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Evolutionary Constrained Optimization: A Hybrid Approach

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Evolutionary Constrained Optimization

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Abstract

The holy grail of constrained optimization is the development of an efficient, scale invariant, and generic constraint-handling procedure in single- and multi-objective constrained optimization problems. Constrained optimization is a computationally difficult task, particularly if the constraint functions are nonlinear and nonconvex. As a generic classical approach, the penalty function approach is a popular methodology that degrades the objective function value by adding a penalty proportional to the constraint violation. However, the penalty function approach has been criticized for its sensitivity to the associated penalty parameters. Since its inception, evolutionary algorithms (EAs) have been modified in various ways to solve constrained optimization problems. Of them, the recent use of a bi-objective evolutionary algorithm in which the minimization of the constraint violation is included as an additional objective, has received significant attention. In this chapter, we propose a combination of a bi-objective evolutionary approach with the penalty function methodology in a manner complementary to each other. The bi-objective approach provides an appropriate estimate of the penalty parameter, while the solution of the unconstrained penalized function by a classical method induces a convergence property to the overall hybrid algorithm. We demonstrate the working of the procedure on a number of standard numerical test problems. In most cases, our proposed hybrid methodology is observed to take one or more orders of magnitude lesser number of function evaluations to find the constrained minimum solution accurately than some of the best-reported existing methodologies.

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References

  • Angantyr A, Andersson J, Aidanpaa J-O (2003) Constrained optimization based on a multiobjective evolutionary algorithm. In: Proceedings of congress on evolutionary computation, pp 1560–1567

    Google Scholar 

  • Araujo MC, Wanner EF, Guimaraes FG, Takahashi RHC (2009) Constrained optimization based on quadratic approximations in genetic algorithms. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation. Springer, Berlin, pp 193–218

    Google Scholar 

  • Bernardino H, Barbosa H, Lemonge A (2007) A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In: IEEE congress on evolutionary computation, CEC 2007. IEEE, pp 646–653

    Google Scholar 

  • Bernardino HS, Barbosa HJC, Lemonge ACC, Fonseca LG (2009) On GA-AIS hybrids for constrained optimization problems in engineering. Springer, New York

    Google Scholar 

  • Branke J (2008) Consideration of partial user preferences in evolutionary multiobjective optimization. Multiobjective optimization. Springer, New York, pp 157–178

    Google Scholar 

  • Branke J, Deb K (2004) Integrating user preferences into evolutionary multi-objective optimization. In: Jin Y (ed) Knowledge incorporation in evolutionary computation. Springer, Heidelberg, pp 461–477

    Google Scholar 

  • Brest J (2009) Constrained real-parameter optimization with \(\varepsilon \) self-adaptive differential evolution. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation. Springer, Berlin, pp 73–94

    Google Scholar 

  • Burke EK, Smith AJ (2000) Hybrid evolutionary techniques for the maintenance scheduling problem. IEEE Trans Power Syst 15(1):122–128

    Article  Google Scholar 

  • Byrd R, Nocedal J, Waltz R (2006) Large-scale nonlinear optimization. K nitro: an integrated package for nonlinear optimization. Springer, New York

    Google Scholar 

  • Cai Z, Wang Y (2005) A multiobjective optimization-based evolutionary algorithm for constrained optimization. IEEE Trans Evol Comput 10(6):658–675

    Article  Google Scholar 

  • Camponogara E, Talukdar S (1997) A genetic algorithm for constrained and multiobjective optimization. In: 3rd Nordic workshop on genetic algorithms and their applications (3NWGA), pp 49–62

    Google Scholar 

  • Chankong V, Haimes YY (1983) Multiobjective decision making theory and methodology. North-Holland, New York

    MATH  Google Scholar 

  • Coello C, Carlos A (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Article  Google Scholar 

  • Coello C, Carlos A (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(11–12):1245–1287

    Article  MATH  Google Scholar 

  • Coello C, Lamont G, Van Veldhuizen D (2007) Evolutionary algorithms for solving multi-objective problems. Springer, New York

