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Applied Intelligence

, Volume 49, Issue 5, pp 1841–1865 | Cite as

A directional crossover (DX) operator for real parameter optimization using genetic algorithm

  • Amit Kumar Das
  • Dilip Kumar PratiharEmail author
Article
  • 106 Downloads

Abstract

Nature-inspired optimization algorithms have received more and more attention from the researchers due to their several advantages. Genetic algorithm (GA) is one of such bio-inspired optimization techniques, which has mainly three operators, namely selection, crossover, and mutation. Several attempts had been made to make these operators of a GA more efficient in terms of performance and convergence rates. In this paper, a directional crossover (DX) has been proposed for a real-coded genetic algorithm (RGA). As the name suggests, this proposed DX uses the directional information of the search process for creating the children solutions. Moreover, one method has been suggested to obtain this directional information for identifying the most promising areas of the variable space. To measure the performance of an RGA with the proposed crossover operator (DX), experiments are carried out on a set of six popular optimization functions, and the obtained results have been compared to that yielded by the RGAs with other well-known crossover operators. RGA with the proposed DX operator (RGA-DX) has outperformed the other ones, and the same has been confirmed through the statistical analyses. In addition, the performance of the RGA-DX has been compared to that of other five recently proposed optimization techniques on the six test functions and one constrained optimization problem. In these performance comparisons also, the RGA-DX has outperformed the other ones. Therefore, in all the experiments, RGA-DX has been found to yield the better quality of solutions with the faster convergence rate.

Keywords

Evolutionary algorithm Real-coded genetic algorithm Directional crossover Exponential crossover Convergence rate 

