Advertisement

Journal of Intelligent Manufacturing

, Volume 30, Issue 6, pp 2407–2433 | Cite as

A modified particle swarm optimization for large-scale numerical optimizations and engineering design problems

  • Hao LiuEmail author
  • Yue Wang
  • Liangping Tu
  • Guiyan Ding
  • Yuhan Hu
Article

Abstract

Particle swarm optimization (PSO) has attracted the attention of many researchers because of its simple concept and easy implementation. However, it suffers from premature convergence due to quick loss of population diversity. Meanwhile, real-world engineering design problems are generally nonlinear or large-scale or constrained optimization problems. To enhance the performance of PSO for solving large-scale numerical optimizations and engineering design problems, an adaptive disruption strategy which originates from the disruption phenomenon of astrophysics, is proposed to shift the abilities between global exploration and local exploitation. Meanwhile, a Cauchy mutation is utilized to a certain dimension of the best particle to help particle jump out the local optima. Nine well-known large-scale unconstrained problems, ten complicated shifted and/or rotated functions and four famous constrained engineering problems are utilized to validate the performance of the proposed algorithm compared against those of state-of-the-art algorithms. Experimental results and statistic analysis confirm effectiveness and promising performance of the proposed algorithm.

Keywords

Particle swarm optimization Disruption operator Cauchy mutation Engineering design problems 

Notes

Acknowledgements

The authors wish to acknowledge the National Natural Science Foundation of China (Grant No. U1731128); the Doctoral Research Starting Funds of Liaoning Province (Grant No. 201601292); the Youth Science Funds of USTL (Grant No. 2014QN16); the Talent Development Program of USTL (Grant No. 2015RC04) for the financial support.

