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A Critical Review of Adaptive Penalty Techniques in Evolutionary Computation

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Evolutionary Constrained Optimization

Part of the book series: Infosys Science Foundation Series ((ISFSASE))

Abstract

Constrained optimization problems are common in the sciences, engineering, and economics. Due to the growing complexity of the problems tackled, nature-inspired metaheuristics in general, and evolutionary algorithms in particular, are becoming increasingly popular. As move operators (recombination and mutation) are usually blind to the constraints, most metaheuristics must be equipped with a constraint handling technique. Although conceptually simple, penalty techniques usually require user-defined problem-dependent parameters, which often significantly impact the performance of a metaheuristic. A penalty technique is said to be adaptive when it automatically sets the values of all parameters involved using feedback from the search process without user intervention. This chapter presents a survey of the most relevant adaptive penalty techniques from the literature, identifies the main concepts used in the adaptation process, as well as observed shortcomings, and suggests further work in order to increase the understanding of such techniques.

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References

  • Barbosa HJC, Lemonge ACC (2002) An adaptive penalty scheme in genetic algorithms for constrained optimization problems. In: Langdon WB, Cantú-Paz E, Mathias KE, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter MA, Schultz AC, Miller JF, Burke EK (eds) Proceedings of the genetic and evolutionary computation conference (GECCO). Morgan Kaufmann, San Francisco

    Google Scholar 

  • Barbosa HJC, Lemonge ACC (2003a) An adaptive penalty scheme for steady-state genetic algorithms. In: Cantú-Paz E, Foster JA, Deb K, Davis LD, Roy R, O’Reilly U-M, Beyer H-G, Standish R, Kendall G, Wilson S, Harman M, Wegener J, Dasgupta D, Potter MA, Schultz AC, Dowsland KA, Jonoska N, Miller J (eds) Genetic and evolutionary computation (GECCO). Lecture Notes in Computer Science. Springer, Berlin, pp 718–729

    Google Scholar 

  • Barbosa HJC, Lemonge ACC (2003b) A new adaptive penalty scheme for genetic algorithms. Inf Sci 156:215–251

    Google Scholar 

  • Barbosa HJC, Lemonge ACC (2008) An adaptive penalty method for genetic algorithms in constrained optimization problems. Front Evol Robot 34:9–34

    Google Scholar 

  • Barbosa HJC, Bernardino HS, Barreto AMS (2010a) Using performance profiles to analyze the results of the 2006 CEC constrained optimization competition. In: 2010 IEEE congress on evolutionary computation (CEC), pp 1–8

    Google Scholar 

  • Barbosa HJC, Lemonge ACC, Fonseca LG, Bernardino HS (2010b) Comparing two constraint handling techniques in a binary-coded genetic algorithm for optimization problems. In: Deb K, Bhattacharya A, Chakraborti N, Chakroborty P, Das S, Dutta J, Gupta SK, Jain A, Aggarwal V, Branke J, Louis SJ, Tan KC (eds) Simulated evolution and learning. Lecture Notes in Computer Science. Springer, Berlin, pp 125–134

    Google Scholar 

  • Barbosa HJC, Bernardino HS, Barreto AMS (2013) Using performance profiles for the analysis and design of benchmark experiments. In: Di Gaspero L, Schaerf A, Stutzle T (eds) Advances in metaheuristics. Operations Research/computer Science Interfaces Series, vol 53. Springer, New York, pp 21–36

    Google Scholar 

  • Bean J, Alouane A (1992) A Dual Genetic Algorithm For Bounded Integer Programs. Technical Report Tr 92-53, Department of Industrial and Operations Engineering, The University of Michigan

    Google Scholar 

  • Beaser E, Schwartz JK, Bell CB, Solomon EI (2011) Hybrid genetic algorithm with an adaptive penalty function for fitting multimodal experimental data: application to exchange-coupled non-Kramers binuclear iron active sites. J Chem Inf Model 51(9):2164–2173

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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(11–12):1245–1287

    Article  MATH  Google Scholar 

  • Coit DW, Smith AE, Tate DM (1996) Adaptive penalty methods for genetic optimization of constrained combinatorial problems. INFORMS J Comput 8(2):173–182

    Article  MATH  Google Scholar 

  • Costa L, Santo IE, Oliveira P (2013) An adaptive constraint handling technique for evolutionary algorithms. Optimization 62(2):241–253