References

  1. 1.
    Gong X, Plets D, Tanghe E, De Pessemier T, Martens L, Joseph W (2018) An efficient genetic algorithm for large-scale planning of dense and robust industrial wireless networks. Expert Syst Appl 96:311–329Google Scholar
  2. 2.
    Bermejo E, Campomanes-Álvarez C, Valsecchi A, Ibáñez O, Damas S, Cordón O (2017) Genetic algorithms for skull-face overlay including mandible articulation. Inf Sci 420:200–217.  https://doi.org/10.1016/j.ins.2017.08.029 Google Scholar
  3. 3.
    Liao C-L, Lee S-J, Chiou Y-S, Lee C-R, Lee C-H (2018) Power consumption minimization by distributive particle swarm optimization for luminance control and its parallel implementations. Expert Syst Appl 96:479–491Google Scholar
  4. 4.
    Fernández JR, López-Campos JA, Segade A, Vilán JA (2018) A genetic algorithm for the characterization of hyperelastic materials. Appl Math Comput 329:239–250.  https://doi.org/10.1016/j.amc.2018.02.008 MathSciNetGoogle Scholar
  5. 5.
    Morra L, Coccia N, Cerquitelli T (2018) Optimization of computer aided detection systems: an evolutionary approach. Expert Syst Appl 100:145–156Google Scholar
  6. 6.
    Gao H, Pun C-M, Kwong S (2016) An efficient image segmentation method based on a hybrid particle swarm algorithm with learning strategy. Inf Sci 369:500–521.  https://doi.org/10.1016/j.ins.2016.07.017 MathSciNetGoogle Scholar
  7. 7.
    Wang JL, Lin YH, Lin MD (2015) Application of heuristic algorithms on groundwater pumping source identification problems. In: International Conference on Industrial Engineering and Engineering Management (IEEM), 6–9 Dec 2015, pp 858–862.  https://doi.org/10.1109/IEEM.2015.7385770
  8. 8.
    Nazari-Heris M, Mohammadi-Ivatloo B (2015) Application of heuristic algorithms to optimal PMU placement in electric power systems: an updated review. Renew Sust Energ Rev 50:214–228.  https://doi.org/10.1016/j.rser.2015.04.152 Google Scholar
  9. 9.
    Niu M, Wan C, Xu Z (2014) A review on applications of heuristic optimization algorithms for optimal power flow in modern power systems. J Mod Power Syst Clean Energy 2(4):289–297.  https://doi.org/10.1007/s40565-014-0089-4 Google Scholar
  10. 10.
    Ghaheri A, Shoar S, Naderan M, Hoseini SS (2015) The applications of genetic algorithms in medicine. Oman Med J 30(6):406–416.  https://doi.org/10.5001/omj.2015.82 Google Scholar
  11. 11.
    Reina DG, Ruiz P, Ciobanu R, Toral SL, Dorronsoro B, Dobre C (2016) A survey on the application of evolutionary algorithms for Mobile multihop Ad Hoc network optimization problems. Int J Distrib Sens Netw 12(2):2082496.  https://doi.org/10.1155/2016/2082496 Google Scholar
  12. 12.
    Cordón O, Herrera-Viedma E, López-Pujalte C, Luque M, Zarco C (2003) A review on the application of evolutionary computation to information retrieval. Int J Approx Reason 34(2):241–264.  https://doi.org/10.1016/j.ijar.2003.07.010 MathSciNetzbMATHGoogle Scholar
  13. 13.
    Steinbuch R (2010) Successful application of evolutionary algorithms in engineering design. J Bionic Eng 7:S199–S211.  https://doi.org/10.1016/S1672-6529(09)60236-5 Google Scholar
  14. 14.
    Ma R-J, Yu N-Y, Hu J-Y (2013) Application of particle swarm optimization algorithm in the heating system planning problem. Sci World J 2013:11.  https://doi.org/10.1155/2013/718345 Google Scholar
  15. 15.
    Anis Diyana R, Nur Sabrina A, Hadzli H, Noor Ezan A, Suhaimi S, Rohaiza B (2018) Application of particle swarm optimization algorithm for optimizing ANN model in recognizing ripeness of citrus. IOP Conference Series: Materials Science and Engineering 340(1):012015Google Scholar
  16. 16.
    Assareh E, Behrang MA, Assari MR, Ghanbarzadeh A (2010) Application of PSO (particle swarm optimization) and GA (genetic algorithm) techniques on demand estimation of oil in Iran. Energy 35(12):5223–5229.  https://doi.org/10.1016/j.energy.2010.07.043 Google Scholar
  17. 17.
    Cao H, Qian X, Zhou Y (2018) Large-scale structural optimization using metaheuristic algorithms with elitism and a filter strategy. Struct Multidiscip Optim 57(2):799–814.  https://doi.org/10.1007/s00158-017-1784-3 Google Scholar
  18. 18.
    Schutte JF, Koh B, Reinbolt JA, Haftka RT, George AD, Fregly BJ (2005) Evaluation of a particle swarm algorithm for biomechanical optimization. J Biomech Eng 127(3):465–474Google Scholar
  19. 19.
    Das AK, Pratihar DK (2018) A novel restart strategy for solving complex multi-modal optimization problems using real-coded genetic algorithm. In: Abraham A, Muhuri P, Muda A, Gandhi N (eds) Intelligent systems design and applications. ISDA 2017. Advances in Intelligent Systems and Computing, vol 736. Springer, ChamGoogle Scholar
  20. 20.
    Das AK, Pratihar DK (2018) Performance improvement of a genetic algorithm using a novel restart strategy with elitism principle. International Journal of Hybrid Intelligent Systems (Pre-press):1–15.  https://doi.org/10.3233/HIS-180257
  21. 21.