    MATH  Google Scholar 

  • Coello CAC (2000) Treating objectives as constraints for single objective optimization. Eng Optim 32(3):275–308

    Article  Google Scholar 

  • Coello CAC (2013) List of references on constraint-handling techniques used with evolutionary algorithms. http://www.cs.cinvestav.mx/~constraint/

  • Coit D, Smith A, Tate D (1996) Adaptive penalty methods for genetic optimization of constrained combinatorial problems. INFORMS J Comput 8:173–182

    Article  MATH  Google Scholar 

  • Dadios E, Ashraf J (2006) Genetic algorithm with adaptive and dynamic penalty functions for the selection of cleaner production measures: a constrained optimization problem. Clean Technol Environ Policy 8(2):85–95

    Article  Google Scholar 

  • Deb K (1991) Optimal design of a welded beam structure via genetic algorithms. AIAA J 29(11):2013–2015

    Article  Google Scholar 

  • Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  Google Scholar 

  • Deb K, Lele S, Datta R (2007) A hybrid evolutionary multi-objective and SQP based procedure for constrained optimization. In: Proceedings of the 2nd international conference on advances in computation and intelligence. Springer, pp 36–45

    Google Scholar 

  • Deep K et al (2008) A self-organizing migrating genetic algorithm for constrained optimization. Appl Math Comput 198(1):237–250

    Article  MATH  MathSciNet  Google Scholar 

  • Echeverri MG, Lezama JML, Romero R (2009) An efficient constraint handling methodology for multi-objective evolutionary algorithms. Revista Facultad de Ingenieria-Universidad de Antioquia 49:141–150

    Google Scholar 

  • El-Mihoub T, Hopgood A, Nolle L, Battersby A, Date S (2006) Hybrid genetic algorithms: a review. Eng Lett 3(2):124–137

    Google Scholar 

  • Elsayed S, Sarker R, Essam D (2011) Multi-operator based evolutionary algorithms for solving constrained optimization problems. Comput Oper Res 38(12):1877–1896

    Article  MATH  MathSciNet  Google Scholar 

  • Fatourechi M, Bashashati A, Ward R, Birch G (2005) A hybrid genetic algorithm approach for improving the performance of the LF-ASD brain computer interface. In: IEEE international conference on acoustics, speech, and signal processing. Proceedings (ICASSP’05), vol 5

    Google Scholar 

  • Gen M, Cheng R (1996) A survey of penalty techniques in genetic algorithms. In: Proceedings of IEEE international conference on evolutionary computation. IEEE Press

    Google Scholar 

  • Hedar A, Fukushima M (2003) Simplex coding genetic algorithm for the global optimization of nonlinear functions. In: Tanino T, Tanaka T, Inuiguchi M (eds) Multi-objective programming and goal programming., Advances in soft computingSpringer, New York, pp 135–140

    Chapter  Google Scholar 

  • Homaifar A, Lai SH-V, Qi X (1994) Constrained optimization via genetic algorithms. Simulation 62(4):242–254

    Article  Google Scholar 

  • Knowles J, Corne D, Deb K (2008) Multiobjective problem solving from nature: from concepts to applications., Natural computing seriesSpringer, New York

    Book  Google Scholar 

  • Kumar A, Sharma D, Deb K (2007) A hybrid multi-objective optimisation procedure using PCX based NSGA-II and sequential quadratic programming. In: Proceedings of the congress on evolutionary computation (CEC-2007). Singapore, pp 3011–3018

    Google Scholar 

  • Kuri-Morales A, Gutiérrez-García J (2002) Penalty function methods for constrained optimization with genetic algorithms: a statistical analysis. MICAI 2002: Adv Artif Intell 34(2):187–200

    Google Scholar 

  • Leguizamón G, Coello C (2009) Boundary search for constrained numerical optimization problems. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation. Springer, Berlin, pp 25–49

