[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Convergence analysis of flow direction algorithm and its improvement

  • Optimization
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Flow direction algorithm (FDA) is a new physics-based optimization algorithm for solving global optimization problems. Although the FDA has shown effectiveness in many areas, there has been a lack of rigorous theoretical guarantees. This paper first proves that FDA is globally convergent with probability 1 by establishing a Markov process model. Furthermore, to enhance the FDA’s exploration and exploitation abilities, we propose an improved FDA algorithm (IFDA) by introducing random opposition-based learning and an adaptive neighbour generation strategy. Finally, extensive experiments and statistical tests are investigated on the classical benchmark functions, CEC 2019 benchmark function, and wireless sensor network coverage optimization problem with several state-of-the-art algorithms, demonstrating the proposed algorithm’s efficiency and effectiveness.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

Data will be made available on request.

References

  • Ahmadianfar I, Bozorg-Haddad O, Chu X (2020) Gradient-based optimizer: a new metaheuristic optimization algorithm. Inf Sci 540:131–159

    MathSciNet  MATH  Google Scholar 

  • Ahmadianfar I, Heidari AA, Gandomi AH et al (2021) Run beyond the metaphor: an efficient optimization algorithm based on runge kutta method. Expert Syst Appl 181(115):079

    Google Scholar 

  • Ahmadianfar I, Heidari AA, Noshadian S et al (2022) Info: an efficient optimization algorithm based on weighted mean of vectors. Expert Syst Appl 195(116):516

    Google Scholar 

  • Chauhan S, Vashishtha G (2023) A synergy of an evolutionary algorithm with slime mould algorithm through series and parallel construction for improving global optimization and conventional design problem. Eng Appl Artif Intell 118(105):650

    Google Scholar 

  • Chauhan S, Vashishtha G, Kumar A (2022a) Approximating parameters of photovoltaic models using an amended reptile search algorithm. J Amb Intell Human Comput pp 1–16

  • Chauhan S, Vashishtha G, Kumar A, et al. (2022b) Conglomeration of reptile search algorithm and differential evolution algorithm for optimal designing of fir filter. Circuits, Syst Signal Process pp 1–22

  • Cheraghalipour A, Hajiaghaei-Keshteli M, Paydar MM (2018) Tree growth algorithm (TGA): a novel approach for solving optimization problems. Eng Appl Artif Intell 72:393–414

    Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the 6th international symposium on micro machine and human science, IEEE, pp 39–43

  • Erol OK, Eksin I (2006) A new optimization method: big bang-big crunch. Adv Eng Softw 37(2):106–111

    Google Scholar 

  • Faramarzi A, Heidarinejad M, Stephens B et al (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105–190

    Google Scholar 

  • Formato RA (2010) Central force optimization applied to the PBM suite of antenna benchmarks. Comput Res Repos 1003:1–89

    Google Scholar 

  • Hashim FA, Houssein EH, Mabrouk MS et al (2019) Henry gas solubility optimization: a novel physics-based algorithm. Futur Gener Comput Syst 101:646–667

    Google Scholar 

  • Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872

    Google Scholar 

  • Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Google Scholar 

  • Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput 44:148–175

    Google Scholar 

  • Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471

    MathSciNet  MATH  Google Scholar 

  • Karami H, Anaraki MV, Farzin S et al (2021) Flow direction algorithm (FDA): a novel optimization approach for solving optimization problems. Comput Ind Eng 156:107–224

    Google Scholar 

  • Kaveh A, Dadras A (2017) A novel meta-heuristic optimization algorithm: thermal exchange optimization. Adv Eng Softw 110:69–84

    Google Scholar 

  • Li S, Chen H, Wang M et al (2020) Slime mould algorithm: a new method for stochastic optimization. Futur Gener Comput Syst 111:300–323

    Google Scholar 

  • Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Google Scholar 

  • Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  • Mirjalili S, Gandomi AH, Mirjalili SZ et al (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Google Scholar 

  • Mohammadi-Balani A, Nayeri MD, Azar A et al (2021) Golden eagle optimizer: a nature-inspired metaheuristic algorithm. Comput Ind Eng 152(107):050

    Google Scholar 

  • 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 16:5–13

    MathSciNet  MATH  Google Scholar 

  • O’Callaghan JF, Mark DM (1984) The extraction of drainage networks from digital elevation data. Comput Vision, Graphics, Image Process 28(3):323–344

    Google Scholar 

  • Price K, Awad N, Ali M, et al (2018) The 100-digit challenge: problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization. Nanyang Technological University

  • Qian W, Li M (2018) Convergence analysis of standard particle swarm optimization algorithm and its improvement. Soft Comput 22(12):4047–4070

    MATH  Google Scholar 

  • Nn Qin, Jl Chen (2018) An area coverage algorithm for wireless sensor networks based on differential evolution. Int J Distrib Sens Netw 14(8):1550147718796734

    Google Scholar 

  • Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Google Scholar 

  • Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713. https://doi.org/10.1109/TEVC.2008.919004

    Article  Google Scholar 

  • Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  • Tan Y (2015) Fireworks algorithm. Germany, Springer, Heidelberg

    MATH  Google Scholar 

  • Tang D, Dong S, Jiang Y et al (2015) Itgo: Invasive tumor growth optimization algorithm. Appl Soft Comput 36:670–698

