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Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains

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Abstract

Nowadays, large scale optimisation problems arise as a very interesting field of research, because they appear in many real-world problems (bio-computing, data mining, etc.). Thus, scalability becomes an essential requirement for modern optimisation algorithms. In a previous work, we presented memetic algorithms based on local search chains. Local search chain concerns the idea that, at one stage, the local search operator may continue the operation of a previous invocation, starting from the final configuration reached by this one. Using this technique, it was presented a memetic algorithm, MA-CMA-Chains, using the CMA-ES algorithm as its local search component. This proposal obtained very good results for continuous optimisation problems, in particular with medium-size (with up to dimension 50). Unfortunately, CMA-ES scalability is restricted by several costly operations, thus MA-CMA-Chains could not be successfully applied to large scale problems. In this article we study the scalability of memetic algorithms based on local search chains, creating memetic algorithms with different local search methods and comparing them, considering both the error values and the processing cost. We also propose a variation of Solis Wets method, that we call Subgrouping Solis Wets algorithm. This local search method explores, at each step of the algorithm, only a random subset of the variables. This subset changes after a certain number of evaluations. Finally, we propose a new memetic algorithm based on local search chains for high dimensionality, MA-SSW-Chains, using the Subgrouping Solis Wets’ algorithm as its local search method. This algorithm is compared with MA-CMA-Chains and different reference algorithms, and it is shown that the proposal is fairly scalable and it is statistically very competitive for high-dimensional problems.

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Notes

  1. See the website http://sci2s.ugr.es/EAMHCO/ for a large repository of approaches to this kind of problems.

References

  • Auger A, Hansen N (2005a) Performance evaluation of an advanced local search evolutionary algorithm. In: 2005 IEEE congress on evolutionary computation, pp 1777–1784

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

  • van den Bergh F, Engelbrencht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 3:225–239

    Article  Google Scholar 

  • Caponio A, Cascella GL, Neri F, Salvatore N, Sumner M (2007) A fast adaptive memetic algorithm for off-line and on-line control design of PMSM drivers. IEEE Trans Syst Man Cybern B 37(1):28–41 (Special Issue on Memetic Algorithms)

    Article  Google Scholar 

  • Davis L (1991) Handbook of genetic algorithms. Van Nostrand Reinhold, New York

    Google Scholar 

  • Eshelman L (1991) The CHC adaptive search algorithm. How to have safe search when engaging in nontraditional genetic recombination. In: Foundations of genetic algorithms, pp 265–283

  • Eshelman L, Caruana A, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Foundation of genetic algorithms, vol 2, pp 187–202

  • Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms in genetic algorithms by preventing incest. Foundation of genetic algorithms, vol 2, pp 187–202

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

  • García S, Herrera F (2008) An extension on statistical comparisons of classifiers over multiple data sets for all pairwise comparisons. J Mach Learn Res 9:2677–2694

    Google Scholar 

  • García S, Fernández A, Luengo J, Herrera F (2009a) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13(10):959–977

    Article  Google Scholar 

  • García S, Molina D, Lozano M, Herrera F (2009b) 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 15:617–644

    Article  MATH  Google Scholar 

  • Gol-Alikhani M, Javadian N, Tavakkoli-Moghaddam R (2009) A novel hybrid approach combining electromagnetism-like method with Solis and Wets local search for continuous optimization problems. J Glob Optim 44(2):227–234

    Article  MathSciNet  MATH  Google Scholar 

  • Goldberg DE, Voessner S (1999) Optimizing global-local search hybrids. In: Banzhaf W et al (ed) Proceedings of the genetic and evolutionary computation conference (GECCO 1999). Morgan Kaufmann, San Mateo, California, pp 220–28

  • Hansen N (2005) Compilation of results on the CEC benchmark function set. In: 2005 IEEE congress on evolutionary computation

  • Hansen N (2009) Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed. In: GECCO’09: proceedings of the 11th annual conference companion on genetic and evolutionary computation conference, pp 2389–2396

  • Hansen N (2010) The CMA evolutionary strategy: a tutorial technical report. The French National Institute of Research in Computer Science and Control INRIA. http://www.lri.fr/∼hansen/cmatutorial.pdf

  • Hansen N, Kern S (2004) Evaluating the CMA evolution strategy on multimodal test functions. In: Yao X et al (ed) Proceedings of the parallel problem solving for nature—PPSN VIII, LNCS 3242. Springer, Berlin, pp 282–291

  • Hansen N, Ostermeier A (1996) Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. In: Proceeding of the IEEE international conference on evolutionary computation (ICEC’96), pp 312–317

  • Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol Comput 1(11):1–18

    Article  Google Scholar 

  • Hart WE (1994) Adaptive global optimization with local search. PhD thesis, University of California, San Diego, CA

  • Herrera F, Lozano M (2000) Two-loop real-coded genetic algorithms with adaptive control of mutation step sizes. Appl Intell 13(3):187–204

    Article  Google Scholar 

  • Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for the behavioral analysis. Artif Intell Rev 12(4):265–319

    Article  MATH  Google Scholar 

  • Hongfeng X, Guanzheng T (2009) High-dimension simplex genetic algorithm and its application to optimize hyper-high dimension functions. WRI global congress on intelligent systems, vol 2, pp 39–43

  • Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: IEE international conference on neural networks, pp 1942–1948

  • Kita H (2001) A comparison study of self-adaptation in evolutionary strategies and real-coded genetic algorithms. Evol Comput J 9(2):223–241