References

  1. Akay, B., & Karaboga, D. (2012). Artificial bee colony algorithm for large-scale problems and engineering design optimization. Journal of Intelligent Manufacturing, 23(4), 1001–1014.CrossRefGoogle Scholar
  2. Alexandridis, A., Chondrodima, E., & Sarimveis, H. (2016). Cooperative learning for radial basis function networks using particle swarm optimization. Applied Soft Computing, 49(Supplement C), 485–497.CrossRefGoogle Scholar
  3. Ali, M. M., & Zhu, W. X. (2013). A penalty function-based differential evolution algorithm for constrained global optimization. Computational Optimization and Applications, 54(3), 707–739.CrossRefGoogle Scholar
  4. Andrews, P. (2006). An investigation into mutation operators for particle swarm optimization. In Proceedings of the 2006 IEEE congress on evolutionary computation, IEEE (pp. 1044–1051).Google Scholar
  5. Angeline, P. (1998). Using selection to improve particle swarm optimization. In Proceedings of the 1998 IEEE international conference on evolutionary computation, the 1998 IEEE world congress on computational intelligence, IEEE (pp. 84–89).Google Scholar
  6. Arora, J. (2004). Introduction to optimum design (2nd ed.). Cambridge: Academic Press.Google Scholar
  7. Baykasoglu, A., & Akpinar, S. (2015). Weighted superposition attraction (wsa): A swarm intelligence algorithm for optimization problems c part 2: Constrained optimization. Applied Soft Computing, 37(Supplement C), 396–415.CrossRefGoogle Scholar
  8. Baykasoglu, A., & Ozsoydan, F. B. (2015). Adaptive firefly algorithm with chaos for mechanical design optimization problems. Applied Soft Computing, 36(Supplement C), 152–164.CrossRefGoogle Scholar
  9. Baykasoglu, A., & Ozsoydan, F. B. (2017). Evolutionary and population-based methods versus constructive search strategies in dynamic combinatorial optimization. Information Sciences, 420, 159–183.CrossRefGoogle Scholar
  10. Chen, Y. P., Peng, W. C., & Jian, M. C. (2007). Particle swarm optimization with recombination and dynamic linkage discovery. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 37(6), 1460–1470.CrossRefGoogle Scholar
  11. Chi, R., Su, Y., Zhang, D., Chi, X., & Zhang, H. (2017). A hybridization of cuckoo search and particle swarm optimization for solving optimization problems. Neural Computing and Applications.Google Scholar
  12. Coello Coello, C. A. (2000). Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry, 41(2), 113–127.CrossRefGoogle Scholar
  13. De, A., Awasthi, A., & Tiwari, M. K. (2015). Robust formulation for optimizing sustainable ship routing and scheduling problem. IFAC-PapersOnLine, 48(3), 368–373.CrossRefGoogle Scholar
  14. De, A., Mamanduru, V. K. R., Gunasekaran, A., Subramanian, N., & Tiwari, M. K. (2016). Composite particle algorithm for sustainable integrated dynamic ship routing and scheduling optimization. Computers and Industrial Engineering, 96(Supplement C), 201–215.CrossRefGoogle Scholar
  15. De, A., Kumar, S. K., Gunasekaran, A., & Tiwari, M. K. (2017). Sustainable maritime inventory routing problem with time window constraints. Engineering Applications of Artificial Intelligence, 61(Supplement C), 77–95.CrossRefGoogle Scholar
  16. Ding, G. Y., Liu, H., & He, X. Q. (2013). A novel disruption operator in particle swarm optimization. Applied Mechanics and Materials, 380–384, 1216–1220.CrossRefGoogle Scholar
  17. Dogan, B., & Olmez, T. (2015). A new metaheuristic for numerical function optimization: Vortex search algorithm. Information Sciences, 293, 125–145.CrossRefGoogle Scholar
  18. Eberhart, R., & Shi, Y. (2001). Tracking and optimizing dynamic systems with particle swarms. In Proceedings of the 2001 IEEE congress on evolutionary computation, IEEE (Vol. 1, pp. 94–100).Google Scholar
  19. Eberhart, R. C., & Shi, Y. (2000). Comparing inertia weights and constriction factors in particle swarm optimization. In Proceedings of the 2000 IEEE congress on evolutionary computation (pp. 84–88).Google Scholar
  20. Garca, S., Fernndez, 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. Information Sciences, 180, 2044–2064.CrossRefGoogle Scholar
  21. Guo, W., Li, W., Zhang, Q., Wang, L., Wu, Q., & Ren, H. (2014). Biogeography-based particle swarm optimization with fuzzy elitism and its applications to constrained engineering problems. Engineering Optimization, 46(11), 1465–1484.CrossRefGoogle Scholar
  22. Harwit, M. (2006). Astrophysical concepts. New York: Springer.Google Scholar
  23. He, Q., & Wang, L. (2007). A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Applied Mathematics and Computation, 186(2), 1407–1422.CrossRefGoogle Scholar
  24. Jiang, B., Wang, N., & Wang, L. (2013). Particle swarm optimization with age-group topology for multimodal functions and data clustering. Communications in Nonlinear Science and Numerical Simulation, 18, 3134–3145.CrossRefGoogle Scholar
  25. Kannan, B. K., & Kramer, S. N. (1994). An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. Journal of Mechanical Design, 116(2), 405–411.CrossRefGoogle Scholar
  26. Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. Tech. rep.Google Scholar
  27. Karagoz, S., & Yildiz, A. R. (2017). A comparison of recent metaheuristic algorithms for crashworthiness optimisation of vehicle thin-walled tubes considering sheet metal forming effects. International Journal of Vehicle Design, 73(1–3), 179–188.CrossRefGoogle Scholar