    Kogiso N, Watson LT, Gürdal Z, Haftka RT (1994) Genetic algorithms with local improvement for composite laminate design. Structural Optimization 7(4):207–218.  https://doi.org/10.1007/bf01743714 Google Scholar
  22. 22.
    Kogiso N, Watson LT, GÜRdal Z, Haftka RT, Nagendra S (1994) Design of composite laminates by a genetic algorithm with memory. Mech Compos Mater Struct 1(1):95–117.  https://doi.org/10.1080/10759419408945823 Google Scholar
  23. 23.
    Soremekun G, Gürdal Z, Haftka RT, Watson LT (2001) Composite laminate design optimization by genetic algorithm with generalized elitist selection. Comput Struct 79(2):131–143.  https://doi.org/10.1016/S0045-7949(00)00125-5 Google Scholar
  24. 24.
    Mestria M (2018) New hybrid heuristic algorithm for the clustered traveling salesman problem. Comput Ind Eng 116:1–12.  https://doi.org/10.1016/j.cie.2017.12.018 Google Scholar
  25. 25.
    Nama S, Saha AK (2018) A new hybrid differential evolution algorithm with self-adaptation for function optimization. Appl Intell 48(7):1657–1671.  https://doi.org/10.1007/s10489-017-1016-y Google Scholar
  26. 26.
    Singh A, Banda J (2017) Hybrid artificial bee colony algorithm based approaches for two ring loading problems. Appl Intell 47(4):1157–1168.  https://doi.org/10.1007/s10489-017-0950-z Google Scholar
  27. 27.
    Srivastava S, Sahana SK (2017) Nested hybrid evolutionary model for traffic signal optimization. Appl Intell 46(1):113–123.  https://doi.org/10.1007/s10489-016-0827-6 Google Scholar
  28. 28.
    Canayaz M, Karci A (2016) Cricket behaviour-based evolutionary computation technique in solving engineering optimization problems. Appl Intell 44(2):362–376.  https://doi.org/10.1007/s10489-015-0706-6 Google Scholar
  29. 29.
    Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47.  https://doi.org/10.1016/j.advengsoft.2017.01.004 Google Scholar
  30. 30.
    Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133.  https://doi.org/10.1016/j.knosys.2015.12.022 Google Scholar
  31. 31.
    Cuevas E, Cienfuegos M, Zaldívar D, Pérez-Cisneros M (2013) A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Syst Appl 40(16):6374–6384.  https://doi.org/10.1016/j.eswa.2013.05.041 Google Scholar
  32. 32.
    Gonçalves MS, Lopez RH, Miguel LFF (2015) Search group algorithm: a new metaheuristic method for the optimization of truss structures. Comput Struct 153:165–184.  https://doi.org/10.1016/j.compstruc.2015.03.003 Google Scholar
  33. 33.
    Verma R, Lakshminiarayanan PA (2006) A case study on the application of a genetic algorithm for optimization of engine parameters. Proc IMechE, Part D: J Automobile Engineering 220(4):471–479.  https://doi.org/10.1243/09544070D09204 Google Scholar
  34. 34.
    Wu H, Hsiao W, Lin C, Cheng T (2011) Application of genetic algorithm to the development of artificial intelligence module system. In: 2nd international conference on intelligent control and information processing, 25–28 July 2011. pp 290–294.  https://doi.org/10.1109/ICICIP.2011.6008251
  35. 35.
    Canyurt OE, Öztürk HK (2006) Three different applications of genetic algorithm (GA) search techniques on oil demand estimation. Energy Convers Manag 47(18):3138–3148.  https://doi.org/10.1016/j.enconman.2006.03.009 Google Scholar
  36. 36.
    Barros GAB, Carvalho LFBS, Silva VRM, Lopes RVV (2011) An application of genetic algorithm to the game of checkers. In: Brazilian symposium on games and digital entertainment, 7–9 Nov. 2011. pp 63–69.  https://doi.org/10.1109/SBGAMES.2011.14
  37. 37.
    Holland JH (1992) Adaptation in natural and artificial systems. An introductory analysis with application to biology, control, and artificial intelligence. MIT Press, CambridgeGoogle Scholar
  38. 38.
    Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Longman Publishing Co., BostonzbMATHGoogle Scholar
  39. 39.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Section 22.3 , gray codes, Numerical recipes: the art of scientific computing, 3rd edn. Cambridge University Press, New YorkzbMATHGoogle Scholar
  40. 40.
    MacKay DJ, Mac Kay DJ (2003) Information theory, inference and learning algorithms. Cambridge university press, CambridgeGoogle Scholar
  41. 41.
    Das AK, Pratihar DK (2017) A direction-based exponential crossover operator for real-coded genetic algorithm. Paper presented at the seventh international conference on theoretical, applied, computational and experimental mechanics, IIT Kharagpur, IndiaGoogle Scholar
  42. 42.
    Herrera F, Lozano M (2000) Two-loop real-coded genetic algorithms with adaptive control of mutation step sizes. Appl Intell 13(3):187–204.  https://doi.org/10.1023/a:1026531008287 Google Scholar
  43. 43.
    Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif Intell Rev 12(4):265–319zbMATHGoogle Scholar
  44. 44.
    Jomikow C, Michalewicz Z (1991) An experimental comparison of binary and floating point representations in genetic algorithm. In: Proceedings of the fourth international conference on genetic algorithms, pp 31–36Google Scholar
  45. 45.
