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Prior knowledge guided differential evolution

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Abstract

Differential evolution (DE) has become one of the most popular paradigms of evolutionary algorithms. Over the past two decades, some prior knowledge has been obtained in the DE research community. It is an interesting topic to enhance the performance of DE by taking advantage of such prior knowledge. Along this line, a prior knowledge guided DE (called PKDE) is proposed in this paper. In PKDE, we extract two levels of prior knowledge, i.e., the macro- and micro-levels. In order to integrate these two levels of prior knowledge in an effective way, the control parameters of PKDE are tuned based on two distributions (i.e., Cauchy and normal distribution), with the aim of alleviating the premature convergence at the early stage and speeding up the convergence toward the global optimal solution at the later stage. In addition, the self-adaptive mutation strategy is implemented based on our previous study. PKDE is compared with eight DE variants and seven non-DE algorithms on two sets of benchmark test functions from IEEE CEC2005 and IEEE CEC2014. Systematic experiments demonstrate that the overall performance of PKDE is very competitive.

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References

  • Abbass HA (2002) The self-adaptive pareto differential evolution algorithm. In: Proceedings of the 2002 congress on evolutionary computation, pp 831–836

  • Akay B, Karaboga D (2012) A modified artificial bee colony algorithm for real-parameter optimization. Inf Sci 192:120–142

    Article  Google Scholar 

  • Ali M, Siarry P, Pant M (2012) An efficient differential evolution based algorithm for solving multi-objective optimization problems. Eur J Oper Res 217(2):404–416

    MathSciNet  MATH  Google Scholar 

  • Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In: IEEE congress on evolutionary computation, pp 1769–1776

  • 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 Evol Comput 10(6):646–657

    Article  Google Scholar 

  • Brest J, Maučec MS (2008) Population size reduction for the differential evolution algorithm. Appl Intell 29(3):228–247

    Article  Google Scholar 

  • Cai Y, Wang J (2013) Differential evolution with neighborhood and direction information for numerical optimization. IEEE Trans Cybern 43(6):2202–2215

    Article  Google Scholar 

  • Chen L, Zheng Z, Liu H-L, Xie S (2014) An evolutionary algorithm based on covariance matrix leaning and searching preference for solving CEC 2014 benchmark problems. In: IEEE congress on evolutionary computation, pp 2672–2677

  • Das S, Konar A, Chakraborty UK (2005) Two improved differential evolution schemes for faster global search. In: Proceedings of the 2005 conference on genetic and evolutionary computation, 2005. ACM, pp 991–998

  • Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31

    Article  Google Scholar 

  • Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3(2):124–141

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

    Article  MathSciNet  MATH  Google Scholar 

  • Elsayed SM, Sarker RA, Essam DL, Hamza NM (2014) Testing united multi-operator evolutionary algorithms on the CEC2014 real-parameter numerical optimization. In: IEEE congress on evolutionary computation, pp 1650–1657

  • Erlich I, Rueda JL, Wildenhues S, Shewarega F (2014) Evaluating the mean–variance mapping optimization on the IEEE-CEC 2014 test suite. In: IEEE congress on evolutionary computation, pp 1625–1632

  • Fan Q, Yan X (2015) Differential evolution algorithm with self-adaptive strategy and control parameters for P-xylene oxidation process optimization. Soft Comput 19(5):1363–1391

    Article  Google Scholar 

  • Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32(200):675–701

    Article  MATH  Google Scholar 

  • Gämperle R, Müller SD, Koumoutsakos P (2002) A parameter study for differential evolution. Adv Intell Syst Fuzzy Syst Evolut Comput 10:293–298

    Google Scholar 

  • García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15(6):617–644

    Article  MATH  Google Scholar 

  • Ghosh A, Das S, Chowdhury A, Giri R (2011) An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Inf Sci 181(18):3749–3765

    Article  MathSciNet  Google Scholar 

  • Gong W, Cai Z (2013) Differential evolution with ranking-based mutation operators. IEEE Trans Cybern 43(6):2066–2081

    Article  Google Scholar 

  • Islam SM, Das S, Ghosh S, Roy S, Suganthan PN (2012) An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization. IEEE Trans Syst Man Cybern B 42(2):482–500

    Article  Google Scholar 

  • Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Am Stat Assoc 47(260):583–621

    Article  MATH  Google Scholar 

  • Liang J, Qu B, Suganthan P (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. In: Computational intelligence laboratory, zhengzhou

  • Liao T, Stützle T, Montes de Oca MA, Dorigo M (2014) A unified ant colony optimization algorithm for continuous optimization. Eur J Oper Res 234(3):597–609

