Advertisement

A Two-stage State Transition Algorithm for Constrained Engineering Optimization Problems

  • Jie Han
  • Chunhua Yang
  • Xiaojun Zhou
  • Weihua Gui
Regular Paper Control Theory and Applications

Abstract

In this study, a state transition algorithm (STA) is investigated into constrained engineering design optimization problems. After an analysis of the advantages and disadvantages of two well-known constraint-handling techniques, penalty function method and feasibility preference method, a two-stage strategy is incorporated into STA, in which, the feasibility preference method is adopted in the early stage of an iteration process whilst it is changed to the penalty function method in the later stage. Then, the proposed STA is used to solve three benchmark problems in engineering design and an optimization problem in power-dispatching control system for the electrochemical process of zinc. The experimental results have shown that the optimal solutions obtained by the proposed method are all superior to those by typical approaches in the literature in terms of both convergency and precision.

Keywords

Constrained engineering optimization feasibility preference method penalty function method state transition algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    S. Mohammadloo, M. H. Alizadeh, and M. Jafari, “Multivariable autopilot design for sounding rockets using intelligent eigenstructure assignment technique,” International Journal of Control Automation and Systems, vol. 12, no. 1, pp. 208–219, 2014. [click]CrossRefGoogle Scholar
  2. [2]
    Z. Mohamed, M. Kitani, S. Kaneko, and G. Capi. “Humanoid robot arm performance optimization using multi objective evolutionary algorithm,” International Journal of Control, Automation and Systems, vol. 12, no. 1, pp. 870–877, 2014. [click]CrossRefGoogle Scholar
  3. [3]
    Y. Minami, “Design of model following control systems with discrete-valued signal constraints,” International Journal of Control, Automation and Systems, vol. 14, no. 1, pp. 331–339, 2016. [click]CrossRefGoogle Scholar
  4. [4]
    R. Madiouni, S. Bouallègue, J. Haggège, and P. Siarry. “Robust RST control design based on multi-objective particle swsarm optimization approach,” International Journal of Control, Automation and Systems, vol. 14, no. 6, pp. 1607–1617, 2016. [click]CrossRefzbMATHGoogle Scholar
  5. [5]
    Q. Zhang, Q. Wang, and G. Li. “Switched system identification based on the constrained multi-objective optimization problem with application to the servo turntable,” International Journal of Control, Automation and Systems, vol. 14, no. 5, pp. 1153–1159, 2016. [click]CrossRefGoogle Scholar
  6. [6]
    K. E. Parsopoulos and M. N. Vrahatis, “Particle swarm optimization method for constrained optimization problems,” Proceedings of the Euro-International Symposiumon Computational Intelligence 2002, vol. 76, no. 1, pp. 214–220, 2002.zbMATHGoogle Scholar
  7. [7]
    J. Han, T. X. Dong, X. J. Zhou, C. H. Yang, and W. H. Gui, “State transition algorithm for constrained optimization problems,” Proceedings of the 33rd Chinese Control Conference, pp. 7543–7548, 2014.Google Scholar
  8. [8]
    A. H. Gandomi, X.-S. Yang, and A. H. Alavi, “Mixed variable structural optimization using firefly algorithm,” Computers & Structures, vol. 89, no. 23-24, pp. 2325–2336, Dec. 2011. [click]CrossRefGoogle Scholar
  9. [9]
    C. A. C. Coello, “Use of a self-adaptive penalty approach for engineering optimization problems,” Comput. Ind., vol. 41, pp. 113–127, 2000.CrossRefGoogle Scholar
  10. [10]
    N. B. Guedria, “Improved accelerated PSO algorithm for mechanical engineering optimization problems,” Applied Soft Computing, vol. 40, pp. 455–467, 2016. [click]CrossRefGoogle Scholar
  11. [11]
    Q. Yuan and F. Qian, “A hybrid genetic algorithm for twice continuously differentiable NLP problems,” Comput. Chem. Eng., vol. 34, pp. 36–41, 2010. [click]CrossRefGoogle Scholar
  12. [12]
    Q. He and L. Wang, “An effective co-evolutionary particle swarm optimization for constrained engineering design problems,” Eng. Appl. Artif. Intell., vol. 20, pp. 89–99, 2007. [click]CrossRefGoogle Scholar
  13. [13]
    C. A. C. Coello and R. L. Becerra, “Efficient evolutionary optimization through theuse of a cultural algorithm,” Eng. Optim., vol. 36, pp. 219–236, 2004. [click]CrossRefGoogle Scholar
  14. [14]