    Chuang Y-C, Chen C-T, Hwang C (2015) A real-coded genetic algorithm with a direction-based crossover operator. Inf Sci 305:320–348.  https://doi.org/10.1016/j.ins.2015.01.026 Google Scholar
  46. 46.
    Wright AH (1991) Genetic algorithms for real parameter optimization. In: Rawlins GJE (ed) Foundations of genetic algorithms, vol 1. Elsevier, pp 205–218.  https://doi.org/10.1016/B978-0-08-050684-5.50016-1
  47. 47.
    Radcliffe NJ (1991) Equivalence class analysis of genetic algorithms. Complex Syst 5(2):183–205MathSciNetzbMATHGoogle Scholar
  48. 48.
    Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs, 3rd edn. Springer-Verlag, New YorkzbMATHGoogle Scholar
  49. 49.
    Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Whitley LD (ed) Foundations of genetic algorithms, vol 2. Elsevier, pp 187–202.  https://doi.org/10.1016/B978-0-08-094832-4.50018-0
  50. 50.
    Voigt H-M, Mühlenbein H, Cvetkovic D (1995) Fuzzy recombination for the breeder genetic algorithm. In: Proceedings of the 6th international conference on genetic algorithms. Morgan Kaufmann Publishers Inc., pp 104–113Google Scholar
  51. 51.
    Deb K, Agrawal RB (1994) Simulated binary crossover for continuous search space. Complex Syst 9(3):1–15MathSciNetzbMATHGoogle Scholar
  52. 52.
    Ono I, Kita H, Kobayashi S (2003) A real-coded genetic algorithm using the unimodal Normal distribution crossover. In: Ghosh A, Tsutsui S (eds) Advances in evolutionary computing: theory and applications. Springer Berlin Heidelberg, Berlin, pp 213–237.  https://doi.org/10.1007/978-3-642-18965-4_8 Google Scholar
  53. 53.
    Ono I, Kita H, Kobayashi S (1999) A robust real-coded genetic algorithm using unimodal normal distribution crossover augmented by uniform crossover: effects of self-adaptation of crossover probabilities. In: Proceedings of the 1st annual conference on genetic and evol comput - volume 1, Orlando, Florida, 1999. Morgan Kaufmann Publishers Inc., San Mateo, CA, pp 496–503Google Scholar
  54. 54.
    Kita H, Ono I, Kobayashi S (1999) Multi-parental extension of the unimodal normal distribution crossover for real-coded genetic algorithms. In: Proceedings of the 1999 congress on evolutionary computation, pp 1588–1595.  https://doi.org/10.1109/CEC.1999.782672
  55. 55.
    Herrera F, Lozano M (1996) Adaptation of genetic algorithm parameters based on fuzzy logic controllers. Genetic Algorithms and Soft Computing 8:95–125Google Scholar
  56. 56.
    Herrera F, Lozano M, Verdegay JL (1996) Dynamic and heuristic fuzzy connectives-based crossover operators for controlling the diversity and convergence of real-coded genetic algorithms. Int J Intell Syst 11(12):1013–1040zbMATHGoogle Scholar
  57. 57.
    Tsutsui S, Yamamura M, Higuchi T (1999) Multi-parent recombination with simplex crossover in real coded genetic algorithms In: Proceedings of the 1st annual conference on genetic and evol comput - volume 1, Orlando, Florida. Morgan Kaufmann Publishers Inc., pp 657–664Google Scholar
  58. 58.
    Deb K, Anand A, Joshi D (2002) A computationally efficient evolutionary algorithm for real-parameter optimization. Evol Comput 10(4):371–395.  https://doi.org/10.1162/106365602760972767 Google Scholar
  59. 59.
    Deep K, Thakur M (2007) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188(1):895–911.  https://doi.org/10.1016/j.amc.2006.10.047 MathSciNetzbMATHGoogle Scholar
  60. 60.
    Kuo H-C, Lin C-H (2013) A directed genetic algorithm for global optimization. Appl Math Comput 219(14):7348–7364.  https://doi.org/10.1016/j.amc.2012.12.046 MathSciNetzbMATHGoogle Scholar
  61. 61.
    Lim SM, Sulaiman MN, Sultan ABM, Mustapha N, Tejo BA (2014) A new real-coded genetic algorithm crossover: Rayleigh crossover. Journal of Theoretical & Applied Information Technology 62(1):262–268Google Scholar
  62. 62.
    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82Google Scholar
  63. 63.
    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61.  https://doi.org/10.1016/j.advengsoft.2013.12.007 Google Scholar
  64. 64.
    Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Computer Science and Informatics 26:30–45Google Scholar
  65. 65.
    Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338.  https://doi.org/10.1016/S0045-7825(99)00389-8 zbMATHGoogle Scholar
  66. 66.
    Van Den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176(8):937–971MathSciNetzbMATHGoogle Scholar
  67. 67.
    Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18Google Scholar
  68. 68.
    García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064Google Scholar
  69. 69.
    Derrac J, García S, Hui S, Suganthan PN, Herrera F (2014) Analyzing convergence performance of evolutionary algorithms: a statistical approach. Inf Sci 289:41–58.  https://doi.org/10.1016/j.ins.2014.06.009 Google Scholar
  70. 70.
    Deb K, H-g B (2001) Self-adaptive genetic algorithms with simulated binary crossover. Evol Comput 9(2):197–221.  https://doi.org/10.1162/106365601750190406 Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology KharagpurKharagpurIndia

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