    Google Scholar 

  • Liang JJ, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan PN, Coello CAC, Deb K (2006) Problem definitions and evaluation criteria for the CEC 2006: special session on constrained real-parameter optimization. Technical report, Nanyang Technological University, Singapore

    Google Scholar 

  • Lin C, Chuang C (2007) A rough set penalty function for marriage selection in multiple-evaluation genetic algorithms. Rough Sets Knowl Technol, pp 500–507

    Google Scholar 

  • Matthew P et al (2009) Selection and penalty strategies for genetic algorithms designed to solve spatial forest planning problems. Int J For Res 2009:1–15

    Google Scholar 

  • Mezura-Montes E (2009) Constraint-handling in evolutionary optimization. Springer, Berlin

    Book  Google Scholar 

  • Mezura-Montes E, Palomeque-Ortiz A (2009) Self-adaptive and deterministic parameter control in differential evolution for constrained optimization. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation. Springer, Berlin, pp 95–120

    Google Scholar 

  • Mezura-Montes E, Coello CAC (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput 1(4):173–194

    Article  Google Scholar 

  • Michalewicz Z, Janikow CZ (1991) Handling constraints in genetic algorithms. In: Proceedings of the fourth international conference on genetic algorithms, pp 151–157

    Google Scholar 

  • Michalewicz Z, Schoenauer M (1996) Evolutionary algorithms for constrained parameter optimization problems. Evol Comput 4(1):1–32

    Article  Google Scholar 

  • Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, Boston

    MATH  Google Scholar 

  • Moler C (2004) Numerical computing with MATLAB. Society for Industrial Mathematics

    Google Scholar 

  • Myung H, Kim J (1998) Hybrid interior-Lagrangian penalty based evolutionary optimization. In: Evolutionary programming VII, Springer, pp 85–94

    Google Scholar 

  • Nanakorn P, Meesomklin K (2001) An adaptive penalty function in genetic algorithms for structural design optimization. Comput Struct 79(29–30):2527–2539

    Article  Google Scholar 

  • Powell D, Skolnick MM (1993) Using genetic algorithms in engineering design optimization with nonlinear constraints. In: Proceedings of the fifth international conference on genetic algorithms, pp 424–430

    Google Scholar 

  • Ray T, Singh H, Isaacs A, Smith W (2009) Infeasibility driven evolutionary algorithm for constrained optimization. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation. Springer, Berlin, pp 145–165

    Google Scholar 

  • Reklaitis GV, Ravindran A, Ragsdell KM (1983) Engineering optimization methods and applications. Wiley, New York

    Google Scholar 

  • Richardson JT, Palmer MR, Liepins GE, Hilliard MR (1989) Some guidelines for genetic algorithms with penalty functions. In: Proceedings of the 3rd international conference on genetic algorithms, Morgan Kaufmann Publishers Inc, pp 191–197

    Google Scholar 

  • Runarsson T, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294

    Article  Google Scholar 

  • Sha J, Xu M (2011) Applying hybrid genetic algorithm to constrained trajectory optimization. In: 2011 international conference on Electronic and mechanical engineering and information technology (EMEIT). IEEE, vol 7, pp 3792–3795

    Google Scholar 

  • Sharma D, Kumar A, Deb K, Sindhya K (2007) Hybridization of SBX based NSGA-II and sequential quadratic programming for solving multi-objective optimization problems. In: IEEE congress on evolutionary computation, CEC 2007. IEEE, pp 3003–3010

    Google Scholar 

  • Sindhya K, Deb K, Miettinen K (2008) A local search based evolutionary multi-objective optimization approach for fast and accurate convergence. Parallel problem solving from nature-PPSN X. Springer, Heidelberg

    Google Scholar 

  • Surry PD, Radcliffe N J, Boyd ID (1995) A multi-objective approach to constrained optimisation of gas supply networks: the COMOGA method. In: Evolutionary computing. AISB workshop. Springer, pp 166–180

