Skip to main content
Erschienen in: Soft Computing 3/2010

01.02.2010 | Original Paper

Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure

Erschienen in: Soft Computing | Ausgabe 3/2010

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A self-adaptive differential evolution algorithm incorporate Pareto dominance to solve multi-objective optimization problems is presented. The proposed approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. The experiments were performed using eighteen benchmark test functions. The experiment results show that, compared with three other multi-objective optimization evolutionary algorithms, the proposed MOSADE is able to find better spread of solutions with better convergence to the Pareto front and preserve the diversity of Pareto optimal solutions more efficiently.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Abbass HA (2002) The self-adaptive Pareto differential evolution algorithm. In: Proceedings of the IEEE congress on evolutionary computation. Honolulu, Hawaii, pp 831–836 Abbass HA (2002) The self-adaptive Pareto differential evolution algorithm. In: Proceedings of the IEEE congress on evolutionary computation. Honolulu, Hawaii, pp 831–836
Zurück zum Zitat Abbass HA, Sarker R, Newton C (2001) PDE: a pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the IEEE congress on evolutionary computation (CEC2001), Piscataway, pp 971–978 Abbass HA, Sarker R, Newton C (2001) PDE: a pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the IEEE congress on evolutionary computation (CEC2001), Piscataway, pp 971–978
Zurück zum Zitat Alfredo G, Luis V, Coello CC et al. (2006) A new proposal for multi-objective optimization using differential evolution and rough sets theory. In: Proceedings of the 8th annual conference on genetic and evolutionary computation, Seattle, Washington, pp 675–682 Alfredo G, Luis V, Coello CC et al. (2006) A new proposal for multi-objective optimization using differential evolution and rough sets theory. In: Proceedings of the 8th annual conference on genetic and evolutionary computation, Seattle, Washington, pp 675–682
Zurück zum Zitat Babu BV, Mathew M, Jehan L (2003) Differential evolution for multi-objective optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2003), Canberra, pp 2696–2703 Babu BV, Mathew M, Jehan L (2003) Differential evolution for multi-objective optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2003), Canberra, pp 2696–2703
Zurück zum Zitat Bleuler S, Laumanns M, Thiele L et al. (2003) PISA—a platform and programming language independent interface for search algorithms. In: Conference on evolutionary multi-criterion optimization (EMO2003), pp 494–508 Bleuler S, Laumanns M, Thiele L et al. (2003) PISA—a platform and programming language independent interface for search algorithms. In: Conference on evolutionary multi-criterion optimization (EMO2003), pp 494–508
Zurück zum Zitat Brest J, Greiner S, Boškovic B et al (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657. doi:10.1109/TEVC.2006.872133 CrossRef Brest J, Greiner S, Boškovic B et al (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657. doi:10.​1109/​TEVC.​2006.​872133 CrossRef
Zurück zum Zitat Deb K, Thiele L, Laumanns M et al. (2001) Scalable test problems for evolutionary multi-objective optimization. Technical report, Comput Eng and Networks Lab (TIK), ETH Zurich, Switzerland Deb K, Thiele L, Laumanns M et al. (2001) Scalable test problems for evolutionary multi-objective optimization. Technical report, Comput Eng and Networks Lab (TIK), ETH Zurich, Switzerland
Zurück zum Zitat Durillo JJ, Nebro AJ, Luna F et al. (2006) jMetal: a java framework for developing multi-objective optimization metaheurstics. Departamento de Lenguajes y Ciencias de la Computación, Technical report, University of Málaga, E.T.S·I. Informática, Campus de Teations Durillo JJ, Nebro AJ, Luna F et al. (2006) jMetal: a java framework for developing multi-objective optimization metaheurstics. Departamento de Lenguajes y Ciencias de la Computación, Technical report, University of Málaga, E.T.S·I. Informática, Campus de Teations
Zurück zum Zitat Fonseca CM, Fleming PJ (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms. IEEE Trans Syst Man Cybern 28(1):38–47. doi:10.1109/3468.650320 CrossRef Fonseca CM, Fleming PJ (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms. IEEE Trans Syst Man Cybern 28(1):38–47. doi:10.​1109/​3468.​650320 CrossRef
Zurück zum Zitat García S, Molina D, Lozano M et al. (2008) A study on the use of Non-parametric tests for analyzing the evolutionary algorithm’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics (in press) García S, Molina D, Lozano M et al. (2008) A study on the use of Non-parametric tests for analyzing the evolutionary algorithm’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics (in press)
Zurück zum Zitat Iorio AW, Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. In: Proceedings of advances in artificial intelligence (AI2004), pp 861–872 Iorio AW, Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. In: Proceedings of advances in artificial intelligence (AI2004), pp 861–872
Zurück zum Zitat Kukkonen S, Lampinen J (2004) An extension of generalized differential evolution for multi-objective optimization with constraints. In: Parallel problem solving from nature (PPSN2004), pp752–761 Kukkonen S, Lampinen J (2004) An extension of generalized differential evolution for multi-objective optimization with constraints. In: Parallel problem solving from nature (PPSN2004), pp752–761
Zurück zum Zitat Kukkonen S, Lampinen J (2005) GDE3: the third evolution step of generalized differential evolution. In: Proceedings of the IEEE congress on evolutionary computation (CEC2005), Edinburgh, pp 443–450 Kukkonen S, Lampinen J (2005) GDE3: the third evolution step of generalized differential evolution. In: Proceedings of the IEEE congress on evolutionary computation (CEC2005), Edinburgh, pp 443–450
