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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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    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.
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    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.

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