Advertisement

Soft Computing

, Volume 23, Issue 14, pp 5571–5582 | Cite as

Empirical study of particle swarm optimization inspired by Lotka–Volterra model in Ecology

  • Xianxiang WuEmail author
  • Muye Sun
  • Xiao Chen
  • Juan Wang
  • Baolong Guo
Methodologies and Application
  • 134 Downloads

Abstract

Particle swarm optimization (PSO) has been proved to be an effective technique in solving complex global optimization problems. Many modified versions of the original PSO algorithm emerged during the last 15 years. Many of those existing methods employ all particles in a single population which adopts the similar monotonic strategy. The loss of diversity resulted in the premature convergence problem. In this paper, we proposed a suite of multi-swarm Lotka–Volterra model inspired particle swarm optimization algorithms (MSLVPSO) to address the premature convergence problem. The intraspecific and interspecific cooperation and competition strategy of the proposed model dramatically increased diversity of particles. As a result, it makes the particles more likely to break away from the local optimum. In addition, we derived the method to set parameters and developed several cooperative–competitive schemes. We evaluated the proposed MSLVPSO algorithms using a variety of benchmark functions. We also compared our proposed method with typical single-swarm PSO algorithms. Our experimental results show that the proposed MSLVPSO optimizers outperform other state-of-the-art algorithms.

Keywords

Particle swarm optimization (PSO) Premature convergence problem Diversity loss Lotka–Volterra model Cooperative–competitive coevolution 

Notes

Acknowledgements

This research was supported in part by National Natural Science Foundation of China under Grants 61671356, 61571346, 61601352, 61704127 and 61105066, in part by Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant 17JK0989, in part by Fundamental Research Funds for the Central Universities under Grant JB141305. In addition, we are grateful to the anonymous reviewers and editors for their valuable suggestions and comments on the initial version of the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

References

  1. Blackwell T (2005) Particle swarms and population diversity. Soft Comput 9(11):793–802CrossRefzbMATHGoogle Scholar
  2. Blackwell T (2012) A study of collapse in bare bones particle swarm optimization. IEEE Trans Evolut Comput 16(3):354–372CrossRefGoogle Scholar
  3. Blackwell TM, Bentley PJ (2002) Dynamic search with charged swarms. In: Proceedings of the genetic and evolutionary computation conference, pp 19–26Google Scholar
  4. Blackwell T, Branke J (2006) Multiswarms, exclusion, and anti-convergence in dynamic environments. IEEE Trans Evolut Comput 10(4):459–472CrossRefGoogle Scholar
  5. Castillo O, Soto C, Valdez F (2018) A review of fuzzy and mathematic methods for dynamic parameter adaptation in the Firefly algorithm. In: Advances in data analysis with computational intelligence methods. In: Studies in computational intelligence, vol 738. Springer, ChamGoogle Scholar
  6. Clerc M, Kennedy J (2002) The particle swarm—explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evolut Comput 6(1):58–73CrossRefGoogle Scholar
  7. Dong D, Jie J, Zeng J et al (2008) Chaos-mutation-based Particle Swarm Optimizer for dynamic environment. In: 3rd international conference on intelligent system and knowledge engineering, 2008. ISKE 2008, vol 1, pp 1032–1037, 17–19 Nov 2008Google Scholar
  8. Eberhart RC, Shi Y (2000) Comparing inertia weights and constriction factors in particle swarm optimization. Proc 2000 Congr Evolut Comput 1:84–88CrossRefGoogle Scholar
  9. Eberhart RC, Yuhui S (2001) Tracking and optimizing dynamic systems with particle swarms. Proc 2001 Congr Evolut Comput 1:94–100CrossRefGoogle Scholar
  10. Gao Y-l, Duan Y-h (2007) A new particle swarm optimization algorithm with random inertia weight and evolution strategy. In: International conference on computational intelligence and security workshops, 2007. CISW 2007, pp 199–203, 15–19Google Scholar
  11. Gao Y, Yao Z, Xie S (2006) Particle swarm optimization algorithm based on population density. Syst Eng Electron 28(6):922–924zbMATHGoogle Scholar
  12. Ge D, Chen S, Wang Z et al (2018) Particle swarm evolutionary computation-based framework for optimizing the risk and cost of low-demand systems of nuclear power plants. J Nuclear Sci Technol 55(1):19–28CrossRefGoogle Scholar
  13. Higashi N, Iba H (2003) Particle swarm optimization with Gaussian mutation. In: Proceedings of the 2003 IEEE on swarm intelligence symposium, pp 72–79, 24–26Google Scholar
  14. Hu X, Eberhart RC (2002) Adaptive particle swarm optimization: detection and response to dynamic systems. Proc 2002 Congr Evolut Comput 2:1666–1670Google Scholar
  15. Jia D, Li L, Zhang Y et al (2006) Particle swarm optimization combined with chaotic and Gaussian mutation. In: The sixth world congress on intelligent control and automation, 2006. WCICA 2006, vol 1, pp 3281–3285Google Scholar
  16. Kennedy J, Eberhart R (1995) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942–1948CrossRefGoogle Scholar
  17. Li C, Yang S, Nguyen TT (2012) A self-learning particle swarm optimizer for global optimization problems. IEEE Trans Syst Man Cybern Part B Cybern 42(3):627–646CrossRefGoogle Scholar
  18. Lotka AJ (1910) Contribution to the theory of periodic reaction. J Phys Chem 14(3):271–274CrossRefGoogle Scholar
  19. Ma K, Hu S, Yang J (2018) Appliances scheduling via cooperative multi-swarm PSO under day-ahead prices and photovoltaic generation. Appl Soft Comput 62:504–513CrossRefGoogle Scholar
  20. Mikki SM, Kishk AA (2006) Quantum particle swarm optimization for electromagnetics. IEEE Trans Antennas Propag 54(10):2764–2775CrossRefGoogle Scholar
  21. Nabizadeh S, Rezvanian A, Meybodi MR (2012) Tracking extrema in dynamic environment using Multi-Swarm Cellular PSO with local search. Int J Electron Inform 1(1):29–37Google Scholar
  22. Ni Q, Du H, Pan Q et al (2017) An improved dynamic deployment method for wireless sensor network based on multi-swarm particle swarm optimization. Nat Comput 16(1):5–13MathSciNetCrossRefGoogle Scholar
  23. Odum EP, Barrett GW (2005) Fundamentals of ecology, 5th edn. Brooks Cole, Pacific GroveGoogle Scholar
  24. Pant M, Thangaraj R, Singh VP et al (2008) Particle swarm optimization using Sobol mutation. In: First international conference on emerging trends in engineering and technology, 2008. ICETET ’08, pp 367–372, 16–18 July 2008Google Scholar
  25. Qiu N, Gao Y, Fang J et al (2018) Topological Design of multi-cell hexagonal tubes under axial and lateral loading cases using a modified particle swarm algorithm. Appl Math Model 53:567–583CrossRefGoogle Scholar
  26. Rawal A, Rajagopalan P, Miikkulainen R (2010) Constructing competitive and cooperative agent behavior using coevolution. In: 2010 IEEE symposium on computational intelligence and games (CIG), pp 107–114, Aug 2010Google Scholar
  27. Thangaraj R, Pant M, Abraham A (2009) A new diversity guided particle swarm optimization with mutation. In: World congress on nature & biologically inspired computing, 2009. NaBIC 2009, pp 294–299, 9–11 Dec 2009Google Scholar
  28. Verhulst PH (1838) Notice sur la loi que la population poursuit dans son accroissement. Correspondance Mathématique et Physique 10:113–121Google Scholar
  29. Volterra V (1926) Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Mem Acad Lincei Roma 2:31–113zbMATHGoogle Scholar
  30. Wang G, Gandomi AH, Alavi AH et al (2016) A hybrid method based on krill herd and quantum-behaved particle swarm optimization. Neural Comput Appl 27(4):989–1006CrossRefGoogle Scholar
  31. Wang H, Liu Y, Li C et al (2007) A hybrid particle swarm algorithm with Cauchy mutation. In: Swarm intelligence symposium, 2007. SIS 2007. IEEE, pp 356–360, 1–5 April 2007Google Scholar
  32. Wang F, Zhang H, Li K et al (2018) A hybrid particle swarm optimization algorithm using adaptive learning strategy. Inf Sci.  https://doi.org/10.1016/j.ins.2018.01.027 MathSciNetGoogle Scholar
  33. Waples RS, Gaggiotti O (2006) What is a population? An empirical evaluation of some genetic methods for identifying the number of gene pools and their degree of connectivity. Mol Ecol 15(6):1419–1439CrossRefGoogle Scholar
  34. Wu X, Cheng B, Cao J et al (2008) Particle swarm optimization with normal cloud mutation. In: 7th World congress on intelligent control and automation, 2008. WCICA 2008, pp 2828-2832, 25–27 June 2008Google Scholar
  35. Wu X-X, Guo B-L, Wang J (2010) Lotka–Volterra model based particle swarm optimization. Control Decis 25(11):1619–1624zbMATHGoogle Scholar
  36. Yan Y, Guo B (2008) Particle swarm optimization inspired by r- and K-selection in ecology. In: IEEE congress on evolutionary computation, 2008. CEC 2008, pp 1117–1123, 1–6 June 2008Google Scholar
  37. Yasuda T, Ohkura K, Matsumura Y (2010) Extended pso with partial randomization for large scale multimodal problems. In: World automation congress (WAC), pp 1–6, 19–23 Sept. 2010Google Scholar
  38. Ye W, Feng W, Fan S (2017) A novel multi-swarm particle swarm optimization with dynamic learning strategy. Appl Soft Comput 61:832–843CrossRefGoogle Scholar
  39. Zhao Y, Guo B, Wu X et al (2014) Image recostruction algorithm for ECT based on dual particle swarm collaborative optimization. J Comput Res Dev 51(9):2094–2100Google Scholar
  40. Zheng LM, Wang Q, Zhang SX et al (2017) Population recombination strategies for multi-objective particle swarm optimization. Soft Comput 21:4693CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Intelligent Control and Image Engineering, School of Aerospace Science and TechnologyXidian UniversityXi’anPeople’s Republic of China
  2. 2.School of Technology and EngineeringXi’an Fanyi UniversityXi’anPeople’s Republic of China

Personalised recommendations