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A CMA-ES with Multiplicative Covariance Matrix Updates

Published: 11 July 2015 Publication History

Abstract

Covariance matrix adaptation (CMA) mechanisms are core building blocks of modern evolution strategies. Despite sharing a common principle, the exact implementation of CMA varies considerably between different algorithms. In this paper, we investigate the benefits of an exponential parametrization of the covariance matrix in the CMA-ES. This technique was first proposed for the xNES algorithm. It results in a multiplicative update formula for the covariance matrix. We show that the exponential parameterization and the multiplicative update are compatible with all mechanisms of CMA-ES. The resulting algorithm, xCMA-ES, performs at least on par with plain CMA-ES. Its advantages show in particular with updates that actively decrease the sampling variance in specific directions, i.e., for active constraint handling.

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cover image ACM Conferences
GECCO '15: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation
July 2015
1496 pages
ISBN:9781450334723
DOI:10.1145/2739480
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Published: 11 July 2015

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Author Tags

  1. cma-es
  2. covariance matrix adaptation
  3. evolution strategies
  4. exponential coordinates
  5. multiplicative update

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  • Danish National Advanced Technology Foundation

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GECCO '15 Paper Acceptance Rate 182 of 505 submissions, 36%;
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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  • (2022)Adaptive Ranking-Based Constraint Handling for Explicitly Constrained Black-Box OptimizationEvolutionary Computation10.1162/evco_a_0031030:4(503-529)Online publication date: 1-Dec-2022
  • (2021)Natural Evolution Strategy for Unconstrained and Implicitly Constrained Problems with Ridge Structure2021 IEEE Symposium Series on Computational Intelligence (SSCI)10.1109/SSCI50451.2021.9659906(1-7)Online publication date: 5-Dec-2021
  • (2020)Diagonal Acceleration for Covariance Matrix Adaptation Evolution StrategiesEvolutionary Computation10.1162/evco_a_0026028:3(405-435)Online publication date: 1-Sep-2020
  • (2020)Radio Access Scheduling using CMA-ES for Optimized QoS in Wireless Networks2020 IEEE Globecom Workshops (GC Wkshps10.1109/GCWkshps50303.2020.9367458(1-6)Online publication date: Dec-2020
  • (2020)Variable metric evolution strategies by mutation matrix adaptationInformation Sciences10.1016/j.ins.2020.05.091541(136-151)Online publication date: Dec-2020
  • (2020)The Hessian Estimation Evolution StrategyParallel Problem Solving from Nature – PPSN XVI10.1007/978-3-030-58112-1_41(597-609)Online publication date: 31-Aug-2020
  • (2019)Adaptive ranking based constraint handling for explicitly constrained black-box optimizationProceedings of the Genetic and Evolutionary Computation Conference10.1145/3321707.3321717(700-708)Online publication date: 13-Jul-2019
  • (2017)Simplify Your Covariance Matrix Adaptation Evolution StrategyIEEE Transactions on Evolutionary Computation10.1109/TEVC.2017.268032021:5(746-759)Online publication date: Oct-2017
  • (2017)An efficient rank-1 update for Cholesky CMA-ES using auxiliary evolution path2017 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2017.7969406(913-920)Online publication date: Jun-2017
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