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An effective improved differential evolution algorithm to solve constrained optimization problems

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Abstract

An effective extended differential evolution algorithm is proposed to deal with constrained optimization problems. The proposed algorithm adopts a new mechanism to cope with constrained problems by transforming the equality into inequality first. Then, two kinds of offspring generation approaches are applied to balance the diversity and the convergence speed of the population during evolution, and seven criteria are designed to compare feasible solution over infeasible solution. The performance of the novel algorithm is evaluated on a set of well-known constrained problems from CEC2006. The experimental results are quite competitive when comparing the proposed algorithm against state-of-the-art optimization algorithms.

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References

  • Ali MM, Kajee-Bagdadi Z (2009) A local exploration-based differential evolution algorithm for constrained global optimization. Appl Math Comput 208(1):31–48

    MathSciNet  MATH  Google Scholar 

  • Arora M, Kohliand S (2017) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Des Eng. https://doi.org/10.1016/j.jcde.2017.02.005

    Article  Google Scholar 

  • Asafuddoula M, Ray T, Sarker R (2015) An improved self-adaptive constraint sequencing approach for constrained optimization problems. Appl Math Comput 253:23–39

    MathSciNet  MATH  Google Scholar 

  • Babu BV, Jehan MML (2003) Differential evolution for multi-objective optimization. In: Proceedings of IEEE congress on evolutionary computing, pp 2696–2703

  • Barbosa HJC, Lemonge ACC (2003) A new adaptive penalty scheme for genetic algorithms. Inf Sci 156(3–4):215–251

    Article  MathSciNet  Google Scholar 

  • Brajevic I (2015) Crossover-based artificial bee colony algorithm for constrained optimization problems. Neural Comput Appl 26(7):1587–1601

    Article  Google Scholar 

  • Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evolut Comput 10(2):646–657

    Article  Google Scholar 

  • Cai Z, Wang Y (2006) A multiobjective optimization-based evolutionary algorithm for constrained optimization. IEEE Trans Evolut Comput 10(6):658–675

    Article  Google Scholar 

  • Chuang Y-C, Chen C-T, Hwang C (2016) A simple and efficient real-coded genetic algorithm for constrained optimization. Appl Soft Comput 38:87–105

    Article  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 

  • Deb K (1995) Optimization for engineering design: algorithms and examples. Prentice-Hall, New Delhi

    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 

  • Elsayed SM, Sarker RA, Essam DL (2012) On an evolutionary approach for constrained optimization problem solving. Appl Soft Comput 12(10):3208–3227

    Article  Google Scholar 

  • Elsayed SM, Sarker RA, Essam DL (2014) A self-adaptive combined strategies algorithm for constrained optimization using differential evolution. Appl Math Comput 241:267–282

    MathSciNet  MATH  Google Scholar 

  • Fan QQ, Yan XF (2016) Self-adaptive differential evolution algorithm with zoning evolution of control parameters and adaptive mutation strategies. IEEE Trans Cybernet 46(1):219–232

    Article  Google Scholar 

  • Fan Q, Yan X, Xue Y (2016) Prior knowledge guided differential evolution. Soft Comput 21(22):6841–6858

    Article  Google Scholar 

  • Gamperle R, Muller SD, Koumoutsakos P (2002) A parameter study for differential evolution. In: Proceedings of advances intelligent system, fuzzy system, evolutionary computing, Crete, Greece, pp 293–298

  • Gao WF, Yen GG, Liu SY (2015) A dual-population differential evolution with coevolution for constrained optimization. IEEE Trans Cybernet 45(5):1108–1121

    Google Scholar 

  • Garcia-Martinez C, Lozano M, Herrera F, Molina D, Sanchez AM (2008) Global and local real-coded genetic algorithms based on parent-centric crossover operators. Eur J Oper Res 185(3):1088–1113

    Article  MATH  Google Scholar 

  • Garg H (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Appl Math Comput 274:292–305

    MathSciNet  MATH  Google Scholar 

  • Ghasemishabankareh B, Li X, Ozlen M (2016) Cooperative coevolutionary differential evolution with improved augmented Lagrangian to solve constrained optimisation problems. Inf Sci 369:441–456

