Handling multi-objective optimization problems with a comprehensive indicator and layered particle swarm optimizer

Xianzi Zhang; Yanmin Liu; Jie Yang; Jun Liu; Xiaoli Shu; Xianzi Zhang; Yanmin Liu; Jie Yang; Jun Liu; Xiaoli Shu

doi:10.3934/mbe.2023666

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14866-14898. doi: 10.3934/mbe.2023666

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Research article

Handling multi-objective optimization problems with a comprehensive indicator and layered particle swarm optimizer

1.
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
2.
School of Mathematics, Zunyi Normal College, Zunyi 563002, China

Received: 23 March 2023 Revised: 21 June 2023 Accepted: 26 June 2023 Published: 10 July 2023

The multi-objective particle swarm optimization algorithm has several drawbacks, such as premature convergence, inadequate convergence, and inadequate diversity. This is particularly true for complex, high-dimensional, multi-objective problems, where it is easy to fall into a local optimum. To address these issues, this paper proposes a novel algorithm called IMOPSOCE. The innovations for the proposed algorithm mainly contain three crucial factors: 1) an external archive maintenance strategy based on the inflection point distance and distribution coefficient is designed, and the comprehensive indicator (CM) is used to remove the non-dominated solutions with poor comprehensive performance to improve the convergence of the algorithm and diversity of the swarm; 2) using the random inertia weight strategy to efficiently control the movement of particles, balance the exploration and exploitation capabilities of the swarm, and avoid excessive local and global searches; and 3) offering different flight modes for particles at different levels after each update to further enhance the optimization capacity. Finally, the algorithm is tested on 22 typical test functions and compared with 10 other algorithms, demonstrating its competitiveness and outperformance on the majority of test functions.
- distribution coefficient,
- distance of inflection point,
- multi-objective optimization,
- multi-objective particle swarm optimization
Citation: Xianzi Zhang, Yanmin Liu, Jie Yang, Jun Liu, Xiaoli Shu. Handling multi-objective optimization problems with a comprehensive indicator and layered particle swarm optimizer[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14866-14898. doi: 10.3934/mbe.2023666

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Abstract

The multi-objective particle swarm optimization algorithm has several drawbacks, such as premature convergence, inadequate convergence, and inadequate diversity. This is particularly true for complex, high-dimensional, multi-objective problems, where it is easy to fall into a local optimum. To address these issues, this paper proposes a novel algorithm called IMOPSOCE. The innovations for the proposed algorithm mainly contain three crucial factors: 1) an external archive maintenance strategy based on the inflection point distance and distribution coefficient is designed, and the comprehensive indicator (CM) is used to remove the non-dominated solutions with poor comprehensive performance to improve the convergence of the algorithm and diversity of the swarm; 2) using the random inertia weight strategy to efficiently control the movement of particles, balance the exploration and exploitation capabilities of the swarm, and avoid excessive local and global searches; and 3) offering different flight modes for particles at different levels after each update to further enhance the optimization capacity. Finally, the algorithm is tested on 22 typical test functions and compared with 10 other algorithms, demonstrating its competitiveness and outperformance on the majority of test functions.

References

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