Soft Computing

, Volume 15, Issue 11, pp 2201–2220 | Cite as

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

  • Daniel Molina
  • Manuel Lozano
  • Ana M. Sánchez
  • Francisco Herrera
Focus

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.

Keywords

Memetic algorithms Continuous optimisation Large scale problems Local search chains 

Notes

Acknowledgments

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

References

  1. Auger A, Hansen N (2005a) Performance evaluation of an advanced local search evolutionary algorithm. In: 2005 IEEE congress on evolutionary computation, pp 1777–1784Google Scholar
  2. Auger A, Hansen N (2005b) A restart CMA evolution strategy with increasing population size. In: 2005 IEEE congress on evolutionary computation, pp 1769–1776Google Scholar
  3. van den Bergh F, Engelbrencht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 3:225–239CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. Davis L (1991) Handbook of genetic algorithms. Van Nostrand Reinhold, New YorkGoogle Scholar
  6. 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 265–283Google Scholar
  7. Eshelman L, Caruana A, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Foundation of genetic algorithms, vol 2, pp 187–202Google Scholar
  8. Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms in genetic algorithms by preventing incest. Foundation of genetic algorithms, vol 2, pp 187–202Google Scholar
  9. 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 60–66Google Scholar
  10. García S, Herrera F (2008) An extension on statistical comparisons of classifiers over multiple data sets for all pairwise comparisons. J Mach Learn Res 9:2677–2694Google Scholar
  11. 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):959–977CrossRefGoogle Scholar
  12. 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 15:617–644MATHCrossRefGoogle Scholar
  13. 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):227–234MathSciNetMATHCrossRefGoogle Scholar
  14. 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 220–28Google Scholar
  15. Hansen N (2005) Compilation of results on the CEC benchmark function set. In: 2005 IEEE congress on evolutionary computationGoogle Scholar
  16. 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 2389–2396Google Scholar
  17. 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
  18. 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 282–291Google Scholar
  19. 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 312–317Google Scholar
  20. 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):1–18CrossRefGoogle Scholar
  21. Hart WE (1994) Adaptive global optimization with local search. PhD thesis, University of California, San Diego, CAGoogle Scholar
  22. Herrera F, Lozano M (2000) Two-loop real-coded genetic algorithms with adaptive control of mutation step sizes. Appl Intell 13(3):187–204CrossRefGoogle Scholar
  23. Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for the behavioral analysis. Artif Intell Rev 12(4):265–319MATHCrossRefGoogle Scholar
  24. 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 39–43Google Scholar
  25. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: IEE international conference on neural networks, pp 1942–1948Google Scholar
  26. Kita H (2001) A comparison study of self-adaptation in evolutionary strategies and real-coded genetic algorithms. Evol Comput J 9(2):223–241MathSciNetCrossRefGoogle Scholar
  27. 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 432–439Google Scholar
  28. Krasnogor N, Smith JE (2005) A tutorial for competent memetic algorithms: model, taxonomy, and design issue. IEEE Trans Evol Comput 9(5):474–488CrossRefGoogle Scholar
  29. Land Shannon MW (1998) Evolutionary algorithms with local search for combinational optimization. PhD thesis, University of California, San Diego, CAGoogle Scholar
  30. Lozano M, Herrera F, Krasnogor N, Molina D (2004) Real-coded memetic algorithms with crossover hill-climbing. Evol Comput 12(2):273–302CrossRefGoogle Scholar
  31. Merz P (2000) Memetic algorithms for combinational optimization problems: Fitness landscapes and effective search strategies. PhD thesis, Gesamthochschule Siegen, University of Siegen, GermanyGoogle Scholar
  32. 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 830–837Google Scholar
  33. Molina D, Lozano M, García-Martínez C, Herrera F (2010) Memetic algorithms for continuous optimization based on local search chains. Evol Comput 18(1):27–63CrossRefGoogle Scholar
  34. 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, CaliforniaGoogle Scholar
  35. Moscato PA (1999) Memetic algorithms: a short introduction. McGraw-Hill, London, pp 219–234Google Scholar
  36. Nelder JA, Mead R (1965) A simplex method for functions minimizations. Comput J 7(4):308–313MATHGoogle Scholar
  37. Nguyen QH, Ong YS, Lim MH (2009) A probabilistic memetic framework. IEEE Trans Evol Comput 13(3):604–623CrossRefGoogle Scholar
  38. Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evoly Comput 12(1):107–125CrossRefGoogle Scholar
  39. Soon OY, Keane AJ (2004) Meta-lamarckian learning in memetic algorithms. IEEE Trans Evolu Comput 4(2):99–110Google Scholar
  40. Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer, BerlinGoogle Scholar
  41. Renders JM, Flasse SP (1996) Hybrid methods using genetic algorithms for global optimization. IEEE Trans Syst Man Cybern 26(2):246–258Google Scholar
  42. Schwefel HP (1981) Numerical optimization of computer models. Wiley, New YorkMATHGoogle Scholar
  43. Solis FJ, Wets RJ (1981) Minimization by random search techniques. Math Oper Res 6:19–30MathSciNetMATHCrossRefGoogle Scholar
  44. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359MathSciNetMATHCrossRefGoogle Scholar
  45. 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
  46. 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 2–9Google Scholar
  47. 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
  48. 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
  49. Tseng LY, Chen C (2007) Multiple trajectory search for multiobjective optimization. In: 2007 IEEE congress on evolutionary computation, pp 3609–3616Google Scholar
  50. Tseng LY, Chen C (2008) Multiple trajectory search for large scale global optimization. In: 2008 IEEE congress on evolutionary computation, pp 3057–3064Google Scholar
  51. Zar JH (1999) Biostatistical analysis. Prentice Hall, Englewood, NJGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Daniel Molina
    • 1
  • Manuel Lozano
    • 2
  • Ana M. Sánchez
    • 3
  • Francisco Herrera
    • 2
  1. 1.Department of Computer Languages and SystemsUniversity of CádizCádizSpain
  2. 2.Department of Computer Science and Artificial InteligenceUniversity of GranadaGranadaSpain
  3. 3.Department of Software EngineeringUniversity of GranadaGranadaSpain

Personalised recommendations