Skip to main content
SpringerLink
Log in
Book cover

Asia-Pacific Conference on Simulated Evolution and Learning

SEAL 2017: Simulated Evolution and Learning pp 260–271Cite as

A Fast Objective Reduction Algorithm Based on Dominance Structure for Many Objective Optimization

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10593))

Abstract

The performance of the most existing classical evolutionary multiobjective optimization (EMO) algorithms, especially for Pareto-based EMO algorithms, generally deteriorates over the number of objectives in solving many-objective optimization problems (MaOPs), in which the number of objectives is greater than three. Objective reduction methods that transform an MaOP into the one with few objectives, are a promising way for solving MaOPs. The dominance-based objective reduction methods, e.g. k-EMOSS and \(\delta \)-MOSS, omitting an objective while preserving the dominant structure of the individuals as much as possible, can achieve good performance. However, these algorithms have higher computational complexity. Therefore, this paper presents a novel measure for measuring the capacity of preserving the dominance structure of an objective set, i.e., the redundancy of an objective to an objective set. Subsequently, we propose a fast algorithm to find a minimum set of objectives preserving the dominance structure as much as possible. We compare the proposed algorithm with its counterparts on eleven test instances. Numerical studies show the effectiveness of the proposed algorithm.

This work was supported by the National Natural Science Foundation of China under Grants 61672444, 61673121 and 61703108, in part by the Natural Science Foundation of Guangdong Province under Grant 2017A030310467, and in part by the Projects of Science and Technology of Guangzhou under Grant 201508010008, the SZSTI Grant: JCYJ20160531194006833, the Faculty Research Grant of Hong Kong Baptist University (HKBU) under Project: FRG2/16-17/051, and the MPCF Project of Knowledge Transfer Office in HKBU: MPCF-004-2017/18.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bader, J., Zitzler, E.: HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 19(1), 45–76 (2011)

    Article  Google Scholar 

  2. Bandyopadhyay, S., Mukherjee, A.: An algorithm for many-objective optimization with reduced objective computations: a study in differential evolution. IEEE Trans. Evol. Comput. 19(3), 400–413 (2015)

    Article  Google Scholar 

  3. Brockhoff, D., Zitzler, E.: Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization. In: Runarsson, T.P., Beyer, H.-G., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 533–542. Springer, Heidelberg (2006). doi:10.1007/11844297_54

    Chapter  Google Scholar 

  4. Brockhoff, D., Zitzler, E.: Objective reduction in evolutionary multiobjective optimization: theory and applications. Evol. Comput. 17(2), 135–166 (2009)

    Article  Google Scholar 

  5. Cheung, Y.M., Gu, F.: Online objective reduction for many-objective optimization problems. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1165–1171 (2014)

    Google Scholar 

  6. Cheung, Y.M., Gu, F., Liu, H.L.: Objective extraction for many-objective optimization problems: algorithm and test problems. IEEE Trans. Evol. Comput. 20(5), 755–772 (2016)

    Article  Google Scholar 

  7. Deb, K.: Multiobjective Optimization using Evolutionary Algorithms. Wiley, New York (2001)

    MATH  Google Scholar 

  8. Deb, K., Mohan, M., Mishra, S.: Evaluating the \(\varepsilon \)-domination based multi-objective evolutionary algorithm for a quick computation of pareto-optimal solutions. Evol. Comput. 13(4), 501–525 (2005)

    Article  Google Scholar 

  9. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  10. Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)

    Article  Google Scholar 

  11. Eckart, Z., Marco, L., Lothar, T.: SPEA2: improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Proceedings of Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, pp. 95–100 (2001)

    Google Scholar 

  12. Farina, M., Amato, P.: A fuzzy definition of “optimality” for many-criteria optimization problems. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 34(3), 315–326 (2004)

    Article  Google Scholar 

  13. Guo, X., Wang, X., Wang, M., Wang, Y.: A new objective reduction algorithm for many-objective problems: employing mutual information and clustering algorithm. In: Proceedings of 2012 Eighth International Conference on Computational Intelligence and Security, pp. 11–16 (2012)

    Google Scholar 

  14. Ishibuchi, H., Akedo, N., Nojima, Y.: Behavior of multi-objective evolutionary algorithms on many-objective knapsack problems. IEEE Trans. Evol. Comput. 19(2), 264–283 (2014)

    Article  Google Scholar 

  15. Ishibuchi, H., Masuda, H., Nojima, Y.: Pareto fronts of many-objective degenerate test problems. IEEE Trans. Evol. Comput. 20(5), 807–813 (2016)

    Article  Google Scholar 

  16. Jaimes, A.L., Coello, C.A.C., Urías Barrientos, J.E.: Online objective reduction to deal with many-objective problems. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 423–437. Springer, Heidelberg (2009). doi:10.1007/978-3-642-01020-0_34

    Chapter  Google Scholar 

  17. Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19(5), 694–716 (2015)

