Skip to main content

Advertisement

SpringerLink
Log in

Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Recently, evolutionary multiobjective optimization (EMO) algorithms have been utilized for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems (MoGFS), where EMO algorithms are used to search for non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. In this paper, we examine the ability of EMO algorithms to efficiently search for Pareto optimal or near Pareto optimal fuzzy rule-based systems for classification problems. We use NSGA-II (elitist non-dominated sorting genetic algorithm), its variants, and MOEA/D (multiobjective evolutionary algorithm based on decomposition) in our multiobjective fuzzy genetics-based machine learning (MoFGBML) algorithm. Classification performance of obtained fuzzy rule-based systems by each EMO algorithm is evaluated for training data and test data under various settings of the available computation load and the granularity of fuzzy partitions. Experimental results in this paper suggest that reported classification performance of MoGFS in the literature can be further improved using more computation load, more efficient EMO algorithms, and/or more antecedent fuzzy sets from finer fuzzy partitions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

References

  • Abbass HA (2003) Speeding up backpropagation using multiobjective evolutionary algorithms. Neural Comput 15(11):2705–2726

    Article  MATH  Google Scholar 

  • Alcala R, Ducange P, Herrera F, Lazzerini B, Marcelloni F (2009) A multiobjective evolutionary approach to concurrently learn rule and data bases of linguistic fuzzy-rule-based systems. IEEE Trans Fuzzy Syst 17(5):1106–1122

    Article  Google Scholar 

  • Alcala-Fdez J, Sanchez L, Garcia S, del Jesus MJ, Ventura S, Garrell JM, Otero J, Romero C, Bacardit J, Rivas VM, Fernandez JC, Herrera F (2009) KEEL: a software tool to assess evolutionary algorithms to data mining problems. Soft Comput 13(3):307–318

    Article  Google Scholar 

  • Alonso JM, Magdalena L (2009) A conceptual framework for understanding a fuzzy system. In: Proceedings of IFSA-EUSFLAT 2009, pp 119–124

  • Baraldi P, Pedroni N, Zio E (2009) Application of a niched Pareto genetic algorithm for selecting features for nuclear transients classification. Int J Intell Syst 24(2):118–151

    Article  MATH  Google Scholar 

  • Coello CAC, Dehuri S, Ghosh S (eds) (2009) Swarm intelligence for multi-objective problems in data mining. Springer, Berlin

  • Coello CAC, van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer, Boston

    MATH  Google Scholar 

  • Cococcioni M (2009) The evolutionary multiobjective optimization of fuzzy rule-based systems bibliography page. http://www2.ing.unipi.it/∼r000439/emofrbss.html

  • Cordon O, del Jesus MJ, Herrera F (1999) A proposal on reasoning methods in fuzzy rule-based classification systems. Int J Approx Reason 20(1):21–45

    Google Scholar 

  • Cordon O, Gomide F, Herrera F, Hoffmann F, Magdalena L (2004) Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets Syst 141(1):5–31

    Article  MathSciNet  MATH  Google Scholar 

  • Cordon O, Herrera F, Hoffmann F, Magdalena L (2001) Genetic fuzzy systems. World Scientific, Singapore

    MATH  Google Scholar 

  • Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester

    MATH  Google Scholar 

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

    Article  Google Scholar 

  • Ducange P, Lazzerini B, Marcelloni F (2010) Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets. Soft Comput 14(7):713–728

    Article  Google Scholar 

  • Fonseca CM, Fleming PJ (1996) On the performance assessment and comparison of stochastic multiobjective optimizers. Lect Notes Comput Sci 1141:584–593

    Article  Google Scholar 

  • Gacto MJ, Alcala R, Herrera F (2009) Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems. Soft Comput 13(5):419–436

    Article  Google Scholar 

  • Ghosh A, Dehuri KS, Ghosh S (eds) (2008) Multi-objective evolutionary algorithms for knowledge discovery from databases. Springer, Berlin

  • Gonzalez J, Rojas I, Ortega J, Pomares H, Fernandez J, Diaz AF (2003) Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation. IEEE Trans Neural Netw 14(6):1478–1495

    Article  Google Scholar 

  • Herrera F (2005) Genetic fuzzy systems: status, critical considerations and future directions. Int J Comput Intell Res 1(1):59–67

    Google Scholar 

  • Herrera F (2008) Genetic fuzzy systems: taxonomy, current research trends and prospects. Evolut Intell 1(1):27–46

    Article  MathSciNet  Google Scholar 

  • Ishibuchi H (2007) Multiobjective genetic fuzzy systems: review and future research directions. In: Proceedings of 2007 IEEE international conference on fuzzy systems, pp 913–918

  • Ishibuchi H, Doi T, Nojima Y (2006) Incorporation of scalarizing fitness functions into evolutionary multiobjective optimization algorithms. Lect Notes Comput Sci 4193:493–502

    Article  Google Scholar 

  • Ishibuchi H, Murata T, Turksen IB (1995a) Selecting linguistic classification rules by two-objective genetic algorithms. In: Proceedings of 1995 IEEE international conference on systems, man and cybernetics, pp 1410–1415

  • Ishibuchi H, Nozaki K, Yamamoto N, Tanaka H (1995b) Selecting fuzzy if–then rules for classification problems using genetic algorithms. IEEE Trans Fuzzy Syst 3(3):260–270

    Article  Google Scholar 

  • Ishibuchi H, Murata T, Turksen IB (1997) Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems. Fuzzy Sets Syst 89(2):135–150

    Article  Google Scholar 

  • Ishibuchi H, Nakashima T, Murata T (1999) Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. IEEE Trans Syst Man Cybern Part B Cybern 29(5):601–618

