Skip to main content
Erschienen in: Soft Computing 12/2018

18.04.2017 | Methodologies and Application

A novel constraint-handling technique based on dynamic weights for constrained optimization problems

verfasst von: Chaoda Peng, Hai-Lin Liu, Fangqing Gu

Erschienen in: Soft Computing | Ausgabe 12/2018

Einloggen

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

search-config
loading …

Abstract

Bi-objective constraint-handling technique may be one of the most promising constraint techniques for constrained optimization problems. It regards the constraints as an extra objective and using Pareto ranking as selection operator. These algorithms achieve a good convergence by utilizing potential infeasible individuals, but not be good at maintaining the diversity of the population. It is significant to balance the diversity of the population and the convergence of the algorithm. This paper proposes a novel constraint-handling technique based on biased dynamic weights for constrained evolutionary algorithm. The biased weights are used to select different individuals with low objective values and low degree of constraint violations. Furthermore, along with the evolution, more emphasis is placed on the individuals with lower objective values and lower degree of constraint violations by adjusting the biased weights dynamically, which forces the search to a promising feasible region. Thus, the proposed algorithm can keep a good balance between the convergence and the diversity of the population. Moreover, we compared the proposed algorithm with other state-of-the-art algorithms on 42 benchmark problems. The experimental results showed the reliability and stabilization of the proposed algorithm.

