Human behaviour-based particle swarm optimization (HPSO) is an improved particle swarm optimization (PSO) algorithm, which can effectively increase the diversity of population, convergence speed and precision by changing particles’ flight schema. In this paper, the first- and second-order stabilities of HPSO on the assumption that the personal optimum, the global optimum and the global worst particle are mutual independence during the whole evolutionary process, while the expectations and variances of particles’ positions vary with time so that our calculations do not require the stagnation assumption. The first- and second-order stabilities of HPSO are expressed by stochastic recurrence relation. The convergence boundaries of HPSO are obtained, and which show that the stabilities of HPSO are independent of the expectations and variances of the personal best and the global best. In addition, the reason for choosing the coefficient of the impelled/penalized term in HPSO is analysed, and the results of simulation experiments further confirm the theoretical analysis. Finally, HPSO is used to solve four real-world engineering design problems. Experimental results further confirm the theoretic results and illustrate that the performance of HPSO is promising and competitive.

基于人类行为的粒子群优化算法（HPSO）是一种改进的粒子群优化算法（PSO），可以通过改变粒子的飞行模式有效地增加种群的多样性，收敛速度和精度。在本文中，HPSO的一阶和二阶稳定性假定个人最优，全局最优和全局最坏粒子在整个进化过程中是相互独立的，而粒子位置的期望和方差随时间，以便我们的计算不需要停滞假设。HPSO的一阶和二阶稳定性由随机递归关系表示。获得了HPSO的收敛边界，并且表明HPSO的稳定性独立于个人最佳和全球最佳的期望和差异。此外，分析了在HPSO中选择加罚项的系数的原因，仿真实验的结果进一步证实了理论分析。最后，HPSO用于解决四个实际工程设计问题。实验结果进一步证实了理论结果，并说明HPSO的性能是有前途的和有竞争力的。