  28. Kennedy, J. (1999). Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In Proceedings of the 1999 IEEE congress on evolutionary computation, IEEE (Vol. 3, pp. 1931–1938).Google Scholar
  29. Kennedy, J. (2003). Bare bones particle swarms. In Proceedings of the 2003 IEEE swarm intelligence symposium, IEEE (pp. 80–87).Google Scholar
  30. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of the 1995 IEEE international conference on neural networks, IEEE (Vol. 4, pp. 1942–1948).Google Scholar
  31. Kennedy, J., & Mendes, R. (2002). Population structure and particle swarm performance. In Proceedings of the 2002 IEEE congress on evolutionary computation, IEEE (Vol. 2, pp. 1671–1676).Google Scholar
  32. Kiani, M., & Yildiz, A. R. (2016). A comparative study of non-traditional methods for vehicle crashworthiness and nvh optimization. Archives of Computational Methods in Engineering, 23(4), 723–734.CrossRefGoogle Scholar
  33. Kiran, M. S., & Gunduz, M. (2013). A recombination-based hybridization of particle swarm optimization and artificial bee colony algorithm for continuous optimization problems. Applied Soft Computing, 13(4), 2188–2203.CrossRefGoogle Scholar
  34. Kiran, M. S., Gundz, M., & Baykan, O. K. (2012). A novel hybrid algorithm based on particle swarm and ant colony optimization for finding the global minimum. Applied Mathematics and Computation, 219, 1515–1521.CrossRefGoogle Scholar
  35. Krohling, R. A., & Mendel, E. (2009). Bare bones particle swarm optimization with Gaussian or Cauchy jumps. In Proceedings of the 2009 IEEE congress on evolutionary computation, IEEE (pp. 3285–3291).Google Scholar
  36. Leu, M. S., Yeh, M. F., & Wang, S. C. (2013). Particle swarm optimization with grey evolutionary analysis. Applied Soft Computing, 13(10), 4047–4062.CrossRefGoogle Scholar
  37. Li, L. D., Xiaodong, L., & Xinghuo, Y. (2008). Power generation loading optimization using a multi-objective constraint-handling method via pso algorithm. In 2008 6th IEEE international conference on industrial informatics (pp. 1632–1637).Google Scholar
  38. Liang, J. J., & Suganthan, P. N. (2005). Dynamic multi-swarm particle swarm optimizer with local search. In Proceedings of the 2005 IEEE congress on evolutionary computation, IEEE, (Vol. 1, pp. 522–528).Google Scholar
  39. Liang, J. J., Qin, A. K., Suganthan, P. N., & Baskar, S. (2006). Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Transactions on Evolutionary Computation, 10(3), 281–295.CrossRefGoogle Scholar
  40. Lim, W. H., & Mat Isa, N. A. (2014). Particle swarm optimization with increasing topology connectivity. Engineering Applications of Artificial Intelligence, 27, 80–102.CrossRefGoogle Scholar
  41. Liu, J., Wu, C., Wu, G., & Wang, X. (2015). A novel differential search algorithm and applications for structure design. Applied Mathematics and Computation, 268, 246–269.CrossRefGoogle Scholar
  42. Liu, J., Teo, K. L., Wang, X., & Wu, C. (2016). An exact penalty function-based differential search algorithm for constrained global optimization. Soft Computing, 20(4), 1305–1313.CrossRefGoogle Scholar
  43. Lu, H., & Chen, W. (2006). Dynamic-objective particle swarm optimization for constrained optimization problems. Journal of Combinatorial Optimization, 12(4), 409–419.CrossRefGoogle Scholar
  44. Mendes, R., Kennedy, J., & Neves, J. (2004). The fully informed particle swarm: simpler, maybe better. IEEE Transactions on Evolutionary Computation, 8(3), 204–210.CrossRefGoogle Scholar
  45. Mezura-Montes, E., & Coello, C. A. C. (2005). Useful infeasible solutions in engineering optimization with evolutionary algorithms. MICAI, Springer, 3789, 652–662.Google Scholar
  46. Nasir, M., Das, S., Maity, D., Sengupta, S., Halder, U., & Suganthan, P. N. (2012). A dynamic neighborhood learning based particle swarm optimizer for global numerical optimization. Information Sciences, 209, 16–36.CrossRefGoogle Scholar
  47. Ni, Q., & Deng, J. (2013). A new logistic dynamic particle swarm optimization algorithm based on random topology. The Scientific World Journal, 2013, 8.CrossRefGoogle Scholar
  48. Ozsoydan, F. B., & Sipahioglu, A. (2013). Heuristic solution approaches for the cumulative capacitated vehicle routing problem. Optimization, 62(10), 1321–1340.CrossRefGoogle Scholar
  49. Parsopoulos, K. E., & Vrahatis, M. N. (2004). Upso: A unified particle swarm optimization scheme. Lecture Series on Computer and Computational Sciences, 1, 868–873.Google Scholar
  50. Parsopoulos, K. E., & Vrahatis, M. N. (2005). Unified particle swarm optimization for solving constrained engineering optimization problems. Lecture Notes in Computer Science, 3612, 582–591.CrossRefGoogle Scholar
  51. Peram, T., Veeramachaneni, K., & Mohan, C. K. (2003). Fitness-distance-ratio based particle swarm optimization. In Proceedings of the 2003 IEEE swarm intelligence symposium, IEEE (pp. 174–181).Google Scholar
  52. Pholdee, N., Bureerat, S., & Yildiz, A. R. (2017). Hybrid real-code population-based incremental learning and differential evolution for many-objective optimisation of an automotive floor-frame. International Journal of Vehicle Design, 73(1–3), 20–53.CrossRefGoogle Scholar
