skip to main content
10.1145/2739480.2754754acmconferencesArticle/Chapter ViewAbstractPublication PagesgeccoConference Proceedingsconference-collections
research-article

Injecting CMA-ES into MOEA/D

Published: 11 July 2015 Publication History

Abstract

MOEA/D is an aggregation-based evolutionary algorithm which has been proved extremely efficient and effective for solving multi-objective optimization problems. It is based on the idea of decomposing the original multi-objective problem into several single-objective subproblems by means of well-defined scalarizing functions. Those single-objective subproblems are solved in a cooperative manner by defining a neighborhood relation between them. This makes MOEA/D particularly interesting when attempting to plug and to leverage single-objective optimizers in a multi-objective setting. In this context, we investigate the benefits that MOEA/D can achieve when coupled with CMA-ES, which is believed to be a powerful single-objective optimizer. We rely on the ability of CMA-ES to deal with injected solutions in order to update different covariance matrices with respect to each subproblem defined in MOEA/D. We show that by cooperatively evolving neighboring CMA-ES components, we are able to obtain competitive results for different multi-objective benchmark functions.

References

[1]
A. Auger and N. Hansen. A restart CMA evolution strategy with increasing population size. In B. McKay et al., editors, CEC'2005, volume 2, pages 1769--1776, 2005.
[2]
C. E. Bonferroni. Teoria statistica delle classi e calcolo delle probabilita. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze, 8:3--62, 1936.
[3]
C. A. Coello Coello and N. Cruz Cortés. Solving Multiobjective Optimization Problems using an Artificial Immune System. Genetic Programming and Evolvable Machines, 6(2):163--190, June 2005.
[4]
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA--II. IEEE Transactions on Evolutionary Computation, 6(2):182--197, April 2002.
[5]
N. Hansen. The CMA evolution strategy: a comparing review. In J. Lozano, P. Larranaga, I. Inza, and E. Bengoetxea, editors, Towards a new evolutionary computation. Advances on estimation of distribution algorithms, pages 75--102. Springer, 2006.
[6]
N. Hansen. Injecting external solutions into CMA-ES. Technical report, INRIA, 2011.
[7]
N. Hansen, A. Auger, R. Ros, S. Finck, and P. Posík. Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009. In J. Branke et al., editors, GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), pages 1689--1696. ACM, July 2010.
[8]
N. Hansen, S. Niederberger, L. Guzzella, and P. Koumoutsakos. A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion. IEEE Transactions on Evolutionary Computation, 13(1):180--197, 2009.
[9]
N. Hansen and A. Ostermeier. Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation, 9(2):159--195, 2001.
[10]
C. Igel, N. Hansen, and S. Roth. Covariance matrix adaptation for multi-objective optimization. Evolutionary Computation, 15(1):1--28, 2007.
[11]
C. Igel, T. Suttorp, and N. Hansen. Steady-state selection and efficient covariance matrix update in the multi-objective cma-es. In Evolutionary Multi-Criterion Optimization, pages 171--185. Springer Berlin Heidelberg, 2007.
[12]
H. Ishibuchi and T. Murata. Multi-Objective Genetic Local Search Algorithm. In T. Fukuda and T. Furuhashi, editors, Proceedings of the 1996 International Conference on Evolutionary Computation, pages 119--124, Nagoya, Japan, 1996. IEEE.
[13]
J. Knowles, L. Thiele, and E. Zitzler. A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers. 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland, feb 2006. revised version.
[14]
H. Li and Q. Zhang. Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II. IEEE Transactions on Evolutionary Computation, 13(2):284--302, April 2009.
[15]
K. Miettinen. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston, Massachuisetts, 1999.
[16]
H. Scheffé. Experiments With Mixtures. Journal of the Royal Statistical Society, Series B (Methodological), 20(2):344--360, 1958.
[17]
Q. Zhang and H. Li. MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE TEVC, 11(6):712--731, December 2007.
[18]
Q. Zhang, A. Zhou, S. Zhao, P. N. Suganthan, W. Liu, and S. Tiwari. Multiobjective Optimization Test Instances for the CEC 2009 Special Session and Competition. Technical Report CES-487, University of Essex and Nanyang Technological University, 2008.
[19]
E. Zitzler and S. Künzli. Indicator-based selection in multiobjective search. In PPSN VIII, pages 832--842. Springer, 2004.
[20]
E. Zitzler and L. Thiele. Multiobjective Optimization Using Evolutionary Algorithms -- A Comparative Case Study. In A. E. Eiben, editor, PPSN V, pages 292--301, Amsterdam, September 1998. Springer-Verlag.