Zurück zum Zitat Madavan NK (2002) Multiobjective optimization using a Pareto differential evolution approach. In: Proceedings of the congress on evolutionary computation. Honolulu, Hawaii, pp 1145–1150 Madavan NK (2002) Multiobjective optimization using a Pareto differential evolution approach. In: Proceedings of the congress on evolutionary computation. Honolulu, Hawaii, pp 1145–1150
Zurück zum Zitat Nobakhti A, Wang H (2006) A Self-adaptive differential evolution with application on the ALSTOM gasifier. In: Proceedings of the 2006 American control conference, Minnesota, pp 4489–4494 Nobakhti A, Wang H (2006) A Self-adaptive differential evolution with application on the ALSTOM gasifier. In: Proceedings of the 2006 American control conference, Minnesota, pp 4489–4494
Zurück zum Zitat Parsopoulos KE, Tasoulis DK, Pavlidis NG et al. (2004) Vector evaluated differential evolution for multiobjective optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2004), Portland, pp 204–211 Parsopoulos KE, Tasoulis DK, Pavlidis NG et al. (2004) Vector evaluated differential evolution for multiobjective optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2004), Portland, pp 204–211
Zurück zum Zitat Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC2005), Edinburgh, Scotland 2:1785–1791 Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: Proceedings of the IEEE congress on evolutionary computation (CEC2005), Edinburgh, Scotland 2:1785–1791
Zurück zum Zitat Price K (1997) Differential evolution vs. the functions of the 2nd ICEO. In: IEEE conference on evolutionary computation, Indianapolis, pp 153–157 Price K (1997) Differential evolution vs. the functions of the 2nd ICEO. In: IEEE conference on evolutionary computation, Indianapolis, pp 153–157
Zurück zum Zitat Robič T, Filipič B (2005) DEMO: differential evolution for multiobjective optimization. In: Third international conference on evolutionary multi-criterion optimization (EMO2005), Guanajuato, Mexico, pp 520–533 Robič T, Filipič B (2005) DEMO: differential evolution for multiobjective optimization. In: Third international conference on evolutionary multi-criterion optimization (EMO2005), Guanajuato, Mexico, pp 520–533
Zurück zum Zitat Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the first international conference on genetic algorithms. Lawrence, Erlbaum, pp 93–100 Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the first international conference on genetic algorithms. Lawrence, Erlbaum, pp 93–100
Zurück zum Zitat Van Veldhuizen DA, Lamont GB (1998) Multiobjective evolutionary algorithm research: a history and analysis. Technical report, Department of Electrical and Computer Engineering. Graduate School of Engineering, Air Force Inst Technol, Wright Patterson Van Veldhuizen DA, Lamont GB (1998) Multiobjective evolutionary algorithm research: a history and analysis. Technical report, Department of Electrical and Computer Engineering. Graduate School of Engineering, Air Force Inst Technol, Wright Patterson
Zurück zum Zitat Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Proceedings of the IEEE congress on evolutionary computation (CEC2004), Portland, Oregon 2:1980–1987 Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Proceedings of the IEEE congress on evolutionary computation (CEC2004), Portland, Oregon 2:1980–1987
Zurück zum Zitat Xue F, Sanderson AC, Graves RJ (2003) Multi-objective differential evolution and its application to enterprise planning. In: Proceedings of the IEEE international conference on Robo & Auto, Taipei, pp 3535–3541 Xue F, Sanderson AC, Graves RJ (2003) Multi-objective differential evolution and its application to enterprise planning. In: Proceedings of the IEEE international conference on Robo & Auto, Taipei, pp 3535–3541
Zurück zum Zitat Zhang J, Sanderson AC (2008) Self-adaptive multi-objective differential evolution with direction information provided by archived inferior solutions. In: Proceedings of the IEEE congress on evolutionary computation (CEC2008), Hongkong, pp 2801–2810 Zhang J, Sanderson AC (2008) Self-adaptive multi-objective differential evolution with direction information provided by archived inferior solutions. In: Proceedings of the IEEE congress on evolutionary computation (CEC2008), Hongkong, pp 2801–2810
Zurück zum Zitat Zhou A, Jin Y, Zhang Q et al. (2006) Combing model-based and generics-based offspring generation for multi-objective optimization using a convergence criterion. In: 2006 congress on evolutionary computation, pp 3234–3241 Zhou A, Jin Y, Zhang Q et al. (2006) Combing model-based and generics-based offspring generation for multi-objective optimization using a convergence criterion. In: 2006 congress on evolutionary computation, pp 3234–3241
Zurück zum Zitat Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271. doi:10.1109/4235.797969 CrossRef Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271. doi:10.​1109/​4235.​797969 CrossRef
Zurück zum Zitat Zitzler E, Laumanns M, Thiele L (2001) SPEA2: Improving the strength pareto evolutionary algorithm. Technical report, Comput Eng and Networks Lab (TIK), ETH Zurich, Switzerland Zitzler E, Laumanns M, Thiele L (2001) SPEA2: Improving the strength pareto evolutionary algorithm. Technical report, Comput Eng and Networks Lab (TIK), ETH Zurich, Switzerland
Metadaten
Titel
Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure
Publikationsdatum
01.02.2010
Erschienen in
Soft Computing / Ausgabe 3/2010
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-008-0394-9

Weitere Artikel der Ausgabe 3/2010

Soft Computing 3/2010 Zur Ausgabe