  53. Ratnaweera, A., & Halgamuge, S. K. (2004). Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation, 8(3), 240–255.CrossRefGoogle Scholar
  54. Sadollah, A., Bahreininejad, A., Eskandar, H., & Hamdi, M. (2013). Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problems. Applied Soft Computing, 13(5), 2592–2612.CrossRefGoogle Scholar
  55. Sarafrazi, S., Nezamabadi-pour, H., & Saryazdi, S. (2011). Disruption: A new operator in gravitational search algorithm. Scientia Iranica, 18(3), 539–548.CrossRefGoogle Scholar
  56. Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. In Proceedings of the 1998 IEEE world congress on computational intelligence, the 1998 IEEE international conference on evolutionary computation, IEEE (pp. 69–73).Google Scholar
  57. Shi, Y., & Eberhart, R. (2001). Fuzzy adaptive particle swarm optimization. In Proceedings of the 2001 congress on evolutionary computation, IEEE (Vol. 1, pp. 101–106).Google Scholar
  58. Soleimani, H., & Kannan, G. (2015). A hybrid particle swarm optimization and genetic algorithm for closed-loop supply chain network design in large-scale networks. Applied Mathematical Modelling, 39(14), 3990–4012.CrossRefGoogle Scholar
  59. Storn, R., & Price, K. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.CrossRefGoogle Scholar
  60. Suganthan, P. N., Hansen, N., Liang, J. J., Deb, K., Chen, Y., Auger, A., & Tiwari, S. (2005). Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL Report 2005005.Google Scholar
  61. Sun, J., Fang, W., Palade, V., Wu, X., & Xu, W. (2011). Quantum-behaved particle swarm optimization with gaussian distributed local attractor point. Applied Mathematics and Computation, 218, 3763–3775.CrossRefGoogle Scholar
  62. Sun, J., Wu, X., Palade, V., Fang, W., Lai, C. H., & Xu, W. (2012). Convergence analysis and improvements of quantum-behaved particle swarm optimization. Information Sciences, 193, 81–103.CrossRefGoogle Scholar
  63. Wang, H., Sun, H., Li, C., Rahnamayan, S., & Js, Pan. (2013). Diversity enhanced particle swarm optimization with neighborhood search. Information Sciences, 223, 119–135.CrossRefGoogle Scholar
  64. Xu, G. (2013). An adaptive parameter tuning of particle swarm optimization algorithm. Applied Mathematics and Computation, 219(9), 4560–4569.CrossRefGoogle Scholar
  65. Yeniay, O. (2005). Penalty function methods for constrained optimization with genetic algorithms. Mathematical and Computational Applications, 10(1), 45–56.CrossRefGoogle Scholar
  66. Yildiz, A. R. (2009). A novel particle swarm optimization approach for product design and manufacturing. The International Journal of Advanced Manufacturing Technology, 40(5), 617.CrossRefGoogle Scholar
  67. Yildiz, A. R. (2012). A new hybrid particle swarm optimization approach for structural design optimization in the automotive industry. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 226(10), 1340–1351.Google Scholar
  68. Yildiz, A. R. (2013). Comparison of evolutionary-based optimization algorithms for structural design optimization. Engineering Applications of Artificial Intelligence, 26(1), 327–333.CrossRefGoogle Scholar
  69. Yildiz, A. R., & Saitou, K. (2011). Topology synthesis of multicomponent structural assemblies in continuum domains. Journal of Mechanical Design, 133(1), 011008.CrossRefGoogle Scholar
  70. Yildiz, A. R., & Solanki, K. N. (2012). Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach. The International Journal of Advanced Manufacturing Technology, 59(1), 367–376.CrossRefGoogle Scholar
  71. Yildiz, A. R., Kurtulus, E., Demirci, E., Yildiz, B. S., & Karagoz, S. (2016a). Optimization of thin-wall structures using hybrid gravitational search and nelder-mead algorithm. Materials Testing, 58(1), 75–78.CrossRefGoogle Scholar
  72. Yildiz, B. S. (2017). A comparative investigation of eight recent population-based optimisation algorithms for mechanical and structural design problems. International Journal of Vehicle Design, 73(1–3), 208–218.CrossRefGoogle Scholar
  73. Yildiz, B. S., & Lekesiz, H. (2017). Fatigue-based structural optimisation of vehicle components. International Journal of Vehicle Design, 73(1–3), 54–62.CrossRefGoogle Scholar
  74. Yildiz, B. S., Lekesiz, H., & Yildiz, A. R. (2016b). Structural design of vehicle components using gravitational search and charged system search algorithms. Materials Testing, 58(1), 79–81.CrossRefGoogle Scholar
  75. Zavala, A. E. M., Aguirre, A. H., Diharce, E. R. V., & Rionda, S. B. (2008). Constrained optimization with an improved particle swarm optimization algorithm. International Journal of Intelligent Computing and Cybernetics, 1(3), 425–453.CrossRefGoogle Scholar
  76. Zhan, Z. H., Zhang, J., Li, Y., & Chung, H. S. (2009). Adaptive particle swarm optimization. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 39(6), 1362–1381.CrossRefGoogle Scholar
  77. Zhang, W. J., & Xie, X. F. (2003). Depso: Hybrid particle swarm with differential evolution operator. IEEE International Conference on Systems Man and Cybernetics, 4, 3816–3821.Google Scholar

Copyright information

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

Authors and Affiliations

  • Hao Liu
    • 1
    Email author
  • Yue Wang
    • 1
  • Liangping Tu
    • 1
  • Guiyan Ding
    • 1
  • Yuhan Hu
    • 1
  1. 1.School of ScienceUniversity of Science and Technology LiaoningAnshanChina

Personalised recommendations