Abstract
The mathematical description of the basic elements of particle swarm optimization (PSO) algorithm is summarized. It is proved that the solution space of PSO is normed space, and the iterative relationship of PSO is defined as the compressed mapping of normed space. The existence and uniqueness of PSO particle convergence position are strictly proved by using the related theory of Banach space and compressed mapping principle, and the mathematical description of convergence analysis of PSO algorithm is summarized. By introducing the probability theory and the classical theory of stochastic process, the parameter conditions for the stability of PSO algorithm are derived. It is proved that the probability of PSO algorithm converging to the global optimal position is 1.
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© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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He, S. (2022). Mathematical Basis of Particle Swarm Optimization Algorithm. In: Atiquzzaman, M., Yen, N., Xu, Z. (eds) 2021 International Conference on Big Data Analytics for Cyber-Physical System in Smart City. Lecture Notes on Data Engineering and Communications Technologies, vol 103. Springer, Singapore. https://doi.org/10.1007/978-981-16-7469-3_100
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DOI: https://doi.org/10.1007/978-981-16-7469-3_100
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