    Article  Google Scholar 

  • Ishibuchi H, Narukawa K, Tsukamoto N, Nojima Y (2008) An empirical study on similarity-based mating for evolutionary multiobjective combinatorial optimization. Eur J Oper Res 188(1):57–75

    Article  MATH  Google Scholar 

  • Ishibuchi H, Nojima Y (2007a) Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning. Int J Approx Reason 44(1):4–31

    Article  MathSciNet  MATH  Google Scholar 

  • Ishibuchi H, Nojima Y (2007b) Optimization of scalarizing functions through evolutionary multiobjective optimization. Lect Notes Comput Sci 4403:51–65

    Article  Google Scholar 

  • Ishibuchi H, Nozaki K, Tanaka H (1992) Distributed representation of fuzzy rules and its application to pattern classification. Fuzzy Sets Syst 52(1):21–32

    Article  Google Scholar 

  • Ishibuchi H, Yamamoto T (2003) Evolutionary multiobjective optimization for generating an ensemble of fuzzy rule-based classifiers. Lect Notes Comput Sci 2723:1077–1088

    Article  Google Scholar 

  • Ishibuchi H, Yamamoto T (2004) Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining. Fuzzy Sets Syst 141(1):59–88

    Article  MathSciNet  MATH  Google Scholar 

  • Ishibuchi H, Yamamoto T (2005) Rule weight specification in fuzzy rule-based classification systems. IEEE Trans Fuzzy Syst 13(4):428–435

    Article  Google Scholar 

  • Ishibuchi H, Yamamoto T, Nakashima T (2001) Fuzzy data mining: effect of fuzzy discretization. In: Proceedings of 2001 IEEE international conference on data mining, pp 241–248

  • Jaszkiewicz A (2002) On the performance of multiple-objective genetic local search on the 0/1 knapsack problem—a comparative experiment. IEEE Trans Evolut Comput 6(4):402–412

    Article  Google Scholar 

  • Jaszkiewicz A (2004) On the computational efficiency of multiple objective metaheuristics: the knapsack problem case study. Eur J Oper Res 158(2):418–433

    Article  MathSciNet  MATH  Google Scholar 

  • Jin Y (2000) Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement. IEEE Trans Fuzzy Syst 8(2):212–221

    Article  Google Scholar 

  • Jin J (ed) (2006) Multi-objective machine learning. Springer, Berlin

  • Jin Y, Sendhoff B (2008) Pareto-based multiobjective machine learning: an overview and case studies. IEEE Trans Syst Man Cybern Part C 38(3):397–415

    Article  Google Scholar 

  • Murata T, Ishibuchi H, Gen M (2001) Specification of genetic search directions in cellular multi-objective genetic algorithm. Lect Notes Comput Sci 1993:82–95

    Article  MathSciNet  Google Scholar 

  • Oliveira LS, Morita M, Sabourin R, Bortolozzi F (2005) Multi-objective genetic algorithms to create ensemble of classifiers. Lect Notes Comput Sci 3410:592–606

    Article  Google Scholar 

  • Pulkkinen P, Koivisto H (2008) Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms. Int J Approx Reason 48(2):526–543

    Article  Google Scholar 

  • Pulkkinen P, Koivisto H (2010) A dynamically constrained multiobjective genetic fuzzy system for regression problems. IEEE Trans Fuzzy Syst 18(1):161–177

    Article  Google Scholar 

  • Rodriguez-Vazquez K, Fleming PJ (1998) Multi-objective genetic programming for nonlinear system identification. Electron Lett 34(9):930–931

    Article  Google Scholar 

  • Rodriguez-Vazquez K, Fonseca CM, Fleming PJ (2004) Identifying the structure of nonlinear dynamic systems using multiobjective genetic programming. IEEE Trans Syst Man Cybern Part A 34(4):531–545

    Article  Google Scholar 

  • Roubos H, Setnes M (2001) Compact and transparent fuzzy models and classifiers through iterative complexity reduction. IEEE Trans Fuzzy Syst 9(4):516–524

    Article  Google Scholar 

  • Sato H, Aguirre HE, Tanaka K (2007) Controlling dominance area of solutions and its impact on the performance of MOEAs. Lect Notes Comput Sci 4403:5–20

    Article  Google Scholar 

  • Setnes M, Roubos H (2000) GA-fuzzy modeling and classification: complexity and performance. IEEE Trans Fuzzy Syst 8(5):509–522

    Article  Google Scholar 

  • Setzkorn C, Paton RC (2005) On the use of multi-objective evolutionary algorithms for the induction of fuzzy classification rule systems. Biosystems 81(2):101–112

    Article  Google Scholar 

  • Tan KC, Khor EF, Lee TH (2005) Multiobjective evolutionary algorithms and applications. Springer, Berlin

    MATH  Google Scholar 

  • Valente de Oliveira J (1999) Semantic constraints for membership function optimization. IEEE Trans Syst Man Cybern Part A 29(1):128–138

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm. TIK-Report 103. Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich

  • Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evolut Comput 3(4):257–271

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Intelligent Systems, Osaka Prefecture University, Sakai, Osaka, 599-8531, Japan

    Hisao Ishibuchi, Yusuke Nakashima & Yusuke Nojima

Authors
  1. Hisao Ishibuchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yusuke Nakashima
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yusuke Nojima
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hisao Ishibuchi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ishibuchi, H., Nakashima, Y. & Nojima, Y. Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning. Soft Comput 15, 2415–2434 (2011). https://doi.org/10.1007/s00500-010-0669-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-010-0669-9

Keywords

Search

Navigation