix in the Quasi-Newton method in classical optimization. In contrast to most classical methods, fewer assumptions on the nature of the underlying objective function are made. Only the ranking between candidate solutions is exploited for learning the sample distribution and neither derivatives nor even the function values themselves are required by the method.
Homepage: https://www.lri.fr/~hansen/cmaes_inmatlab.html
Programming Languages: Matlab
Dependencies: Matlab
Keywords: optimization; The Unconstrained NLO Problem; Global Optimization
Related Software: CEC 05; EGO; Genocop; MultiMin; GitHub; JADE; SNOBFIT; PSwarm; SPOT; R; NOMAD; NEWUOA; ABC; DACE; WOA; CEC 13; MCS; fminsearch; BOBYQA; SSA
Cited in: 105 Publications
Further Publications: https://www.lri.fr/~hansen/publications.html#hansenReview2006
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Cited by 280 Authors

6 Koumoutsakos, Petros D.
4 Angelikopoulos, Panagiotis
4 Gonzalez, Luis Felipe
4 Hansen, Nikolaus
4 Périaux, Jacques F.
4 Srinivas, Karkenahalli
3 Akimoto, Youhei
3 Auger, Anne
3 Beyer, Hans-Georg
3 Papadimitriou, Costas
3 Sahinidis, Nikolaos V.
2 Ahrari, Ali
2 Amaran, Satyajith
2 Arampatzis, Georgios
2 Balesdent, Mathieu
2 Breunig, U.
2 Bury, Scott J.
2 Fernandes, Edite M. G. P.
2 Gandomi, Amir Hossein
2 García-Martínez, Carlos
2 Hadjidoukas, Panagiotis E.
2 Hartl, Richard F.
2 Herrera, Francisco
2 Igel, Christian
2 Lozano, Manuel
2 Marsden, Alison L.
2 Molina, Daniel
2 Regis, Rommel G.
2 Rocha, Ana Maria A. C.
2 Sharda, Bikram
2 Telek, Miklós
2 Vidal, Thibaut
2 Wälchli, Daniel
1 Abd Elaziz, Mohamed
1 Abdulsamad, Hany
1 Abualigah, Laith
1 Agathos, Konstantinos
1 Ahrari, Reza
1 Almaraashi, Majid
1 Amin, Hesham H.
1 Andreasen, Martin Møller
1 Atai, Ali Asghar
1 Audet, Charles
1 Aulig, Nikola
1 Bader, Samuel B.
1 Baldacci, Roberto
1 Baldi, Pierre
1 Barbaresco, Frédéric
1 Bartoszuk, Maciej
1 Bartz-Beielstein, Thomas
1 Beliakov, Gleb
1 Belousov, Boris
1 Bigeon, Jean
1 Billy, Frédérique
1 Blanco-Cocom, Luis D.
1 Bordas, Stéphane Pierre Alain
1 Boria, Simonetta
1 Borràs, Agnés
1 Bosman, Peter A. N.
1 Botello Rionda, Salvador
1 Boussaïd, Ilhem
1 Brevault, Loïc
1 Brossier, Romain
1 Büche, Dirk
1 Buet, Blanche
1 Bujny, Mariusz
1 Bureerat, Sujin
1 Byrne, Helen Mary
1 Cai, Zhihua
1 Caleb-Solly, Praminda
1 Celora, Giulia L.
1 Chatzi, Eleni
1 Chen, Huangke
1 Cheng, Junrui
1 Cheng, Ran
1 Cheng, Xiang
1 Çınar, Didem
1 Clairambault, Jean
1 Congedo, Pietro Marco
1 Costa, M. Fernanda P.
1 Couderc, Romain
1 Cuadrado, Javier
1 Deabes, Wael
1 Dennis, John E. jun.
1 D’eramo, Carlo
1 Dery, Cosmas
1 Desai, Siddharth
1 Desquilbet, François
1 Diabat, Ali H.
1 DiPillo, Gianni
1 Dorigo, Marco
1 Dréo, Johann
1 Du, Bo
1 Duddeck, Fabian M. E.
1 Durantin, Cédric
1 Economides, Athena E.
1 Fasli, Maria
1 Fercoq, Olivier
1 Finck, Steffen
1 Fujii, Garuda
...and 180 more Authors
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Cited in 53 Serials

11 Computer Methods in Applied Mechanics and Engineering
7 Information Sciences
5 Journal of Global Optimization
5 European Journal of Operational Research
4 Machine Learning
3 Computers and Fluids
3 Journal of Computational and Applied Mathematics
3 Theoretical Computer Science
3 Computers & Operations Research
3 Computational Optimization and Applications
3 Optimization and Engineering
2 Computer Physics Communications
2 Applied Mathematics and Computation
2 Mathematics and Computers in Simulation
2 Algorithmica
2 Applied Mathematical Modelling
2 Mathematical Problems in Engineering
2 Mathematical Programming Computation
1 Artificial Intelligence
1 Inverse Problems
1 Journal of Computational Physics
1 Journal of Optimization Theory and Applications
1 Journal of Algorithms
1 Computational Mechanics
1 AI Communications
1 Annals of Operations Research
1 Pattern Recognition
1 Stochastic Processes and their Applications
1 Computational Economics
1 SIAM Journal on Scientific Computing
1 Open Economies Review
1 Bernoulli
1 Multibody System Dynamics
1 Optimization Methods & Software
1 CEJOR. Central European Journal of Operations Research
1 Probability in the Engineering and Informational Sciences
1 Methodology and Computing in Applied Probability
1 Stochastic Models
1 Journal of Machine Learning Research (JMLR)
1 Natural Computing
1 4OR
1 Mathematical Biosciences and Engineering
1 Optimization Letters
1 Mathematical Geosciences
1 Algorithms
1 Journal of Control Science and Engineering
1 Journal of Computational and Graphical Statistics
1 Arabian Journal for Science and Engineering
1 Journal of Theoretical Biology
1 International Journal of Systems Science. Principles and Applications of Systems and Integration
1 SMAI Journal of Computational Mathematics
1 Electronic Research Archive
1 SN Operations Research Forum

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