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<p>Chaotic systems are deterministic dynamic systems characterized by highly complex and unpredictable behaviors.Parameters of existing chaotic systems typically depend on arbitrary selection, which hinders ensuring optimal parameters and restricts their practical utility. Existing swarm intelligence algorithms fail to deliver effective and accurate solutions due to low search efficiency, susceptibility to local optima, and inability to handle multi-objective(MO) optimization problem. To provide a robust tool for chaotic design, the study proposes a MO Competition of Tribes and Cooperation of Members(MOCTCM) algorithm. Innovatively integrates MO solution management with adaptive parameter adjustment, while fusing Gaussian perturbation and competitive learning to balance exploration and exploitation. Subsequently, MOCTCM was evaluated on three well-established MO optimization benchmark test sets. Experimental results show that, compared to the state-of-the-art MO optimization algorithm, MOCTCM exhibits superior competitiveness in convergence and robustness. Finally, its MO optimization capability was further validated on a 3D MO optimization chaos (3D-MOC) with 9 decision parameters. The optimization objectives were three chaotic performance metrics: Lyapunov exponent (LE), correlation dimension (CD), and 0-1 test. Further evaluation shows that MOCTCM-optimized 3D-MOC exhibits excellent ergodicity and randomness, with chaotic performance significantly surpassing existing chaotic systems. Moreover, MOCTCM outperforms other comparative MO algorithms in chaotic optimization design, highlighting its advantages in balancing exploration and exploitation, maintaining solution diversity, and solving complex optimization problems.</p>

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Optimization design of 3D chaotic system based on a multi-objective competition of tribes and cooperation of members algorithm

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Xiaobing Liu,
  • Qing Ye,
  • Wei Liu,
  • Qian Zhou,
  • Shiqi Luo,
  • Zebin Song

摘要

Chaotic systems are deterministic dynamic systems characterized by highly complex and unpredictable behaviors.Parameters of existing chaotic systems typically depend on arbitrary selection, which hinders ensuring optimal parameters and restricts their practical utility. Existing swarm intelligence algorithms fail to deliver effective and accurate solutions due to low search efficiency, susceptibility to local optima, and inability to handle multi-objective(MO) optimization problem. To provide a robust tool for chaotic design, the study proposes a MO Competition of Tribes and Cooperation of Members(MOCTCM) algorithm. Innovatively integrates MO solution management with adaptive parameter adjustment, while fusing Gaussian perturbation and competitive learning to balance exploration and exploitation. Subsequently, MOCTCM was evaluated on three well-established MO optimization benchmark test sets. Experimental results show that, compared to the state-of-the-art MO optimization algorithm, MOCTCM exhibits superior competitiveness in convergence and robustness. Finally, its MO optimization capability was further validated on a 3D MO optimization chaos (3D-MOC) with 9 decision parameters. The optimization objectives were three chaotic performance metrics: Lyapunov exponent (LE), correlation dimension (CD), and 0-1 test. Further evaluation shows that MOCTCM-optimized 3D-MOC exhibits excellent ergodicity and randomness, with chaotic performance significantly surpassing existing chaotic systems. Moreover, MOCTCM outperforms other comparative MO algorithms in chaotic optimization design, highlighting its advantages in balancing exploration and exploitation, maintaining solution diversity, and solving complex optimization problems.