    Article  MATH  MathSciNet  Google Scholar 

  • Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Am Math Soc 49:1–23

    Article  MATH  MathSciNet  Google Scholar 

  • Dolan E, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math Program 91(2):201–213

    Article  MATH  MathSciNet  Google Scholar 

  • Eiben AE, Smith JE (2003) Introduction to evolutionary computing. Springer, New York

    Book  MATH  Google Scholar 

  • Eiben AE, Jansen B, Michalewicz Z, Paechter B (2000) Solving CSPs using self-adaptive constraint weights: how to prevent EAs from cheating. In: Whitley, LD (ed) Proceedings of the genetic and evolutionary computation conference (GECCO). Morgan Kaufmann, San Francisco, pp 128–134

    Google Scholar 

  • Farmani R, Wright J (2003) Self-adaptive fitness formulation for constrained optimization. IEEE Trans Evol Comput 7(5):445–455

    Article  Google Scholar 

  • Gan M, Peng H, Peng X, Chen X, Inoussa G (2010) An adaptive decision maker for constrained evolutionary optimization. Appl Math Comput 215(12):4172–4184

    Article  MATH  MathSciNet  Google Scholar 

  • Gen M, Cheng R (1996) Optimal design of system reliability using interval programming and genetic algorithms. Comput Ind Eng, (In: Proceedings of the 19th international conference on computers and industrial engineering), vol 31(1–2), pp 237–240

    Google Scholar 

  • Hamida H, Schoenauer M (2000) Adaptive techniques for evolutionary topological optimum design. In: Parmee I (ed) Proceedings of the international conference on adaptive computing in design and manufacture (ACDM). Springer, Devon, pp 123–136

    Google Scholar 

  • Hamida S, Schoenauer M (2002) ASCHEA: new results using adaptive segregational constraint handling. In: Proceedings of the IEEE service center congress on evolutionary computation (CEC), vol 1. Piscataway, New Jersey, pp 884–889

    Google Scholar 

  • Harrell LJ, Ranjithan SR (1999) Evaluation of alternative penalty function implementations in a watershed management design problem. In: Proceedings of the genetic and evolutionary computation conference (GECCO), vol 2. Morgan Kaufmann, pp 1551–1558

    Google Scholar 

  • He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99

    Article  Google Scholar 

  • He Q, Wang L, zhuo Huang F (2008) Nonlinear constrained optimization by enhanced co-evolutionary PSO. In: IEEE congress on evolutionary computation, CEC 2008. (IEEE World Congress on Computational Intelligence), pp 83–89

    Google Scholar 

  • Hughes T (1987) The finite element method: linear static and dynamic finite element analysis. Prentice Hall Inc, New Jersey

    Google Scholar 

  • Koziel S, Michalewicz Z (1998) A decoder-based evolutionary algorithm for constrained parameter optimization problems. In: Eiben A, Bäck T, Schoenauer M, Schwefel H-P (eds) Parallel problem solving from nature (PPSN). LNCS, vol 1498. Springer, Berlin, pp 231–240

    Google Scholar 

  • Krempser E, Bernardino H, Barbosa H, Lemonge A (2012) Differential evolution assisted by surrogate models for structural optimization problems. In: Proceedings of the international conference on computational structures technology (CST). Civil-Comp Press, p 49

    Google Scholar 

  • Lemonge ACC, Barbosa HJC (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59(5):703–736

    Article  MATH  Google Scholar 

  • Lemonge ACC, Barbosa HJC, Bernardino HS (2012) A family of adaptive penalty schemes for steady-state genetic algorithms. In: 2012 IEEE congress on evolutionary computation (CEC). IEEE, pp 1–8

    Google Scholar 

  • 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. Technical report, Nanyang Technological University, Singapore

    Google Scholar 

  • Lin C-H (2013) A rough penalty genetic algorithm for constrained optimization. Inf Sci 241:119–137

    Article  Google Scholar 

  • Lin C-Y, Wu W-H (2004) Self-organizing adaptive penalty strategy in constrained genetic search. Struct Multidiscip Optim 26(6):417–428

    Article  Google Scholar 

  • Luenberger DG, Ye Y (2008) Linear and nonlinear programming. Springer, New York

    MATH  Google Scholar 

  • Mallipeddi R, Suganthan PN (2010) Problem definitions and evaluation criteria for the CEC 2010 competition on constrained real-parameter optimization. Technical report, Nanyang Technological University, Singapore