    Article  MathSciNet  Google Scholar 

  • Krasnogor N, Smith JE (2001) Emergence of profitable search strategies based on a simple inheritance mechanism. In: Proceedings of the 2001 international conference on genetic and evolutionary computation. Morgan Kaufmann, San Mateo, California, pp 432–439

  • Krasnogor N, Smith JE (2005) A tutorial for competent memetic algorithms: model, taxonomy, and design issue. IEEE Trans Evol Comput 9(5):474–488

    Article  Google Scholar 

  • Land Shannon MW (1998) Evolutionary algorithms with local search for combinational optimization. PhD thesis, University of California, San Diego, CA

  • Lozano M, Herrera F, Krasnogor N, Molina D (2004) Real-coded memetic algorithms with crossover hill-climbing. Evol Comput 12(2):273–302

    Article  Google Scholar 

  • Merz P (2000) Memetic algorithms for combinational optimization problems: Fitness landscapes and effective search strategies. PhD thesis, Gesamthochschule Siegen, University of Siegen, Germany

  • Molina D, Lozano M, Herrera F (2009) Memetic algorithm with local search chaining for large scale continuous optimization problems. In: Proceedings of the 2009 IEEE congress on evolutionary computation, pp 830–837

  • Molina D, Lozano M, García-Martínez C, Herrera F (2010) Memetic algorithms for continuous optimization based on local search chains. Evol Comput 18(1):27–63

    Article  Google Scholar 

  • Moscato PA (1989) On evolution, search, optimization, genetic algorithms and martial arts: toward memetic algorithms. Tech. rep., Technical report Caltech concurrent computation program report 826. Caltech, Pasadena, California

  • Moscato PA (1999) Memetic algorithms: a short introduction. McGraw-Hill, London, pp 219–234

    Google Scholar 

  • Nelder JA, Mead R (1965) A simplex method for functions minimizations. Comput J 7(4):308–313

    MATH  Google Scholar 

  • Nguyen QH, Ong YS, Lim MH (2009) A probabilistic memetic framework. IEEE Trans Evol Comput 13(3):604–623

    Article  Google Scholar 

  • Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evoly Comput 12(1):107–125

    Article  Google Scholar 

  • Soon OY, Keane AJ (2004) Meta-lamarckian learning in memetic algorithms. IEEE Trans Evolu Comput 4(2):99–110

    Google Scholar 

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

  • Renders JM, Flasse SP (1996) Hybrid methods using genetic algorithms for global optimization. IEEE Trans Syst Man Cybern 26(2):246–258

    Google Scholar 

  • Schwefel HP (1981) Numerical optimization of computer models. Wiley, New York

    MATH  Google Scholar 

  • Solis FJ, Wets RJ (1981) Minimization by random search techniques. Math Oper Res 6:19–30

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real parameter optimization. Tech. rep., Nanyang Technical University. http://www.ntu.edu.sg/home/epnsugan/index_files/CEC-05/Tech-Report-May-30-05

  • Syswerda G (1989) Uniform crossover in genetic algorithms. In: Schaffer JD (ed) Proceedings of the third international conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 2–9

  • Tang K (2008) Summary of results on CEC’08 competition on large scale global optimization. Tech. rep., Nature Inspired Computation and Application Lab (NICAL). http://nical.ustc.edu.cn/papers/CEC2008_SUMMARY.pdf

  • Tang K, Yao X, Suganthan PN, MacNish C, Chen YP, Chen CM, Yang Z (2007) Benchmark functions for the CEC’2008 special session and competition on large scale global optimization. Tech. rep., Nature Inspired Computation and Application Laboratory, USTC, China. http://nical.ustc.edu.cn/cec08ss.php

  • Tseng LY, Chen C (2007) Multiple trajectory search for multiobjective optimization. In: 2007 IEEE congress on evolutionary computation, pp 3609–3616

  • Tseng LY, Chen C (2008) Multiple trajectory search for large scale global optimization. In: 2008 IEEE congress on evolutionary computation, pp 3057–3064

  • Zar JH (1999) Biostatistical analysis. Prentice Hall, Englewood, NJ

    Google Scholar 

Download references

Acknowledgments

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

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Authors and Affiliations

  1. Department of Computer Languages and Systems, University of Cádiz, Cádiz, Spain

    Daniel Molina

  2. Department of Computer Science and Artificial Inteligence, University of Granada, Granada, Spain

    Manuel Lozano & Francisco Herrera

  3. Department of Software Engineering, University of Granada, Granada, Spain

    Ana M. Sánchez

Authors
  1. Daniel Molina
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  2. Manuel Lozano
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  3. Ana M. Sánchez
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  4. Francisco Herrera
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Corresponding author

Correspondence to Daniel Molina.

Appendix

Appendix

Tables 11, 12, 13, 14, 15, 16 show the average errors obtained by MA-SSW-Chains, MA-MTSLS1-Chains, MA-MTSLS2-Chains, MA-Simplex-Chains, MA-SW-Chains, and MA-CMA-Chains, respectively.

Table 11 Average error obtained by MA-SSW-Chains for each dimension
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Table 12 Average error obtained by MA-MTSLS1-Chains for each dimension
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Table 13 Average error obtained by MA-MTSLS2-Chains for each dimension
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Table 14 Average error obtained by MA-Simplex-Chains for each dimension
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Table 15 Average error obtained by MA-SW-Chains for each dimension
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Table 16 Average error obtained by MA-CMA-Chains for each dimension
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Molina, D., Lozano, M., Sánchez, A.M. et al. Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains. Soft Comput 15, 2201–2220 (2011). https://doi.org/10.1007/s00500-010-0647-2

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