    Article  MathSciNet  MATH  Google Scholar 

  • Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(6):448–462

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Mallipeddi R, Wu G, Lee M, Suganthan P (2014) Gaussian adaptation based parameter adaptation for differential evolution. In: IEEE congress on evolutionary computation, pp 1760–1767

  • Molina D, Lacroix B, Herrera F (2014) Influence of regions on the memetic algorithm for the CEC’2014 special session on real-parameter single objective optimisation. In: IEEE congress on evolutionary computation, pp 1633–1640

  • Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33(1–2):61–106

    Article  Google Scholar 

  • Omran MG, Engelbrecht AP, Salman A (2009) Bare bones differential evolution. Eur J Oper Res 196(1):128–139

    Article  MathSciNet  MATH  Google Scholar 

  • Pan Q-K, Suganthan PN, Wang L, Gao L, Mallipeddi R (2011) A differential evolution algorithm with self-adapting strategy and control parameters. Comput Oper Res 38(1):394–408

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Ronkkonen J, Kukkonen S, Price KV (2005) Real-parameter optimization with differential evolution. In: IEEE congress on evolutionary computation, pp 506–513

  • Salman A, Engelbrecht AP, Omran MG (2007) Empirical analysis of self-adaptive differential evolution. Eur J Oper Res 183(2):785–804

    Article  MATH  Google Scholar 

  • Sarker R, Elsayed S, Ray T (2014) Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans Evol Comput 18(5):689–707

    Article  Google Scholar 

  • Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. ICSI, Berkeley

    MATH  Google Scholar 

  • 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 

  • Storn R, Price K, Lampinen J (2005) Differential evolution—a practical approach to global optimization. Springer, Berlin

    MATH  Google Scholar 

  • Suganthan PN et al (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. In: KanGAL, Report 2005005

  • Tanabe R, Fukunaga AS (2014) Improving the search performance of SHADE using linear population size reduction. In: IEEE congress on evolutionary computation, pp 1658–1665

  • Teng NS, Teo J, Hijazi MHA (2009) Self-adaptive population sizing for a tune-free differential evolution. Soft Comput 13(7):709–724

    Article  Google Scholar 

  • Teo J (2005) Differential evolution with self-adaptive populations. In: Khosla R, Howlett RJ, Jain LC (eds) Knowledge-based intelligent information and engineering systems. Lecture notes in computer science, vol 3681. Springer, Berlin, pp 1284–1290

  • Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Comput 10(8):673–686

    Article  Google Scholar 

  • Tirronen V, Neri F (2009) Differential evolution with fitness diversity self-adaptation. In: Chiong R (ed) Nature-inspired algorithms for optimisation. Studies in computational intelligence, vol 193. Springer, Berlin, pp 199–234

  • Wang H, Rahnamayan S, Sun H, Omran MG (2013) Gaussian bare-bones differential evolution. IEEE Trans Cybern 43(2):634–647

    Article  Google Scholar 

  • Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66

    Article  Google Scholar 

  • Wang Y, Li H, Huang T, Li L (2014) Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Appl Soft Comput 18:232–247

    Article  Google Scholar 

  • Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1(6):80–83

    Article  MathSciNet  Google Scholar 

  • Zaharie D (2002) Parameter adaptation in differential evolution by controlling the population diversity. In: Proceedings of the international workshop on symbolic and numeric algorithms for scientific computing 2002, pp 385–397

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

    Article  Google Scholar 

  • Zhu W, Tang Y, Fang J-A, Zhang W (2013) Adaptive population tuning scheme for differential evolution. Inf Sci 223:164–191

    Article  Google Scholar 

  • Zielinski K, Weitkemper P, Laur R, Kammeyer K (2006) Parameter study for differential evolution using a power allocation problem including interference cancellation. In: IEEE congress on evolutionary computation, pp 1857–1864

Download references

Acknowledgments

This paper was supported in part by National Natural Science Foundation of China under Grant 21176073 and Grant 61273314. Furthermore, the authors would like to thank Dr. Zhang, Dr. Brest, and Dr. Suganthan for providing the source codes of JADE, jDE, and SaDE, respectively, and Dr. Yong Wang, who is an associate professor of Central South University.

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Authors and Affiliations

  1. Logistics Research Center, Shanghai Maritime University, Shanghai, 201306, People’s Republic of China

    Qinqin Fan

  2. Key Laboratory of Advanced Control and Optimization for Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Xuefeng Yan

  3. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Yu Xue

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  1. Qinqin Fan
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  2. Xuefeng Yan
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  3. Yu Xue
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Correspondence to Qinqin Fan.

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Communicated by V. Loia.

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Fan, Q., Yan, X. & Xue, Y. Prior knowledge guided differential evolution. Soft Comput 21, 6841–6858 (2017). https://doi.org/10.1007/s00500-016-2235-6

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