    T. Ray and K. M. Liew, “Society and civilization: an optimization algorithm based on the simulation of social behavior,” IEEE Trans. Evol. Comput., vol. 7, pp. 386–396, 2003. [click]CrossRefGoogle Scholar
  15. [15]
    H. Eskandar, A. Sadollah, A. Bahreininejad, and M. Hamdi, “Water cycle algorithm: a novel metaheuristic optimization method for solving constrained engineering optimization problems,” Comput. Struct., vol. 110-111, pp. 151–166, 2012. [click]CrossRefGoogle Scholar
  16. [16]
    A. Sadollah, A. Bahreininejad, H. Eskandar, and M. Hamdi, “Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems,” Appl. Soft Comput. J., vol. 13, pp. 2592–2612, 2013. [click]CrossRefGoogle Scholar
  17. [17]
    J. Han, C. H. Yang, X. J. Zhou, and W. H. Gui. “A new multi-threshold image segmentation approach using state transition algorithm,” Applied Mathematical Modelling, vol. 4, pp. 588–601, 2017. [click]MathSciNetCrossRefGoogle Scholar
  18. [18]
    J. Han, C. H. Yang, X. J. Zhou, and W. H. Gui, “Dynamic multi-objective optimization arising in ironprecipitation of zinc hydrometallurgy,” Hydrometallurgy, vol. 173, pp. 134–148, 2017.CrossRefGoogle Scholar
  19. [19]
    X. J. Zhou, P. Shi, C. C. Lim, C. H. Yang, and W. H. Gui, “A dynamic state transition algorithm with application to sensor network localization,” Neurocomputing, vol. 273, pp. 237–250, 2018.CrossRefGoogle Scholar
  20. [20]
    X. J. Zhou, C. H. Yang, and W. H. Gui, “State transition algorithm,” Journal of Industrial and Management Optimization, vol. 8, no. 3, pp. 1039–1056, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    X. J. Zhou, C. H. Yang, and W. H. Gui, “Nonlinear system identification and control using state transition algorithm,” Applied Mathematics & Computation, vol. 226, no. 1, pp. 169–179, 2012.MathSciNetzbMATHGoogle Scholar
  22. [22]
    F. X. Zhang, X. J. Zhou, C. H. Yang, and W. H. Gui, “Fractional-order PID controller tuning using continuous state transition algorithm,” Neural Computing and Applications, pp. 1–10, 2016.Google Scholar
  23. [23]
    X. J. Zhou, C. H. Yang, and W. H. Gui, “A matlab toolbox for continuous state transition algorithm,” Proceedings of the 35th Chinese Control Conference, pp. 9172–9177, 2016.Google Scholar
  24. [24]
    C. A. C. Coello, “Theoretical and numerical constrainthandling techniques used with evolutionary algorithms: a survey of the state of the art,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 11, pp. 1245–1287, 2002.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    T. P. Runarsson and X. Yao, “Stochastic ranking for constrained evolutionary optimization,” IEEE Transactions on Evolutionary Computation, vol. 4, no. 3, pp. 284–294, 2000. [click]CrossRefGoogle Scholar
  26. [26]
    Z. X. Cai and Y. Wang, “A multiobjective optimizationbased evolutionary algorithm for constrained optimization,” IEEE Transactions on Evolutionary Computation, vol. 10, no. 6, pp. 658–675, 2006. [click]CrossRefGoogle Scholar
  27. [27]
    Y. Wang and Z. X. Cai, “Combining multiobjective optimization with differential evolution to solve constrained optimization problems,” IEEE Transactions on Evolutionary Computation, vol. 16, no. 1, pp. 117–134, 2012. [click]CrossRefGoogle Scholar
  28. [28]
    K. Deb, “An efficient constraint handling method for genetic algorithms,” Computer Methods in Applied Mechanics and Engineering, vol. 186, no. 2-4, pp. 311–338, 2000. [click]CrossRefzbMATHGoogle Scholar
  29. [29]
    A. R. Conn, N. I. M. Gould, and P. L. Toint, “A globally convergent augmented lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds,” Mathematics of Computation, vol. 66, no. 217, pp. 261–288, 1997.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Ï. Karen, N. Kaya, and F. Öztürk, “Intelligent die design optimization using enhanced differential evolution and response surface methodology,” Journal of Intelligent Manufacturing, vol. 26, no. 5, pp. 1027–1038, 2015. [click]CrossRefGoogle Scholar
  31. [31]
    E. Zahara and Y. T. Kao, “Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems,” Expert Syst. Appl., vol. 36, pp. 3880–3886, 2009. [click]CrossRefGoogle Scholar
  32. [32]
    H. Liu, Z. Cai, and Y. Wang, “Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization,” Appl. Soft Comput. J., vol. 10, pp. 629–640, 2010. [click]CrossRefGoogle Scholar
  33. [33]
