Hybrid Cluster Particle Swarm Optimization (HCPSO)

Author: Tianjiang Says

Contributing institutions: School of Astronautics, Harbin Institute of Technology; National Key Laboratory of Rapid Design and Intelligent Swarm for Micro/Nano Spacecraft

References: Guan Yutong et al. Hyperparameter Auto-Tuning and Homotopy Methods for Spacecraft Long-Range Cooperative Rendezvous, Spacecraft Environment Engineering, 2026.

Definition

Hybrid Cluster Particle Swarm Optimization (HCPSO) is an improved particle swarm optimization algorithm that enhances global search capability by introducing a clustering mechanism and dual-strategy update scheme. HCPSO divides the particle swarm into multiple sub-populations, each searching independently and sharing information under certain conditions, effectively avoiding the tendency of standard PSO to converge to local optima.

Core Principles

Dual-Strategy Velocity Update

HCPSO maintains two sets of velocity update strategies:

Strategy 1 (global best based):

v′(Γ+1)=ω1v(Γ)+c11Λ1(p(Γ)−σ(Γ))+c12Λ2(pg(Γ)−σ(Γ))v'(\Gamma+1) = \omega_1 v(\Gamma) + c_{11}\Lambda_1(p(\Gamma) - \sigma(\Gamma)) + c_{12}\Lambda_2(p_g(\Gamma) - \sigma(\Gamma))

Strategy 2 (sub-population best based):

v′′(Γ+1)=ω2v(Γ)+c21Λ1(p(Γ)−σ(Γ))+c22Λ2(p1(Γ)−σ(Γ))v''(\Gamma+1) = \omega_2 v(\Gamma) + c_{21}\Lambda_1(p(\Gamma) - \sigma(\Gamma)) + c_{22}\Lambda_2(p_1(\Gamma) - \sigma(\Gamma))

Blended update:

v(Γ+1)=μqv′(Γ+1)+(1−μq)v′′(Γ+1)v(\Gamma+1) = \mu_q v'(\Gamma+1) + (1-\mu_q)v''(\Gamma+1)

Selection Probability Mechanism

Switching between the two strategies is governed by a selection probability psp_s:

v(Γ+1)={v′(Γ+1),rand<psv′′(Γ+1),rand≥psv(\Gamma+1) = \begin{cases} v'(\Gamma+1), & \text{rand} < p_s \\ v''(\Gamma+1), & \text{rand} \geq p_s \end{cases}

Application in Trajectory Optimization

In spacecraft cooperative rendezvous problems, HCPSO is used to solve the initial costate for energy-optimal problems. Compared with standard PSO, HCPSO has stronger global search capability and can more effectively find high-quality initial costate solutions.

Application by Zhao Han et al. (2026)

Zhao Han et al. combined HCPSO with DDPG deep reinforcement learning to form the RLEPSO algorithm, achieving autonomous dynamic tuning of algorithm parameters and significantly improving convergence speed and solution quality.

References

  • Guan Yutong, Gao Changsheng, Hu Yudong, Zhao Han. Hyperparameter Auto-Tuning and Homotopy Methods for Spacecraft Long-Range Cooperative Rendezvous[J]. Spacecraft Environment Engineering, 2026. [in Chinese]
  • Kennedy J, Eberhart R. Particle swarm optimization[C]. IEEE International Conference on Neural Networks, 1995.