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Model analysis and application case for complex multi-system evolutionary optimization

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Abstract

A complex system is made up of multiple related and coupled subsystems. Each subsystem has its own set of multiple constraints and objectives, and is commonly found in real-world applications. Biogeography-based complex system optimization (BBO/Complex) is a population-based evolutionary intelligence paradigm that has been developed to solve complex system problems. The paper first presents the framework of the proposed method that consists of within-subsystem migration, cross-subsystem migration, and mutation operators. Then a theoretical model of the proposed method is derived using Markov chain and the probability transition matrix of each operator, along with the generalized multinomial theorem. The model provides exact mathematical formulas that predict the limiting probabilities of optimization performance for each possible population in the proposed method. Additionally, simulation results of two sample problems, which include multiple subsystems and multiple objectives, confirm the Markov model derived. Finally, the performance of the proposed method is investigated on an application of a battery charging system, and numerical simulation shows that the proposed method is a promising optimization method for the studied complex system.

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Acknowledgements

This article was supported in part by the National Natural Science Foundation of China under Grant No. 52077213, the U.S. National Science Foundation under Grant No. 1344954, and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LY19F030011.

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Authors and Affiliations

  1. Department of Electrical Engineering, Shaoxing University, Shaoxing, Zhejiang, China

    Haiping Ma & Shengyi Sun

  2. Department of Electrical Engineering and Computer Science, Cleveland State University, Cleveland, OH, USA

    Dawei Du & Dan Simon

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  1. Haiping Ma
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  2. Shengyi Sun
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  3. Dawei Du
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  4. Dan Simon
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Contributions

HM performed the data analyses and wrote the main manuscript text; SS performed the experiment; DD helped perform the analysis with constructive discussions; SD contributed to the conception of the study. All authors reviewed the manuscript.

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Correspondence to Haiping Ma.

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Ma, H., Sun, S., Du, D. et al. Model analysis and application case for complex multi-system evolutionary optimization. Evol. Intel. 17, 2733–2748 (2024). https://doi.org/10.1007/s12065-024-00910-1

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  • DOI: https://doi.org/10.1007/s12065-024-00910-1

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