    Google Scholar 

  • Takahama T, Sakai S (2009) Solving difficult constrained optimization problems by the \(\varepsilon \) constrained differential evolution with gradient-based mutation. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation. Springer, Berlin, pp 51–72

    Google Scholar 

  • Tessema B, Yen G (2006) A self adaptive penalty function based algorithm for constrained optimization. In: IEEE congress on evolutionary computation, CEC 2006. IEEE, pp 246–253

    Google Scholar 

  • Venkatraman S, Yen G (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9(4):424–435

    Article  Google Scholar 

  • Victoire T, Jeyakumar A (2005) A modified hybrid EP-SQP approach for dynamic dispatch with valve-point effect. Int J Electr Power Energy Syst 27(8):594–601

    Article  Google Scholar 

  • Wang Y, Ma W (2006) A penalty-based evolutionary algorithm for constrained optimization. Adv Nat Comput 4221:740–748

    Article  Google Scholar 

  • Wang L, Zhang L, Zheng D (2006) An effective hybrid genetic algorithm for flow shop scheduling with limited buffers. Comput Oper Res 33(10):2960–2971

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Y, Cai Z, Zhou Y, Zeng W (2008) An adaptive tradeoff model for constrained evolutionary optimization. IEEE Trans Evol Comput 12(1):80–92

    Article  Google Scholar 

  • Wang Y, Cai Z (2012) Combining multiobjective optimization with differential evolution to solve constrained optimization problems. IEEE Trans Evol Comput 16(1):117–134

    Article  Google Scholar 

  • Yuan Q, Qian F (2010) A hybrid genetic algorithm for twice continuously differentiable NLP problems. Comput Chem Eng 34(1):36–41

    Article  Google Scholar 

  • Zavala A, Aguirre A, Diharce E (2009) Continuous constrained optimization with dynamic tolerance using the COPSO algorithm. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation. Springer, Berlin, pp 1–23

    Google Scholar 

  • Zhao J, Wang L, Zeng P, Fan W (2011) An effective hybrid genetic algorithm with flexible allowance technique for constrained engineering design optimization. Expert Syst Appl 38(12):15103–15109

    Google Scholar 

  • Zhou Y, Li Y, He J, Kang L (2003) Multi-objective and MGG evolutionary algorithm for constrained optimization. In: The 2003 congress on evolutionary computation, CEC’03. IEEE, vol 1, pp 1–5

    Google Scholar 

  • 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

    Article  Google Scholar 

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Acknowledgments

The original concept of the chapter is published in the following journal: A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach, Kalyanmoy Deb & Rituparna Datta, Engineering Optimization, Volume 45, Issue 5, 2013 (Published online: 26 Jun 2012), Taylor & Francis. It is reprinted by permission of the publisher (Taylor & Francis Ltd, http://www.tandfonline.com) with substantial improvement. The authors would like to thank Taylor & Francis Ltd., for their permission to use the content of the journal.

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Authors and Affiliations

  1. Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Republic of Korea

    Rituparna Datta

  2. Department of Electrical and Computer Engineering, Department of Computer Science and Engineering and Department of Mechanical Engineering, Michigan State University, 428 S. Shaw Lane, 2120 EB, East Lansing, MI, 48824, USA

    Kalyanmoy Deb

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  1. Rituparna Datta
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Correspondence to Rituparna Datta .

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Editors and Affiliations

  1. Dept of Electrical Engineering, Korea Advanced Institute of Sci &Tech, Daejeon, Korea, Republic of (South Korea)

    Rituparna Datta

  2. Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan, USA

    Kalyanmoy Deb

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Datta, R., Deb, K. (2015). Evolutionary Constrained Optimization: A Hybrid Approach. In: Datta, R., Deb, K. (eds) Evolutionary Constrained Optimization. Infosys Science Foundation Series(). Springer, New Delhi. https://doi.org/10.1007/978-81-322-2184-5_10

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  • DOI: https://doi.org/10.1007/978-81-322-2184-5_10

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