    Article  MathSciNet  Google Scholar 

  • Gong WY, Cai ZH, Liang DW (2014a) Engineering optimization by means of an improved constrained differential evolution. Comput Methods Appl Mech Eng 268:884–904

    Article  MathSciNet  MATH  Google Scholar 

  • Gong ZW, Chen CQ, Ge XM (2014b) Risk prediction of low temperature in Nanjing city based on grey weighted Markov model. Natural Hazards 71:1159–1180

    Article  Google Scholar 

  • Gong W, Cai Z, Liang D (2015) Adaptive ranking mutation operator based differential evolution for constrained optimization. IEEE Trans Cybernet 45(4):716–727

    Article  Google Scholar 

  • Hansen N, Ostermeier A (2001) Completely derandomized self adaptation in evolution strategies. Evolut Comput 9(2):159–195

    Article  Google Scholar 

  • Homaifar A, Qi C, Lai S (1994) Constrained optimization via genetic algorithms. Simulation 62(41):242–254

    Article  Google Scholar 

  • Huang VL, Qin AK, Suganthan PN (2006) Self-adaptive differential evolution algorithm for constrained real-parameter optimization. In: Proceedings of the congress on evolutionary computation (CEC’2006), Vancouver, BC, pp 17–24

  • Iorio A, Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. In: Australian conference on artificial intelligence, Cairns, Australia, pp 861–872

  • Jia G, Wang Y, Cai Z, Jin Y (2013) An improved (\(\mu +\lambda )\)-constrained differential evolution for constrained optimization. Inf Sci 222:302–322

    Article  MathSciNet  MATH  Google Scholar 

  • Joines JA, Houck CR (1994) On the use of nonstationary penalty functions to solve nonlinear constrained optimization problems with GA’s. In: Proceedings of 1st IEEE conference on evolutionary computation, Orlando, FL, pp 579–584

  • Karaboga D, Akay B (2011) A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl Soft Comput 11(3):3021–3031

    Article  Google Scholar 

  • Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the 995 EEE international conference on neural networks, Perth, Australia, pp 1942–1948

  • Li X, Yin M (2014) Self-adaptive constrained artificial bee colony for constrained numerical optimization. Neural Comput Appl 24(3):723–734

    Article  MathSciNet  Google Scholar 

  • Liang JJ, Suganthan PN (2006) Dynamic multi-swarm particle swarm optimizer with a novel constraint-handling mechanism. In: Proceedings of the congress on evolutionary computation (CEC’2006), Vancouver, BC, Canada, pp 9–16

  • Liang JJ, Qin AK, Suganthan PN, Baskar S (2006a) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evolut Comput 10(3):281–294

    Article  Google Scholar 

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

  • Liang Y, Wan Z, Fang D (2015) An improved artificial bee colony algorithm for solving constrained optimization problems. Int J Mach Learn Cybernet. https://doi.org/10.1007/s13042-015-0357-2

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lin HB, Fan Z, Cai XY, Li W, Wang S, Li J, Zhang CD (2014) Hybridizing infeasibility driven and constrained domination principle with moea/d for constrained multiobjective evolutionary optimization. In: TAAI, LNAI 8916, pp 249–261

  • Long Q (2014) A constraint handling technique for constrained multi-objective genetic algorithm. Swarm Evolut Comput 15:66–79

    Article  Google Scholar 

  • Long W, Liang X, Cai S (2016) A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2357-x

    Article  Google Scholar 

  • Mahdavi A, Shiri ME (2015) An augmented Lagrangian ant colony based method for constrained optimization. Comput Optim Appl 60(1):263–276

    Article  MathSciNet  MATH  Google Scholar 

  • Mallipeddi R, Suganthan PN (2010) Ensemble of constraint handling techniques. IEEE Trans Evolut Comput 14(4):561–579

    Article  Google Scholar 

  • Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696

    Article  Google Scholar 

  • Mezura-Montes E, Coello CAC (2004) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473

    Article  MathSciNet  MATH  Google Scholar 

  • Mezura-Montes E, Coello CAC (2005) A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans Evolut Comput 9(1):1–17