    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 (1995) A survey of constraint handling techniques in evolutionary computation methods. In: Proceedings of the 4th annual conference on evolutionary programming. MIT Press, pp 135–155

    Google Scholar 

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

    Article  Google Scholar 

  • Montemurro M, Vincenti A, Vannucci P (2013) The automatic dynamic penalisation method (ADP) for handling constraints with genetic algorithms. Comput Methods Appl Mech Eng 256:70–87

    Article  MathSciNet  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 

  • Puzzi S, Carpinteri A (2008) A double-multiplicative dynamic penalty approach for constrained evolutionary optimization. Struct Multidiscip Optim 35(5):431–445

    Article  MATH  MathSciNet  Google Scholar 

  • Rasheed K (1998) An adaptive penalty approach for constrained genetic-algorithm optimization. In: Koza J, Banzhaf W, Chellapilla K, Deb K, Dorigo M, Fogel D, Garzon M, Goldberg D, Iba H, Riolo R (eds) Proceedings of the third annual genetic programming conference. Morgan Kaufmann, San Francisco, pp 584–590

    Google Scholar 

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

    Google Scholar 

  • Rocha AMAC, Fernandes EMDGP (2009) Self-adaptive penalties in the electromagnetism-like algorithm for constrained global optimization problems. In: Proceedings of the 8th world congress on structural and multidisciplinary optimization, Lisbon, Portugal

    Google Scholar 

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

    Article  Google Scholar 

  • Salcedo-Sanz S (2009) A survey of repair methods used as constraint handling techniques in evolutionary algorithms. Comput Sci Rev 3(3):175–192

    Article  MATH  Google Scholar 

  • Schoenauer M, Michalewicz Z (1996) Evolutionary computation at the edge of feasibility. In: Proceedings of parallel problem solving from nature (PPSN). LNCS, Springer, pp 245–254

    Google Scholar 

  • Tessema B, Yen GG (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 

  • Tessema B, Yen G (2009) An adaptive penalty formulation for constrained evolutionary optimization. IEEE Trans Syst, Man Cybern, Part A: Syst Hum 39(3):565–578

    Article  Google Scholar 

  • Vincenti A, Ahmadian MR, Vannucci P (2010) BIANCA: a genetic algorithm to solve hard combinatorial optimisation problems in engineering. J Glob Optim 48(3):399–421

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Y, Cai Z, Zhou Y, Fan Z (2009) Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique. Struct Multidiscip Optim 37(4):395–413

    Article  Google Scholar 

  • Wu B, Yu X, Liu L (2001) Fuzzy penalty function approach for constrained function optimization with evolutionary algorithms. In: Proceedings of the 8th international conference on neural information processing. Citeseer, pp 299–304

    Google Scholar 

  • Wu W-H, Lin C-Y (2004) The second generation of self-organizing adaptive penalty strategy for constrained genetic search. Adv Eng Softw 35(12):815–825

    Article  MATH  MathSciNet  Google Scholar 

  • Yokota T, Gen M, Ida K, Taguchi T (1995) Optimal design of system reliability by an improved genetic algorithm. Trans Inst Electron Inf Comput Eng J78-A(6):702–709 (in Japanese)

    Google Scholar 

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Acknowledgments

The authors thank the reviewers for their comments, which helped improve the quality of the final version, and acknowledge the support from CNPq (grants 308317/2009-2, 310778/2013-1, 300192/2012-6 and 306815/2011-7) and FAPEMIG (grant TEC 528/11).

Author information

Authors and Affiliations

  1. National Laboratory for Scientific Computing—LNCC, Petropolis, Rio de Janeiro, RJ, Brazil

    Helio J. C. Barbosa

  2. Department of Applied and Computational Mechanics, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil

    Afonso C. C. Lemonge

  3. Department of Computer Science, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil

    Helio J. C. Barbosa & Heder S. Bernardino

Authors
  1. Helio J. C. Barbosa
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  2. Afonso C. C. Lemonge
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  3. Heder S. Bernardino
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Corresponding author

Correspondence to Helio J. C. Barbosa .

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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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Barbosa, H.J.C., Lemonge, A.C.C., Bernardino, H.S. (2015). A Critical Review of Adaptive Penalty Techniques in Evolutionary Computation. 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_1

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  • DOI: https://doi.org/10.1007/978-81-322-2184-5_1

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  • Online ISBN: 978-81-322-2184-5

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