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 Asafuddoula M, Ray T, Sarker R (2014) An adaptive hybrid differential evolution algorithm for single objective optimization. Appl Math Comput 231:601–618MathSciNet Asafuddoula M, Ray T, Sarker R (2014) An adaptive hybrid differential evolution algorithm for single objective optimization. Appl Math Comput 231:601–618MathSciNet
Zurück zum Zitat Brest J, Boškovič B, Žumer V (2010) An improved self-adaptive differential evolution algorithm in single objective constrained real-parameter optimization. In: Evolutionary computation, pp 1–8 Brest J, Boškovič B, Žumer V (2010) An improved self-adaptive differential evolution algorithm in single objective constrained real-parameter optimization. In: Evolutionary computation, pp 1–8
Zurück zum Zitat Cai X, Hu Z, Fan Z (2013) A novel memetic algorithm based on invasive weed optimization and differential evolution for constrained optimization. Soft Comput 17(10):1893–1910CrossRef Cai X, Hu Z, Fan Z (2013) A novel memetic algorithm based on invasive weed optimization and differential evolution for constrained optimization. Soft Comput 17(10):1893–1910CrossRef
Zurück zum Zitat Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11):1245–1287MathSciNetCrossRefMATH Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11):1245–1287MathSciNetCrossRefMATH
Zurück zum Zitat Datta R, Deb K (2012) An adaptive normalization based constrained handling methodology with hybrid bi-objective and penalty function approach. In: 2012 IEEE congress on evolutionary computation. IEEE, pp 1–8 Datta R, Deb K (2012) An adaptive normalization based constrained handling methodology with hybrid bi-objective and penalty function approach. In: 2012 IEEE congress on evolutionary computation. IEEE, pp 1–8
Zurück zum Zitat Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338CrossRefMATH Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338CrossRefMATH
Zurück zum Zitat Deb K, Datta R (2013) A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach. Eng Optim 45(5):503–527MathSciNetCrossRef Deb K, Datta R (2013) A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach. Eng Optim 45(5):503–527MathSciNetCrossRef
Zurück zum Zitat Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30 Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30
Zurück zum Zitat Dong N, Wang Y (2014) An unbiased bi-objective optimization model and algorithm for constrained optimization. Int J Pattern Recognit Artif Intell 28(08):1459008CrossRef Dong N, Wang Y (2014) An unbiased bi-objective optimization model and algorithm for constrained optimization. Int J Pattern Recognit Artif Intell 28(08):1459008CrossRef
Zurück zum Zitat Elsayed SM, Sarker RA, Essam DL (2013) An improved self-adaptive differential evolution algorithm for optimization problems. IEEE Trans Ind Inform 9(1):89–99CrossRef Elsayed SM, Sarker RA, Essam DL (2013) An improved self-adaptive differential evolution algorithm for optimization problems. IEEE Trans Ind Inform 9(1):89–99CrossRef
Zurück zum Zitat Gu F, Hl Liu, Tan KC (2012) A multiobjective evolutionary algorithm using dynamic weight design method. Int J Innov Comput Inf Control 8(5B):3677–3688 Gu F, Hl Liu, Tan KC (2012) A multiobjective evolutionary algorithm using dynamic weight design method. Int J Innov Comput Inf Control 8(5B):3677–3688
Zurück zum Zitat Hinterding R, Michalewicz Z (1998) Your brains and my beauty: parent matching for constrained optimisation. In: Evolutionary computation proceedings, the 1998 IEEE international conference on computational intelligence. IEEE, pp 810–815 Hinterding R, Michalewicz Z (1998) Your brains and my beauty: parent matching for constrained optimisation. In: Evolutionary computation proceedings, the 1998 IEEE international conference on computational intelligence. IEEE, pp 810–815
Zurück zum Zitat Ho PY, Shimizu K (2007) Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme. Inf Sci 177(14):2985–3004CrossRef Ho PY, Shimizu K (2007) Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme. Inf Sci 177(14):2985–3004CrossRef
Zurück zum Zitat Jia G, Wang Y, Cai Z, Jin Y (2013) An improved (\(\mu \)+ \(\lambda \))-constrained differential evolution for constrained optimization. Inf Sci 222:302–322MathSciNetCrossRefMATH Jia G, Wang Y, Cai Z, Jin Y (2013) An improved (\(\mu \)+ \(\lambda \))-constrained differential evolution for constrained optimization. Inf Sci 222:302–322MathSciNetCrossRefMATH
Zurück zum Zitat Jiao L, Li L, Shang R, Liu F, Stolkin R (2013) A novel selection evolutionary strategy for constrained optimization. Inf Sci 239:122–141MathSciNetCrossRef Jiao L, Li L, Shang R, Liu F, Stolkin R (2013) A novel selection evolutionary strategy for constrained optimization. Inf Sci 239:122–141MathSciNetCrossRef
Zurück zum Zitat Joines J, Houck CR et al (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with gas. In: Proceedings of the first IEEE conference on evolutionary computation, 1994. IEEE world congress on computational intelligence. IEEE, pp 579–584 Joines J, Houck CR et al (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with gas. In: Proceedings of the first IEEE conference on evolutionary computation, 1994. IEEE world congress on computational intelligence. IEEE, pp 579–584
Zurück zum Zitat Kukkonen S, Lampinen J (2006) Constrained real-parameter optimization with generalized differential evolution. In: IEEE congress on evolutionary computation, pp 207–214 Kukkonen S, Lampinen J (2006) Constrained real-parameter optimization with generalized differential evolution. In: IEEE congress on evolutionary computation, pp 207–214
