Skip to main content

Advertisement

SpringerLink
Log in

An experimental analysis of a new two-stage crossover operator for multiobjective optimization

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Evolutionary algorithms for multiobjective problems utilize three types of operations for progressing toward the higher fitness regions of the search space. Each type of operator contributes in a different way toward the achievement of the common goal. The mutation operation is responsible for diversity maintenance, while the selection operation favors the survival of the fittest. In this paper we focus our attention on the crossover operator. The crossover operator by default is responsible for the search effort and as such deserves our special attention. In particular, we propose a two-stage crossover (TSX) operator for more efficient exploration of the search space. The performance of the proposed TSX operator is assessed in comparison with the simulated binary crossover operator with the assistance of three well-known multiobjective evolutionary algorithms, namely the NSGAII, the SPEA2 and the MOCELL, for the solution of the DTLZ1–7 set of test functions. We also compare the proposed TSX with other popular reproduction operators like the differential evolution and the particle swarm optimization. Finally, we examine the efficacy of the TSX operator in handling problems having five objectives. It is shown with the assistance of the Deb, Thiele, Laumanns and Zitzler set of test functions that the TSX operator can substantially improve the results generated by three popular performance metrics for most of the cases.

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
Fig. 27

Similar content being viewed by others

References

  • Amjady N, Nasiri-Rad H (2009) Nonconvex economic dispatch with AC constraints by a new real coded genetic algorithm. IEEE Trans Power Syst 24(3):1489–1502

    Article  Google Scholar 

  • Banerjee A (2013) A novel probabilistically-guided context-sensitive crossover operator for clustering. Swarm Evolut Comput 13:47–62

    Article  Google Scholar 

  • Barkat-Ullah ASSM, Sarker R, Cornforth D (2008) Search space reduction technique for constrained optimization with tiny feasible space. In: GECCO’08, Atlanta, pp 881–888

  • Bosman PAN, Thierens D (2000) Expanding from discrete to continuous EDAs: the IEDA. In: Proceedings of parallel problem solving from nature, PPSN-VI, pp 767–776

  • Da Ronco CC, Benini E (2013) A simplex crossover based evolutionary algorithm including the genetic diversity as objective. Appl Soft Comput 13:2104–2123

    Article  Google Scholar 

  • Deb K, Agrawal RB (1995) Simulated binary crossover for continuous search space. Complex Syst 9(2):115–148

    MathSciNet  MATH  Google Scholar 

  • Deb K, Saxena DK (2015) On Finding pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In: KanGAL report number 2005011

  • Deb K, Anand A, Joshi D (2002) A computationally efficient evolutionary algorithm for real-parameter optimization. Evolut Comput 10(4):371–395

    Article  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 

  • Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. In: Abraham A, Jain L, Goldberg R (eds) Evolutionary multiobjective optimization, theoretical advances and applications. Springer, New York, pp 105–145

    Chapter  Google Scholar 

  • Deep K, Thakur M (2007) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188:895–911

    MathSciNet  MATH  Google Scholar 

  • Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  • Durillo JJ, Coello CAC (2013) Analysis of leader selection strategies in a multi-objective particle swarm optimizer. In: 2013 IEEE congress on evolutionary computation (CEC), 20–23 June 2013, pp 3153–3160. doi:10.1109/CEC.2013.6557955

  • Durillo JJ, Nebro AJ (2011) jMetal: a Java framework for multi-objective optimization. Adv Eng Softw 42:760–771

    Article  Google Scholar 

  • Elsayed SM, Sarker RA, Essam DL (2011) Multi-operator based evolutionary algorithms for solving constrained optimization problems. Comput Oper Res 38:1877–1896

    Article  MathSciNet  MATH  Google Scholar 

  • Eshelman LJ, Schaffer JD (1993) Real coded genetic algorithms and interval schemata. In: Darrell Whitley L (ed) Foundation of genetic algorithms 2. Morgan Kaufmann Publishers, San Mateo, pp 187–202

    Google Scholar 

  • Fonseca C, Flemming P (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms—part II: application example. IEEE Trans Syst Man Cybern 28:38–47

    Article  Google Scholar 

  • Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–8

    Article  Google Scholar 

  • Hervás-Martínez C, Ortiz-Boyer D, García-Pedrajas N (2002) Theoretical analysis of the confidence interval based crossover for real-coded genetic algorithms. In: Merelo Guervós JJ et al (eds) PPSN VII, LNCS, vol 2439, pp 153–161. Springer, Berlin

  • Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Piscataway, pp 1942–1948

  • Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: Proceedings of the world multiconference on systemics, cybernetics and informatics, Piscataway, pp 4104–4109