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Mezura-Montes E, Velazquez-Reyes J, Coello CA Coello (2006) Modified differential evolution for constrained optimization. In: Proceedings of the congress on evolutionary computation (CEC’2006), Vancouver, BC, pp 25–32

  • Michalewicz Z (1995) A survey of constraint handling techniques in evolutionary computation methods, In: Proceedings of 4th annual conference on evolutionary programming, pp 135–155

  • Mohamed AW (2017) Solving large-scale global optimization problems using enhanced adaptive differential evolution algorithm. Complex Intell Syst. https://doi.org/10.1007/s40747-017-0041-0

    Article  Google Scholar 

  • Pahner U, Hameyer K (2000) Adaptive coupling of differential evolution and multiquadrics approximation for the tuning of the optimization process. IEEE Trans Magn 36(4):1047–1051

    Article  Google Scholar 

  • Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer, Berlin, Heidelberg

  • Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evolut Comput 13(2):398–417

    Article  Google Scholar 

  • Qu BY, Suganthan PN (2011) Constrained multi-objective optimization algorithm with an ensemble of constraint handling methods. Eng Optim 43(4):403–416

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Richardson JT, Palmer MR, Liepins G, Hilliard M (1989) Some guidelines for genetic algorithms with penalty functions. In: Scha er JD (ed) Proceedings of the third international conference on genetic algorithms, Morgan Kau man, San Mateo, pp. 191–197

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

    Article  Google Scholar 

  • SaatyThe TL (1980) The analytic hierarchy process. McGraw-Hill, New York

    Google Scholar 

  • Sharma H, Bansal JC, Arya KV (2012) Fitness based differential evolution. Memet Comput 4(4):303–316

    Article  Google Scholar 

  • Singh HK, Isaacs A, Ray T, Smith W (2008) Infeasibility driven evolutionary algorithm (IDEA) for engineering design optimization. In: Wobcke W, Zhang M (eds) AI 2008, LNAI 5360, pp 104–115

  • Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  • Sun C, Zeng J, Pan J (2011) An improved vector particle swarm optimization for constrained optimization problems. Inf Sci 181(6):1153–1163

    Article  Google Scholar 

  • Sun JY, Garibaldi JM, Zhang YQ, Al-Shawabkeh A (2016) A multi-cycled sequential memetic computing approach for constrained optimisation. Inf Sci 340–341:175–190

    Article  Google Scholar 

  • Takahama T, Sakai S (2006) Constrained optimization by the constrained differential evolution with gradient-based mutation and feasible elites. In: Proceedings of IEEE congress on evolutionary computation, Vancouver, BC, Canada, pp 1–8

  • Takahama T, Sakai S, Iwane N (2005) Constrained optimization by the epsilon constrained hybrid algorithm of particle swarm optimization and genetic algorithm. In: AI 2005: Advances artificial intelligence, lecture notes in artificial intelligence, vol 3809. Springer, pp 389–400

  • Tasgetiren M, Suganthan P, Pan Q, Mallipeddi R, Sarman S (2010) An ensemble of differential evolution algorithm for constrained function optimization. In: 2010 Congress on evolutionary computation, IEEE Service Center, Barcelona, Spain, pp 967–975

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

    Article  Google Scholar 

  • Tessema B, Yen GG (2006) A self-adaptive penalty function based algorithm for constrained optimization. In: Proceedings of IEEE congress on evolutionary computation, Vancouver, BC, Canada, pp 246–253

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

    Article  Google Scholar 

  • Wang Y, Cai ZX (2011) Constrained evolutionary optimization by means of (\(\mu +\lambda )\)-differential evolution and improved adaptive trade-off model. Evolut Comput 19(2):249–285

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wang Y, Cai Z (2012b) A dynamic hybrid framework for constrained evolutionary optimization. IEEE Trans Syst Man Cybernet Part B Cybernet 42(1):203–217

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wang Y, Cai Z, Guo G, Zhou Y (2007) Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems. IEEE Trans Syst Man Cybernet 37:560–575

    Article  Google Scholar 

  • Wang Y, Wang BC, Li HX, Yen Gary G (2016) Incorporating objective function information into the feasibility rule for constrained evolutionary optimization. IEEE Trans Cybernet 46:2938–2952