    Article  Google Scholar 

  18. Liu, H.L., Gu, F., Zhang, Q.: Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans. Evol. Comput. 18(3), 450–455 (2014)

    Article  Google Scholar 

  19. López Jaimes, A., Coello Coello, C.A., Chakraborty, D.: Objective reduction using a feature selection technique. In: Proceedings of 10th Annual Conference on Genetic and Evolutionary Computation, pp. 673–680 (2008)

    Google Scholar 

  20. McClymont, K., Keedwell, E.: Deductive sort and climbing sort: new methods for non-dominated sorting. Evol. Comput. 20(1), 1–26 (2012)

    Article  Google Scholar 

  21. Narukawa, K., Rodemann, T.: Examining the performance of evolutionary many-objective optimization algorithms on a real-world application. In: Proceedings of 2012 Sixth International Conference on Genetic and Evolutionary Computing, pp. 316–319 (2012)

    Google Scholar 

  22. Nicola, B., Naujoks, B., Emmerich, M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)

    Article  MATH  Google Scholar 

  23. Freitas, A.R., Fleming, P.J., Guimaraes, F.: A non-parametric harmony-based objective reduction method for many-objective optimization. In: Proceedings of 2013 IEEE International Conference on Systems, Man, and Cybernetics, pp. 651–656 (2013)

    Google Scholar 

  24. Russo, L.M.S., Francisco, A.P.: Quick hypervolume. IEEE Trans. Evol. Comput. 18(4), 481–502 (2014)

    Article  Google Scholar 

  25. Saxena, D.K., Duro, J.A., Tiwari, A., Deb, K., Zhang, Q.: Objective reduction in many-objective optimization: linear and nonlinear algorithms. IEEE Trans. Evol. Comput. 17(1), 77–99 (2013)

    Article  Google Scholar 

  26. Schutze, O., Lara, A., Coello Coello, C.A.: On the influence of the number of objectives on the hardness of a multiobjective optimization problem. IEEE Trans. Evol. Comput. 15(4), 444–455 (2011)

    Article  Google Scholar 

  27. Singh, H.K., Isaacs, A., Ray, T.: A pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems. IEEE Trans. Evol. Comput. 15(4), 539–556 (2011)

    Article  Google Scholar 

  28. Wang, H., Yao, X.: Objective reduction based on nonlinear correlation information entropy. Soft. Comput. 20(6), 2393–2407 (2016)

    Article  Google Scholar 

  29. Yuan, Y., Ong, Y.S., Gupta, A., Xu, H.: Objective reduction in many-objective optimization: evolutionary multiobjective approaches and comprehensive analysis. IEEE Trans. Evol. Comput. (2017). doi:10.1109/TEVC.2017.2672668

  30. Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)

    Article  Google Scholar 

  31. Zhou, Y., Chen, Z., Zhang, J.: Ranking vectors by means of the dominance degree matrix. IEEE Trans. Evol. Comput. 21(1), 34–51 (2017)

    Article  Google Scholar 

  32. Zhu, C., Xu, L., Goodman, E.D.: Generalization of Pareto-optimality for many-objective evolutionary optimization. IEEE Trans. Evol. Comput. 20(2), 299–315 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Guangdong University of Technology, Guangdong, China

    Fangqing Gu & Hai-Lin Liu

  2. Department of Computer Science, Hong Kong Baptist University (HKBU), Hong Kong SAR, China

    Yiu-ming Cheung

  3. HKBU Institute of Research and Continuing Education, Shenzhen, China

    Yiu-ming Cheung

Authors
  1. Fangqing Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hai-Lin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yiu-ming Cheung
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiu-ming Cheung .

Editor information

Editors and Affiliations

  1. Southern University of Science and Technology, Shenzhen, China

    Yuhui Shi

  2. City University of Hong Kong, Hong Kong, Kowloon, Hong Kong

    Kay Chen Tan

  3. Victoria University of Wellington, Wellington, Wellington, New Zealand

    Mengjie Zhang

  4. Southern University of Science and Technology, Shenzhen, China

    Ke Tang

  5. RMIT University, Melbourne, Victoria, Australia

    Xiaodong Li

  6. City University of Hong Kong, Kowloon Tong, Hong Kong

    Qingfu Zhang

  7. Peking University, Beijing, China

    Ying Tan

  8. University of Leipzig, Leipzig, Germany

    Martin Middendorf

  9. University of Surrey, Guildford, Surrey, United Kingdom

    Yaochu Jin

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Gu, F., Liu, HL., Cheung, Ym. (2017). A Fast Objective Reduction Algorithm Based on Dominance Structure for Many Objective Optimization. In: Shi, Y., et al. Simulated Evolution and Learning. SEAL 2017. Lecture Notes in Computer Science(), vol 10593. Springer, Cham. https://doi.org/10.1007/978-3-319-68759-9_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-68759-9_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68758-2

  • Online ISBN: 978-3-319-68759-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation