Skip to main content
Log in

Cooperative particle swarm optimizer with depth first search strategy for global optimization of multimodal functions

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper presents a Cooperative Particle Swarm Optimizer with Depth First Search Strategy (DFS-CPSO), which has better seacrch capality than classical Particle Swarm Optimizer (PSO) in solving multimodal optimization problems. In order to improve the quality of information exchange, the Depth First Search (DFS) strategy is hybridized to Cooperative Particle Swarm Optimization(CPSO), which makes information transfer more effectively and generates better quality solution. Specifically, DFS strategy enables different components of solution vector to exchange information separately with PSO and increases the diversity of the population, so that the information of solution components could be preserved by multiple iterations in CPSO. Confirmatory experiments are performed to prove the effectiveness of employing the DFS strategy to CPSO. The comparative results demonstrate superior performance of DFS-CPSO in solving high dimensional multimodal functions than CPSO and other advanced methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Wang H, Moon I, Yang S et al (2012) A memetic particle swarm optimization algorithm for multimodal optimization problems. Inform Sci 197:38–52

    Article  Google Scholar 

  2. Seo J, Im C, Heo C et al (2006) Multimodal function optimization based on particle swarm optimization. IEEE Trans Magn 42:1095–1098

    Article  Google Scholar 

  3. Liu Y, Ling X, Shi Z et al (2011) A survey on particle swarm optimization algorithms for multimodal function optimization. J Softw 6:2449–2455

    Google Scholar 

  4. Jamrus T, Chien CF, Gen M et al (2017) Hybrid particle swarm optimization combined with genetic operators for flexible job-shop scheduling under uncertain processing time for semiconductor manufacturing. IEEE Trans Semicond Manuf 31(1):32–41

    Article  Google Scholar 

  5. Khan S, Kamran M, Rehman OU et al (2018) A modified PSO algorithm with dynamic parameters for solving complex engineering design problem. Int J Comput Math 95(11):2308–2329

    Article  Google Scholar 

  6. Liu W, Wang Z, Liu X et al (2018) A novel particle swarm optimization approach for patient clustering from emergency departments. IEEE Trans Evol Comput 23(4):632–644

    Article  MathSciNet  Google Scholar 

  7. Xie Y, Xie S, Chen XX et al, Caccetta L (2015) An integrated predictive model with an on-line updating strategy for iron precipitation in zinc hydrometallurgy. Hydrometallurgy 151(1):62–72

  8. Cao Y, Zhang H, Li W, Chaovalitwongse WA et al (2018) Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Trans Evol Comput 23:718–731

    Article  Google Scholar 

  9. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: International conference on neural networks, pp 1942–1948

  10. Corus D, Dang D, Eremeev A et al (2017) Level-based analysis of genetic algorithms and other search processes. IEEE Trans Evol Comput 22(5):707–719

    Article  Google Scholar 

  11. Lee S, Kim SB (2019) Parallel simulated annealing with a greedy algorithm for bayesian network structure learning. IEEE Trans Knowl Data Eng 32(6):1157–1166

    Article  Google Scholar 

  12. Liang J, Qin AK, Suganthan PN et al (2018) Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Trans Evol Comput 23(4):718–731

    Google Scholar 

  13. Zhang J, Huang D, Liu K (2007) Multi-sub-swarm particle swarm optimization algorithm for multimodal function optimization. In: 2007 IEEE congress on evolutionary computation, pp 3215–3220

  14. Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. In: Congress on evolutionary computation, pp 1945–1950

  15. Chauhan P, Deep K, Pant M (2013) Novel inertia weight strategies for particle swarm optimization. Memet Comput 5(3):229–251

    Article  Google Scholar 

  16. Huang Y, Xu H, Gao H, Ma X, Hussain W (2021) SSUR: an approach to optimizing virtual machine allocation strategy based on user requirements for cloud data center. IEEE Trans Green Commun Netw 5:670–681

    Article  Google Scholar 

  17. Ma X, Gao H, Xu H, Bian M (2019) An IoT-based task scheduling optimization scheme considering the deadline and cost-aware scientific workflow for cloud computing. EURASIP J Wirel Commun Netw 2019:1–19

    Article  Google Scholar 

  18. Gao H, Zhang K, Yang J, Wu F, Liu H (2018) Applying improved particle swarm optimization for dynamic service composition focusing on quality of service evaluations under hybrid networks. Int J Distrib Sensor Netw 14:1550147718761583

    Google Scholar 

  19. Chang W (2017) Multimodal function optimizations with multiple maximums and multiple minimums using an improved PSO algorithm. Appl Soft Comput 60(11):60–72

    Article  Google Scholar 

  20. Zhang X, Liu H, Tu L (2020) A modified particle swarm optimization for multimodal multi-objective optimization. Eng Appl Artif Intell 95(10):103905

    Article  Google Scholar 

  21. Wang F, Zhang H, Li K et al (2018) A hybrid particle swarm optimization algorithm using adaptive learning strategy. Inform Sci 436(4):162–177

    Article  MathSciNet  Google Scholar 

  22. Wang J, Kumbasar T (2019) Parameter optimization of interval Type-2 fuzzy neural networks based on PSO and BBBC methods. IEEE/CAA J Automat Sin 6:247–257

    Article  Google Scholar 

  23. Li C, Yang S, Nguyen TT (2011) A self-learning particle swarm optimizer for global optimization problems. IEEE Trans Syst Man Cybern Part B (Cybernetics) 42(3):627–646

    Google Scholar 

  24. Wang X-H, Li J-J (2004) Hybrid particle swarm optimization with simulated annealing. In: International conference on machine learning and cybernetics, pp 2402–2405

  25. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713

    Article  Google Scholar 

  26. Potter MA, De Jong KA (1994) A cooperative coevolutionary approach to function optimization. In: International conference on parallel problem solving from nature, pp 249–257

  27. Van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 8(3):225–239

    Article  Google Scholar 

  28. Wang J, Kumbasar T (2019) Parameter optimization of interval Type-2 fuzzy neural networks based on PSO and BBBC methods. IEEE/CAA J Automat Sin 6(1):247–257

    Article  Google Scholar 

  29. Gao S, Zhou M, Wang Y, Cheng J, Yachi H, Wang J (2018) Dendritic neuron model with effective learning algorithms for classification, approximation, and prediction. IEEE Trans Neural Netw Learn Syst 30(2):601–614

    Article  Google Scholar 

  30. Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. In: Congress on evolutionary computation, pp 1945–1950

  31. Nickabadi A, Ebadzadeh MM, Safabakhsh R (2011) A novel particle swarm optimization algorithm with adaptive inertia weight. Appl Soft Comput 11(4):3658–3670

    Article  Google Scholar 

  32. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: International symposium on micro machine and human science, pp 39–43

  33. Liang J, Suganthan PN Dynamic multi-swarm particle swarm optimizer, pp 124–129

  34. Peram T, Veeramachaneni K, Mohan CK (2003) Fitness-distance-ratio based particle swarm optimization. In: Swarm intelligence symposium, pp 174–181

  35. Zhang Q et al (2017) Vector coevolving particle swarm optimization algorithm. Inf Sci 394:273–298

    Article  Google Scholar 

  36. Xu X et al (2015) Dynamic multi-swarm particle swarm optimizer with cooperative learning strategy. Appl Soft Comput 29:169–183

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Science Foundation for Distinguished Young Scholars of China under grant No. 61725306,the National Natural Science Foundation of China under grant No. 62003370, the Nature Science Foundation of Hunan province (Grant No. 2021JJ30873) and Changsha Municipal Natural Science Foundation (Grant No. kq2014137).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shiwen Xie.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Xie, Y., Xie, S. et al. Cooperative particle swarm optimizer with depth first search strategy for global optimization of multimodal functions. Appl Intell 52, 10161–10180 (2022). https://doi.org/10.1007/s10489-021-03005-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-03005-x

Keywords

Navigation