  • Koza JR (1992) Genetic programming. MIT Press, Cambridge

    MATH  Google Scholar 

  • Larraenaga P, Lozano JA (2001) Estimation of distribution algorithms: a new tool for evolutionary computation. Kluwer Academic, New York

    Google Scholar 

  • Li H, Zhang Q (2009) Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13(2)

  • Liagkouras K, Metaxiotis K (2014) A new probe guided mutation operator and its application for solving the cardinality constrained portfolio optimization problem. Expert Syst Appl 41(14):6274–6290

    Article  Google Scholar 

  • Liagkouras K, Metaxiotis K (2015) Efficient portfolio construction with the use of multiobjective evolutionary algorithms: best practices and performance metrics. Int J Inf Technol Decis Mak 14(3):535–564. doi:10.1142/S0219622015300013

  • Metaxiotis K, Liagkouras K (2012) Multiobjective evolutionary algorithms for portfolio management: a comprehensive literature review. Expert Syst Appl 39(14):11685–11698

    Article  Google Scholar 

  • MULTIOBJ-1.3 (2008) Speed-constrained multi-objective PSO (SMPSO), DIRICOM

  • Nebro AJ (2013) Dipt. Lenguajes y Cienc. de la Comput., University of Malaga, Malaga

  • Nebro AJ, Durillo JJ, Nieto JG, Coello Coello CA, Luna F, Alba E (2009) SMPSO: a new PSO-based metaheuristic for multi-objective optimization. In: IEEE symposium on computational intelligence in multicriteria decision-making (MCDM 2009), pp 66–73

  • Niu Q, Zhang H, Wang X, Li K, Irwin GW (2014) A hybrid harmony search with arithmetic crossover operation for economic dispatch. Electr Power Energy Syst 62:237–257

    Article  Google Scholar 

  • Ono I, Kobayashi S (1997) A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover. In: Back T (ed) Proceedings of the seventh international conference on genetic algorithms (ICGA-7). Morgan Kaufmann, San Francisco, pp 246–253

    Google Scholar 

  • Price K, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization, natural computing series. Springer, New York

    MATH  Google Scholar 

  • Qi Y, Hou Z, Yin M, Sun H, Huang J (2015) An immune multi-objective optimization algorithm with differential evolution inspired recombination. Appl Soft Comput 29:395–410

    Article  Google Scholar 

  • Silva D, Bastos-Filho C (2013) A multi-objective particle swarm optimizer based on diversity, INTELLI 2013. In: The second international conference on intelligent systems and applications, IARIA

  • Singh HK, Ray T, Smith W (2010) Performance of infeasibility empowered memetic algorithm for CEC 2010 constrained optimization problems. In: Proceedings of the IEEE congress on evolutionary computation (CEC2010), Barcelona, pp 1–8

  • Tsutsui S, Yamamura MT, Higuchi (1999) Multi-parent recombination with simplex crossover in real coded genetic algorithms. In: Proceedings of the GECCO-99, pp 644–657

  • Yoon Y, Kim YH, Moraglio A, Moon BR (2012) A theoretical and empirical study on unbiased boundary-extended crossover for real-valued representation. Inf Sci 183:48–65

    Article  MathSciNet  MATH  Google Scholar 

  • Zeng F, Decraene J, Hean Low MY, Hingston P, Wentong C, Suiping Z, Chandramohan M (2010) Autonomous bee colony optimization for multi-objective function. In: Proceedings of the IEEE congress on evolutionary computation

  • Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Article  Google Scholar 

  • Zitzler E, Thiele L, Laumanns M, Fonseca CM Da, Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117–132

    Article  Google Scholar 

  • Zitzler E, Brockhoff D, Thiele L (2007) The hypervolume indicator revisited: on the design of pareto-compliant indicators via weighted integration. In: Conference on evolutionary multi-criterion optimization (EMO 2007), pp 862–876. Springer, New York

Download references

Author information

Authors and Affiliations

  1. Decision Support Systems Laboratory, Department of Informatics, University of Piraeus, 80, Karaoli & Dimitriou Str., 18534, Piraeus, Greece

    K. Liagkouras & K. Metaxiotis

Authors
  1. K. Liagkouras
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Metaxiotis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Liagkouras.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liagkouras, K., Metaxiotis, K. An experimental analysis of a new two-stage crossover operator for multiobjective optimization. Soft Comput 21, 721–751 (2017). https://doi.org/10.1007/s00500-015-1810-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-015-1810-6

Keywords

Search

Navigation