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Role differentiation and malleable mating for differential evolution: an analysis on large-scale optimisation

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Abstract

Differential Evolution is a simple yet powerful algorithm for continuous optimisation problems. Traditionally, its operators combine the information of randomly chosen vectors of the population. However, four different roles are clearly identified from their formulations: receiving, placing, leading, and correcting vectors. In this work, we propose two mechanisms that emphasise the proper selection of vectors for each role in crossover and mutation operations: (1) the role differentiation mechanism defines the attributes for which vectors are selected for each role; (2) malleable mating allows placing vectors to adapt their mating trends to ensure some similarity relations with the leading and correcting vectors. In addition, we propose a new differential evolution approach that combines these two mechanisms. We have performed experiments on a testbed composed of 19 benchmark functions and five dimensions, ranging from 50 variables to 1,000. Results show that both mechanisms allow differential evolution to statistically improve its results, and that our proposal becomes competitive with regard to representative methods for continuous optimisation.

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References

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

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

  • Bäck T (1994) Selective pressure in evolutionary algorithms: a characterization of selection mechanisms. In: Michalewicz Z (ed) IEEE congress on evolutionary computation. IEEE Press, pp 57–62

  • Bäck T, Fogel DB, Michalewicz Z (1997) Handbook of evolutionary computation. Institute of Physics Publishers

  • Brest J, Greiner S, Boškovic B, Mernik M, Žumer 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, Zamuda A, Boškovic B, Maučec MS, Žumer V (2009) Dynamic optimization using self-adaptive differential evolution. In: Proceedings of the congress on evolutionary computation, pp 415–422

  • Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighbourhood-based mutation operator. IEEE Trans Evol Comput 13(3):526–553

    Article  Google Scholar 

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

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

    Article  Google Scholar 

  • Eiben G, Schut MC (2008) New ways to calibrate evolutionary algorithms. In: Siarry P, Michalewicz Z (eds) Advances in metaheuristics for hard optimization. Springer, Berlin, pp 153–177

  • Eshelman LJ (1991) The CHC adaptive search algorithm: how to have safe search when engaging in nontraditional genetic recombination, foundations of genetic algorithms, vol 1. Morgan Kaufmann, pp 265–283

  • Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Whitley LD (ed) Foundations of genetic algorithms, vol 2. Morgan Kaufmann, pp 187–202

  • Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Global Optim 27(1):105–129

    Article  MathSciNet  MATH  Google Scholar 

  • Fernandes C, Rosa A (2001) A study on non-random mating and varying population size in genetic algorithms using a royal road function. In: Proceedings of the congress on evolutionary computation. IEEE Press, pp 60–66

  • Fernandes C, Rosa AC (2008) Self-adjusting the intensity of assortative mating in genetic algorithms. Soft Comput 12(10):955–979

    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  Google Scholar 

  • Garcia 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 

  • García-Martínez C, Lozano M, Herrera F, Molina D, Sánchez 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 

  • Hansen N (2005) Compilation of results on the CEC benchmark function set. Technical report, Institute of Computational Science, ETH Zurich, Switzerland

  • Herrera F, Lozano M, Molina D (2010a) Components and parameters of DE, real-coded CHC, and G-CMAES. http://www.sci2s.ugr.es/eamhco/descriptions.pdf

  • Herrera F, Lozano M, Molina D (2010b) Test suite for the special issue of Soft Computing on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems. http://www.sci2s.ugr.es/eamhco/updated-functions1-19.pdf

  • Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:65–70

    MathSciNet  MATH  Google Scholar 

  • Iman RL, Davenport JM (1980) Approximations of the critical region of the Friedman statistic. Commun Stat Theor Meth A9(6):571–595

    Google Scholar 

  • Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  MathSciNet  Google Scholar 

  • Langdon WB, Poli R (2007) Evolving problems to learn about particle swarm optimizers and other search algorithms. IEEE Trans Evol Comput 11(5):561–578

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Lozano M, Herrera F (2009) Special issue of soft computing: a fusion of foundations, methodologies and applications on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems. http://www.sci2s.ugr.es/eamhco/CFP.php

  • Mezura-Montes E, Velázquez-Reyes J, Coello CA (2006) Modified differential evolution for constrained optimization. In: Proceedings of the congress on evolutionary computation, pp 332–339

  • Neri F, Tirronen V (2009) Scale factor local search in differential evolution. Memetic Comput 1:153–171

    Article  Google Scholar 

  • Omran M, Salman A, Engelbrecht AP (2005) Self-adaptive differential evolution, computational intelligence and security. Lecture notes in artificial intelligence, vol 3801. Springer, Berlin, pp 192–199

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

  • 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 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Whitley D, Rana S, Dzubera J, Mathias E (1996) Evaluating evolutionary algorithms. Artif Intell 85:245–276

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999

    Article  MathSciNet  Google Scholar 

  • Zaharie D, Petcu D (2004) Adaptive pareto differential evolution and its parallelization. In: Parallel processing and applied mathematics. Lecture notes in computer science, vol 3019, pp 261–268

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

    Article  Google Scholar 

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Acknowledgments

This work was supported by the Research Projects TIN2008-05854 and P08-TIC-4173.

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Authors and Affiliations

  1. Department of Computing and Numerical Analysis, University of Córdoba, 14071, Córdoba, Spain

    Carlos García-Martínez

  2. Department of Computer Science and Artificial Intelligence (CITIC-UGR), University of Granada, 18071, Granada, Spain

    Francisco J. Rodríguez & Manuel Lozano

Authors
  1. Carlos García-Martínez
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  2. Francisco J. Rodríguez
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  3. Manuel Lozano
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Corresponding author

Correspondence to Carlos García-Martínez.

Appendix

Appendix

Tables 15, 16, 17, 18, and 19 show the average results of the algorithms on each function and dimension over 25 runs. Best results are boldfaced. Table 20 presents the minimal, maximal, and median errors of DE-D40 + Mm on each function and dimension over the 25 runs.

Table 15 Results of the algorithms with dimension 50
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Table 16 Results of the algorithms with dimension 100
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Table 17 Results of the algorithms with dimension 200
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Table 18 Results of the algorithms with dimension 500
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Table 19 Results of the algorithms with dimension 1,000
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Table 20 Minimal, maximal, and median error of DE-D40 + Mm
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García-Martínez, C., Rodríguez, F.J. & Lozano, M. Role differentiation and malleable mating for differential evolution: an analysis on large-scale optimisation. Soft Comput 15, 2109–2126 (2011). https://doi.org/10.1007/s00500-010-0641-8

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