Particle swarm optimization (PSO) is one of the most popular stochastic swarm-based metaheuristic algorithms. Kalman filter principle is introduced to predict the global optimum more accurately to enhance convergence. However, the evolution of particles in current Kalman PSO merely depends on the adjustment based on observation. In this paper, a modified Kalman particle swarm optimization (MKPSO) algorithm is proposed. The population is extended with the estimated optimum based on Kalman filtering, in which the prediction model is formulated as the weighted central optimum. Benchmark functions in the CEC14 test suite are adopted to verify the effectiveness of MKPSO. Numerical results show that MKPSO is more effective in mining capability for high-dimensional problems. Besides, the superiority of MKPSO lies in solving hybrid optimization problems. At last, MKPSO is applied to maximize the attainable moments subset of very flexible aircraft (VFA) on account for redundancy of control surfaces. Simulation results reveal that there is a trade-off between flight and control performance for VFA.

粒子群优化（PSO）是最流行的基于随机群的元启发式算法之一。引入卡尔曼滤波原理以更准确地预测全局最优值以增强收敛性。但是，当前的Kalman PSO中粒子的演化仅取决于基于观测的调整。本文提出了一种改进的卡尔曼粒子群算法（MKPSO）。通过基于卡尔曼滤波的估计最优值扩展总体，其中将预测模型公式化为加权中心最优值。采用CEC14测试套件中的基准功能来验证MKPSO的有效性。数值结果表明，MKPSO对高维问题的挖掘能力更有效。此外，MKPSO的优势在于解决混合优化问题。最后，由于控制面的冗余性，MKPSO被用于最大化非常灵活的飞机（VFA）的可达到的力矩子集。仿真结果表明，VFA在飞行性能和控制性能之间需要权衡。