    Article  Google Scholar 

  • Wei L, Chen Z, Li J (2011) Evolution strategies based adaptive Lp LS-SVM. Inf Sci 181(14):3000–3016

    Article  MATH  Google Scholar 

  • Wu X, Wang Y, Yang L, Song S, Wei G, Guo J (2016) Impact of political dispute on international trade based on an international trade inoperability input-output model. J Int Trade Econ Dev 25(1): 1–24

    Article  Google Scholar 

  • Xiaobing Y, Guo S, Guo J, Huang X (2011) Rank B2C e-commerce websites in e-alliance based on AHP and fuzzy TOPSIS. Expert Syst Appl 38(4):3550–3557

    Article  Google Scholar 

  • Yi P, Hong YG, Liu F (2015) Distributed gradient algorithm for constrained optimization with application to load sharing in power systems. Syst Control Lett 83:45–52

    Article  MathSciNet  MATH  Google Scholar 

  • Yi WC, Li XY, Gao L, Zhou YZ, Huang JD (2016) \(\varepsilon \) constrained differential evolution with pre-estimated comparison using gradient-based approximation for constrained optimization problems. Expert Syst Appl 44:37–49

  • Yong W, Zixing C, Yuren Z, Wei Z (2008) An adaptive tradeoff model for constrained evolutionary optimization. IEEE Trans Evolut Comput 12(1):80–92

    Article  Google Scholar 

  • Yu ZS (2008) Solving bound constrained optimization via a new nonmonotone spectral projected gradient method. Appl Numer Math 58(9):1340–1348

    Article  MathSciNet  MATH  Google Scholar 

  • Yu XB, Wang XM, Cao J, Cai M (2015a) An ensemble differential evolution for numerical opimization. Int J Inf Technol Decis Mak 14(4):915–942

    Article  Google Scholar 

  • Yu XB, Cai M, Cao J (2015b) A novel mutation differential evolution for global optimization. J Intell Fuzzy Syst 28(3):1047–1060

    Google Scholar 

  • Yu KJ, Wang X, Wang ZL (2016) Constrained optimization based on improved teaching-learning-based optimization algorithm, Inf Sci 352–353:61–78

    Article  Google Scholar 

  • Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evolut Comput 13(5):945–958

    Article  Google Scholar 

  • Zhang X, Zhang X (2016) Improving differential evolution by differential vector archive and hybrid repair method for global optimization. Soft Comput 21(23):7107–7116

    Article  Google Scholar 

  • Zhang CJ, Lin Q, Gao L, Li XY (2015) Backtracking Search Algorithm with three constraint handling methods for constrained optimization problems. Expert Syst Appl 42(21):7831–7845

    Article  Google Scholar 

  • Zheng JG, Wang X, Liu RH (2012) \(\varepsilon \)-Differential evolution algorithm for constrained optimization problems. J Softw 23(9):2374–2387

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu DT (2007) An affine scaling reduced preconditional conjugate gradient path method for linear constrained optimization. Appl Math Comput 184(2):181–198

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the associate editor and the anonymous reviewers for their very helpful suggestions. This study was funded by China Natural Science Foundation (Grant Numbers 71503134, 91546117, 71373131, 71171116), Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), Key Project of National Social and Scientific Fund Program (16ZDA047), Research Center for Prospering Jiangsu Province with Talents (Grant Number skrc201400-14), Natural Science Foundation of Higher Education of Jiangsu Province of China (16KJB120003), Philosophy and Social Sciences in Universities of Jiangsu (Grant Number 2016SJB630016), and Research Institute for History of Science and Technology (2017KJSKT005).

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Authors and Affiliations

  1. Research Institute for History of Science and Technology, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xiaobing Yu

  2. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xiaobing Yu

  3. China Institute for Manufacture Developing, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xiaobing Yu

  4. School of Economics and Management, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xiaobing Yu, Yiqun Lu, Xiang Luo & Mei Cai

  5. School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xuming Wang

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Communicated by V. Loia.

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Yu, X., Lu, Y., Wang, X. et al. An effective improved differential evolution algorithm to solve constrained optimization problems. Soft Comput 23, 2409–2427 (2019). https://doi.org/10.1007/s00500-017-2936-5

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