Cited By

View all
  • (2024)MOEA/D-CMA Made Better with (l+l)-CMA-ES2024 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC60901.2024.10612007(1-8)Online publication date: 30-Jun-2024
  • (2024)A topology optimization of on-chip planar inductor based on evolutional on/off method and CMA-ESCOMPEL - The international journal for computation and mathematics in electrical and electronic engineering10.1108/COMPEL-10-2023-050343:4(920-931)Online publication date: 2-Apr-2024
  • (2024)Multi-objective cooperation search algorithm based on decomposition for complex engineering optimization and reservoir operation problemsApplied Soft Computing10.1016/j.asoc.2024.112442167(112442)Online publication date: Dec-2024
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

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 ACM 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]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 July 2015

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. covariance matrix adaption evolution strategy
  2. decomposition-based moeas
  3. multi-objective optimization

Qualifiers

  • Research-article

Conference

GECCO '15
Sponsor:

Acceptance Rates

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

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)22
  • Downloads (Last 6 weeks)3
Reflects downloads up to 02 Mar 2025

Other Metrics

Citations

Cited By

View all
  • (2024)MOEA/D-CMA Made Better with (l+l)-CMA-ES2024 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC60901.2024.10612007(1-8)Online publication date: 30-Jun-2024
  • (2024)A topology optimization of on-chip planar inductor based on evolutional on/off method and CMA-ESCOMPEL - The international journal for computation and mathematics in electrical and electronic engineering10.1108/COMPEL-10-2023-050343:4(920-931)Online publication date: 2-Apr-2024
  • (2024)Multi-objective cooperation search algorithm based on decomposition for complex engineering optimization and reservoir operation problemsApplied Soft Computing10.1016/j.asoc.2024.112442167(112442)Online publication date: Dec-2024
  • (2023)A New Hyper-Heuristic Multi-Objective Optimisation Approach Based on MOEA/D FrameworkBiomimetics10.3390/biomimetics80705218:7(521)Online publication date: 2-Nov-2023
  • (2021)A Modified MOEA/D Algorithm for Solving Bi-Objective Multi-Stage Weapon-Target Assignment ProblemIEEE Access10.1109/ACCESS.2021.30791529(71832-71848)Online publication date: 2021
  • (2020)Enhancing Decomposition-Based Algorithms by Estimation of Distribution for Constrained Optimal Software Product SelectionIEEE Transactions on Evolutionary Computation10.1109/TEVC.2019.292241924:2(245-259)Online publication date: Apr-2020
  • (2020)Decomposition Based Multi-objectives Evolutionary Algorithms Challenges and CircumventionIntelligent Computing10.1007/978-3-030-52246-9_6(82-93)Online publication date: 4-Jul-2020
  • (2019)A New Approach to Generate Solutions Combining Crossover and Estimation of Distribution Operators for EMO Algorithm2019 IEEE Symposium Series on Computational Intelligence (SSCI)10.1109/SSCI44817.2019.9002866(2088-2095)Online publication date: Dec-2019
  • (2019)Pareto Optimal Set Approximation by Models: A Linear CaseEvolutionary Multi-Criterion Optimization10.1007/978-3-030-12598-1_36(451-462)Online publication date: 3-Feb-2019
  • (2018)A decomposition-based kernel of Mallows models algorithm for bi- and tri-objective permutation flowshop scheduling problemApplied Soft Computing10.1016/j.asoc.2018.07.01171(526-537)Online publication date: Oct-2018
  • Show More Cited By

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media