    J. Lampinen, “A constraint handling approach for the differential evolution algorithm,” IEEE Proc. 2002 Congr. Evol. Comput. CEC’02 (Cat. No.02TH8600), pp. 1468–1473, 2002.Google Scholar
  34. [34]
    A. Husseinzadeh Kashan, “An efficient algorithm for constrained global optimization and application to mechanical engineering design: league championship algorithm (LCA),” Comput. Des., vol. 43, pp. 1769–1792, 2011. [click]Google Scholar
  35. [35]
    W. C. Yi, Y. Z. Zhou, L. Gao, X. Y. Gao, and C. J. Zhang, “Engineering design optimization using an improved local search based epsilon differential evolution algorithm,” Journal of Intelligent Manufacturing, pp. 1–22, 2016.Google Scholar
  36. [36]
    F. Huang, L. Wang, and Q. He, “An effective coevolutionary differential evolution for constrained optimization,” Appl. Math. Comput., vol. 186, pp. 340–356, 2007. [click]MathSciNetzbMATHGoogle Scholar
  37. [37]
    Q. He and L. Wang, “A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization,” Appl. Math. Comput., vol. 186, pp. 1407–1422, 2007. [click]MathSciNetzbMATHGoogle Scholar
  38. [38]
    L. D. S. Coelho, “Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems,” Expert Syst. Appl., vol. 37, pp. 1676–1683, 2010. [click]CrossRefGoogle Scholar
  39. [39]
    J. S. Arora, Introduction to Optimum Design, McGraw-Hill, New York, 1989.Google Scholar
  40. [40]
    A. D. Belegundu, A Study of Mathematical Programming Methods for Structural Optimization, PhD thesis, Department of Civil and Environmental Engineering, University of Iowa, Iowa, USA, 1982.Google Scholar
  41. [41]
    J. D. Huang, L. Gao, and X. Y. Li, “A teaching clearningbased cuckoo search for constrained engineering design problems,” Advances in Global Optimization, Springer International Publishing, pp. 375–386, 2015.Google Scholar
  42. [42]
    P. C. Ye, G. Pan, Q. G. Huang, and Y. Shi, “A new sequential approximate optimization approach using radial basis functions for engineering optimization,” Intelligent Robotics and Applications, Springer International Publishing, pp. 83–93, 2015. [click]CrossRefGoogle Scholar
  43. [43]
    M. Mahdavi, M. Fesanghary, and E. Damangir, “An improved harmony search algorithm for solving optimization problems,” Applied Mathematics and Computation, vol. 188, pp. 1567–1579, 2007. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    T. Ray and P. Saini, “Engineering design optimization using a swarm with an intelligent information sharing among individuals,” Engineering Optimization, vol. 33, pp. 735–748, 2001. [click]CrossRefGoogle Scholar
  45. [45]
    C. A. C. Coello and E. M. Montes, “Constraint- handling in genetic algorithms through the use of dominance-based tournament selection,” Advanced Engineering Informatics, vol. 16, pp. 193–203, 2002. [click]CrossRefGoogle Scholar
  46. [46]
    E. M. Montes and C. A. C. Coello, “An empirical study about the usefulness of evolution strategies to solve constrained optimization problems,” International Journal of General Systems, vol. 37, pp. 443–473, 2008. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    X. J. Zhou, C. H. Yang, and W. H. Gui, “Modeling and control of nonferrous metallurgical processes on the perspective of global optimization,” Control Theory & Applications, vol. 9, no. 004, pp. 1158–1169, 2015.zbMATHGoogle Scholar
  48. [48]
    C. H. Yang, G. Deconinck, and W. H. Gui, “An optimal power-dispatching control system for the electrochemical process of zinc based on backpropagation and hopfield neural networks,” IEEE Transactions on Industrial Electronics, vol. 50, no. 5, pp. 953–961, 2003.CrossRefGoogle Scholar
  49. [49]
    C. H. Yang, G. Deconinck, W. H. Gui, and Y. G. Li, “An optimal power-dispatching system using neural networks for the electrochemical process of zinc depending on varying prices of electricity,” IEEE Transactions on Neural Networks, vol. 13, no. 1, pp. 229–236, 2002.CrossRefGoogle Scholar
  50. [50]
    D. Y. Zhao, Q. H. Tian, Z. M. Li, and Q. M. Zhu, “A new stepwise and piecewise optimization approach for CO2 pipeline,” International Journal of Greenhouse Gas Control, vol. 49, pp. 192–200, 2016. [click]CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jie Han
    • 1
  • Chunhua Yang
    • 1
  • Xiaojun Zhou
    • 1
  • Weihua Gui
    • 1
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaP. R. China

Personalised recommendations