Zurück zum Zitat Li X, Zhang G (2014) Biased multiobjective optimization for constrained single-objective evolutionary optimization. In: 2014 11th World congress on intelligent control and automation (WCICA). IEEE, pp 891–896 Li X, Zhang G (2014) Biased multiobjective optimization for constrained single-objective evolutionary optimization. In: 2014 11th World congress on intelligent control and automation (WCICA). IEEE, pp 891–896
Zurück zum Zitat Li Z, Liang JJ, He X, Shang Z (2010) Differential evolution with dynamic constraint-handling mechanism. In: Evolutionary computation, pp 1–8 Li Z, Liang JJ, He X, Shang Z (2010) Differential evolution with dynamic constraint-handling mechanism. In: Evolutionary computation, pp 1–8
Zurück zum Zitat Liang J, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan P, Coello CC, Deb K (2006) Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization. J Appl Mech 41:8 Liang J, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan P, Coello CC, Deb K (2006) Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization. J Appl Mech 41:8
Zurück zum Zitat Lin CY, Wu WH (2004) Self-organizing adaptive penalty strategy in constrained genetic search. Struct Multidiscip Optim 26(6):417–428CrossRef Lin CY, Wu WH (2004) Self-organizing adaptive penalty strategy in constrained genetic search. Struct Multidiscip Optim 26(6):417–428CrossRef
Zurück zum Zitat Liu HL, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450–455CrossRef Liu HL, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450–455CrossRef
Zurück zum Zitat Liu J, Teo K, Wang X, Wu C (2015) An exact penalty function-based differential search algorithm for constrained global optimization. Soft Comput 20(4):1305–1313CrossRef Liu J, Teo K, Wang X, Wu C (2015) An exact penalty function-based differential search algorithm for constrained global optimization. Soft Comput 20(4):1305–1313CrossRef
Zurück zum Zitat Mallipeddi R, Suganthan PN (2010) Problem definitions and evaluation criteria for the CEC 2010 competition on constrained real-parameter optimization. Nanyang Technological University Mallipeddi R, Suganthan PN (2010) Problem definitions and evaluation criteria for the CEC 2010 competition on constrained real-parameter optimization. Nanyang Technological University
Zurück zum Zitat Mezura-Montes E, Coello CAC (2005) A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans Evol Comput 9(1):1–17CrossRefMATH Mezura-Montes E, Coello CAC (2005) A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans Evol Comput 9(1):1–17CrossRefMATH
Zurück zum Zitat Mezura-Montes E, Coello CAC (2006) A survey of constraint-handling techniques based on evolutionary multiobjective optimization. In: Workshop paper at PPSN Mezura-Montes E, Coello CAC (2006) A survey of constraint-handling techniques based on evolutionary multiobjective optimization. In: Workshop paper at PPSN
Zurück zum Zitat Michalewicz Z, Attia N (1994) Evolutionary optimization of constrained problems. In: Proceedings of the 3rd annual conference on evolutionary programming, Citeseer, pp 98–108 Michalewicz Z, Attia N (1994) Evolutionary optimization of constrained problems. In: Proceedings of the 3rd annual conference on evolutionary programming, Citeseer, pp 98–108
Zurück zum Zitat Mohamed AW, Sabry HZ (2012) Constrained optimization based on modified differential evolution algorithm. Inf Sci 194:171–208CrossRef Mohamed AW, Sabry HZ (2012) Constrained optimization based on modified differential evolution algorithm. Inf Sci 194:171–208CrossRef
Zurück zum Zitat Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294CrossRef Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294CrossRef
Zurück zum Zitat Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. J Glob Optim 11(4):341–359CrossRefMATH Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. J Glob Optim 11(4):341–359CrossRefMATH
Zurück zum Zitat Takahama T, Sakai S (2010) Constrained optimization by the \(\varepsilon \) constrained differential evolution with an archive and gradient-based mutation. In: Evolutionary computation, pp 389–400 Takahama T, Sakai S (2010) Constrained optimization by the \(\varepsilon \) constrained differential evolution with an archive and gradient-based mutation. In: Evolutionary computation, pp 389–400
Zurück zum Zitat Tasgetiren MF, Suganthan P (2006) A multi-populated differential evolution algorithm for solving constrained optimization problem. In: IEEE congress on evolutionary computation (CEC 2006). IEEE, pp 33–40 Tasgetiren MF, Suganthan P (2006) A multi-populated differential evolution algorithm for solving constrained optimization problem. In: IEEE congress on evolutionary computation (CEC 2006). IEEE, pp 33–40
Zurück zum Zitat Tessema B, Yen GG (2009) An adaptive penalty formulation for constrained evolutionary optimization. Syst Man Cybern A Syst Hum IEEE Trans Evol Comput 39(3):565–578CrossRef Tessema B, Yen GG (2009) An adaptive penalty formulation for constrained evolutionary optimization. Syst Man Cybern A Syst Hum IEEE Trans Evol Comput 39(3):565–578CrossRef
Zurück zum Zitat Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput Evol Comput 9(4):424–435CrossRef Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput Evol Comput 9(4):424–435CrossRef
Zurück zum Zitat Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRef Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRef
Zurück zum Zitat Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074CrossRef Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074CrossRef
Metadaten
Titel
A novel constraint-handling technique based on dynamic weights for constrained optimization problems
verfasst von
Chaoda Peng
Hai-Lin Liu
Fangqing Gu
Publikationsdatum
18.04.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 12/2018
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2603-x

Weitere Artikel der Ausgabe 12/2018

Soft Computing 12/2018 Zur Ausgabe