IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2310-d853996.html
   My bibliography  Save this article

Improved Particle Swarm Optimization Algorithms for Optimal Designs with Various Decision Criteria

Author

Listed:
  • Chang Li

    (Department of Insurance, Shandong University of Finance and Economics, Jinan 250002, China)

  • Daniel C. Coster

    (Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA)

Abstract

Particle swarm optimization (PSO) is an attractive, easily implemented method which is successfully used across a wide range of applications. In this paper, utilizing the core ideology of genetic algorithm and dynamic parameters, an improved particle swarm optimization algorithm is proposed. Then, based on the improved algorithm, combining the PSO algorithm with decision making, nested PSO algorithms with two useful decision making criteria (optimistic coefficient criterion and minimax regret criterion) are proposed . The improved PSO algorithm is implemented on two unimodal functions and two multimodal functions, and the results are much better than that of the traditional PSO algorithm. The nested algorithms are applied on the Michaelis–Menten model and two parameter logistic regression model as examples. For the Michaelis–Menten model, the particles converge to the best solution after 50 iterations. For the two parameter logistic regression model, the optimality of algorithms are verified by the equivalence theorem. More results for other models applying our algorithms are available upon request.

Suggested Citation

  • Chang Li & Daniel C. Coster, 2022. "Improved Particle Swarm Optimization Algorithms for Optimal Designs with Various Decision Criteria," Mathematics, MDPI, vol. 10(13), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2310-:d:853996
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2310/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2310/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dette, Holger & Wong, Weng Kee, 1999. "E-optimal designs for the Michaelis-Menten model," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 405-408, October.
    2. Kangge Zou & Yanmin Liu & Shihua Wang & Nana Li & Yaowei Wu & Nan-Jing Huang, 2021. "A Multiobjective Particle Swarm Optimization Algorithm Based on Grid Technique and Multistrategy," Journal of Mathematics, Hindawi, vol. 2021, pages 1-17, December.
    3. Ren‐Raw Chen & Wiliam Kaihua Huang & Shih‐Kuo Yeh, 2021. "Particle swarm optimization approach to portfolio construction," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 28(3), pages 182-194, July.
    4. Joy King & Weng-Kee Wong, 2000. "Minimax D-Optimal Designs for the Logistic Model," Biometrics, The International Biometric Society, vol. 56(4), pages 1263-1267, December.
    5. Yanmin Wu & Qipeng Song, 2021. "Improved Particle Swarm Optimization Algorithm in Power System Network Reconfiguration," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-10, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jiyuan Wang & Kaiyue Wang & Xiangfang Yan & Chanjuan Wang, 2022. "A Hybrid Learning Particle Swarm Optimization With Fuzzy Logic for Sentiment Classification Problems," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), IGI Global, vol. 16(1), pages 1-23, January.
    2. Juan Pérez & Héctor López-Ospina, 2022. "Competitive Pricing for Multiple Market Segments Considering Consumers’ Willingness to Pay," Mathematics, MDPI, vol. 10(19), pages 1-32, October.
    3. Manuel Jaramillo & Diego Carrión & Jorge Muñoz, 2022. "A Deep Neural Network as a Strategy for Optimal Sizing and Location of Reactive Compensation Considering Power Consumption Uncertainties," Energies, MDPI, vol. 15(24), pages 1-21, December.
    4. Manuel Jaramillo & Diego Carrión, 2022. "An Adaptive Strategy for Medium-Term Electricity Consumption Forecasting for Highly Unpredictable Scenarios: Case Study Quito, Ecuador during the Two First Years of COVID-19," Energies, MDPI, vol. 15(22), pages 1-19, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Masoudi, Ehsan & Holling, Heinz & Wong, Weng Kee, 2017. "Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 330-345.
    2. Sahu, Nitesh & Babu, Prabhu, 2021. "A new monotonic algorithm for the E-optimal experiment design problem," Statistics & Probability Letters, Elsevier, vol. 174(C).
    3. Adewale, Adeniyi J. & Xu, Xiaojian, 2010. "Robust designs for generalized linear models with possible overdispersion and misspecified link functions," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 875-890, April.
    4. J. López Fidalgo & I. M. Ortiz Rodr�guez & Weng Kee Wong, 2011. "Design issues for population growth models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 501-512, November.
    5. Wong, Weng Kee & Melas, Viatcheslav B. & Dette, Holger, 2004. "Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function," Technical Reports 2004,24, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
    7. Belmiro P. M. Duarte & Weng Kee Wong, 2015. "Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach," International Statistical Review, International Statistical Institute, vol. 83(2), pages 239-262, August.
    8. Dette, Holger & Melas, Viatcheslav B. & Strigul, Nikolay, 2003. "Design of experiments for microbiological models," Technical Reports 2003,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Manuel Jaramillo & Diego Carrión, 2022. "An Adaptive Strategy for Medium-Term Electricity Consumption Forecasting for Highly Unpredictable Scenarios: Case Study Quito, Ecuador during the Two First Years of COVID-19," Energies, MDPI, vol. 15(22), pages 1-19, November.
    10. Sheng Wu & Weng Kee Wong & Catherine M. Crespi, 2017. "Maximin optimal designs for cluster randomized trials," Biometrics, The International Biometric Society, vol. 73(3), pages 916-926, September.
    11. Xing, Zongyi & Zhu, Junlin & Zhang, Zhenyu & Qin, Yong & Jia, Limin, 2022. "Energy consumption optimization of tramway operation based on improved PSO algorithm," Energy, Elsevier, vol. 258(C).
    12. Maryam Safarkhani & Mirjam Moerbeek, 2016. "D-optimal designs for a continuous predictor in longitudinal trials with discrete-time survival endpoints," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 146-171, May.
    13. Karvanen, Juha & Kulathinal, Sangita & Gasbarra, Dario, 2009. "Optimal designs to select individuals for genotyping conditional on observed binary or survival outcomes and non-genetic covariates," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1782-1793, March.
    14. Holger Dette & Viatcheslav Melas & Andrey Pepelyshev, 2006. "Local c- and E-optimal Designs for Exponential Regression Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 407-426, June.
    15. García-Ródenas, Ricardo & García-García, José Carlos & López-Fidalgo, Jesús & Martín-Baos, José Ángel & Wong, Weng Kee, 2020. "A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    16. Zhaoyan Zhang & Shaoke Wang & Peiguang Wang & Ping Jiang & Hang Zhou, 2022. "Research on Fault Early Warning of Wind Turbine Based on IPSO-DBN," Energies, MDPI, vol. 15(23), pages 1-18, November.
    17. Mandal, Nripes Kumar & Pal, Manisha, 2013. "Maximin designs for the detection of synergistic effects," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1632-1637.
    18. Dette, Holger & Haines, Linda M. & Imhof, Lorens A., 2003. "Bayesian and maximin optimal designs for heteroscedastic regression models," Technical Reports 2003,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2310-:d:853996. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.