    Google Scholar 

  • Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC’06), IEEE, pp 695–701

  • Tu J, Chen H, Wang M et al (2021) The colony predation algorithm. J Bionic Eng 18:674–710

    Google Scholar 

  • Vashishtha G, Kumar R (2021) Centrifugal pump impeller defect identification by the improved adaptive variational mode decomposition through vibration signals. Eng Res Express 3(3):035041

    Google Scholar 

  • Vashishtha G, Kumar R (2022) An amended grey wolf optimization with mutation strategy to diagnose bucket defects in pelton wheel. Measurement 187(110):272

    Google Scholar 

  • Vashishtha G, Kumar R (2022) Unsupervised learning model of sparse filtering enhanced using wasserstein distance for intelligent fault diagnosis. J Vib Eng Technol 10:1–18

    Google Scholar 

  • Vashishtha G, Chauhan S, Singh M et al (2021) Bearing defect identification by swarm decomposition considering permutation entropy measure and opposition-based slime mould algorithm. Measurement 178(109):389

    Google Scholar 

  • Vashishtha G, Chauhan S, Kumar A et al (2022) An ameliorated African vulture optimization algorithm to diagnose the rolling bearing defects. Meas Sci Technol 33(7):075013

    Google Scholar 

  • Vashishtha G, Chauhan S, Yadav N et al (2022) A two-level adaptive chirp mode decomposition and tangent entropy in estimation of single-valued neutrosophic cross-entropy for detecting impeller defects in centrifugal pump. Appl Acoust 197(108):905

    Google Scholar 

  • Wang GG (2018) Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Comput 10(2):151–164

    Google Scholar 

  • Wang GG, Deb S, Cui Z (2019) Monarch butterfly optimization. Neural Comput Appl 31:1995–2014

    Google Scholar 

  • Wang J, Chen H (2018) Bsas: Beetle swarm antennae search algorithm for optimization problems. arXiv e-prints pp arXiv–1807

  • Xue J, Shen B (2020) A novel swarm intelligence optimization approach: sparrow search algorithm. Syst Sci Control Eng 8(1):22–34

    Google Scholar 

  • Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms, Springer, pp 169–178

  • Yang XS, He X (2013) Bat algorithm: literature review and applications. Int J Bio-inspired Comput 5(3):141–149

    Google Scholar 

  • Yang Y, Chen H, Heidari AA et al (2021) Hunger games search: visions, conception, implementation, deep analysis, perspectives, and towards performance shifts. Expert Syst Appl 177(114):864

    Google Scholar 

  • Yazdani M, Jolai F (2016) Lion optimization algorithm (LOA): a nature-inspired metaheuristic algorithm. J Comput Design Eng 3(1):24–36

    Google Scholar 

  • Zervoudakis K, Tsafarakis S (2020) A mayfly optimization algorithm. Comput Ind Eng 145:106–559

    Google Scholar 

  • Zhang Y, Dw Gong, Xy Sun et al (2014) Adaptive bare-bones particle swarm optimization algorithm and its convergence analysis. Soft Comput 18(7):1337–1352

    Google Scholar 

  • Zhang Y, Huang H, Wu H et al (2019) Theoretical analysis of the convergence property of a basic pigeon-inspired optimizer in a continuous search space. Sci China Inf Sci 62(7):1–9

    MathSciNet  Google Scholar 

  • Zhang Y, Jin Z, Mirjalili S (2020) Generalized normal distribution optimization and its applications in parameter extraction of photovoltaic models. Energy Convers Manage 224(113):301

    Google Scholar 

  • Zhang Y, Li S, Xu B (2021) Convergence analysis of beetle antennae search algorithm and its applications. Soft Comput 25(16):10595–10608

    Google Scholar 

  • Zhou Y, Zhao R, Luo Q et al (2018) Sensor deployment scheme based on social spider optimization algorithm for wireless sensor networks. Neural Process Lett 48:71–94

    Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China under Grants 61573233, the Key Project of Natural Science Foundation of Guangdong Province under grant 2015A030311017, and the team project of the university of Guangdong province (Grant Number 2015KCXTD018)

Funding

This research is supported by the National Natural Science Foundation of China under Grants 61573233, the Key Project of Natural Science Foundation of Guangdong Province under grant 2015A030311017, and the team project of the university of Guangdong province (Grant Number 2015KCXTD018)

Author information

Authors and Affiliations

  1. Department of Mathematics, Shantou University, Tuojiang Street, Shantou, 535063, Guangdong, China

    Wenwen Ye

  2. Department of Mechanical Engineering, Shantou University, Tuojiang Street, Shantou, 535063, Guangdong, China

    Shengping Li

  3. MOE Key Laboratory of Intelligent Manufacturing, Shantou University, Tuojiang Street, Shantou, 535063, Guangdong, China

    Wenwen Ye & Shengping Li

Authors
  1. Wenwen Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shengping Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Material preparation, data collection, and analysis were performed by WY. The first draft of the manuscript was written by WY. SL checked and revised the first draft. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Shengping Li.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ye, W., Li, S. Convergence analysis of flow direction algorithm and its improvement. Soft Comput 27, 14791–14818 (2023). https://doi.org/10.1007/s00500-023-08551-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-08551-9

Keywords

Search

Navigation