A fast PSO algorithm based on Alpha-stable mutation and its application in aerodynamic optimization

基于Alpha-stable的粒子群算法变异策略研究及气动优化应用

AVIC Xi'an Aeronautics Computing Technique Research Institute, Xi'an 710065, China

Received: 6 March 2022

Abstract

提出了一种基于Alpha stable分布的新型变异方法。针对粒子群算法容易陷入局部最优的缺点, 通过对比分析确定了一种调整Alpha stable分布的稳态系数动态变异策略, 使粒子群算法能够在搜索初始阶段具有更强的种群多样性以及算法探索能力, 减少陷入局部最优的可能; 在算法末期增强粒子群优化算法的局部搜索能力, 提高解的精度。将基于Alpha stable变异的粒子群优化算法(Alpha stable particle swarm optimization, ASPSO)与多种改进型粒子群优化算法以及差分进化算法(differential evolution algorithm, DE)进行了比较, 基准测试函数结果表明新建立的ASPSO算法极大地提高了算法的收敛速度和精度。将其应用到RAE2822翼型的单点跨声速减阻优化中, 在保持种群规模等参数相同的情形下, ASPSO算法的优化效果和效率都远高于传统PSO算法, 最终得到的翼型也比PSO优化的翼型具有更高的升阻比, 翼面波阻有明显降低。

摘要

In this paper, a novel mutation method based on Alpha stable distribution is proposed. Aiming at the shortcoming that the particle swarm optimization (PSO) is easy to fall into local optimum, a dynamic mutation strategy of Alpha stable distribution is determined through comparative analysis. This mutation strategy can make the particle swarm optimization algorithm based on Alpha-stable (ASPSO) have stronger population diversity and exploration ability in the initial stage of search, and make the algorithm avoid falling into local optimum. At the end of the algorithm, it can also enhance the local search ability of the particle swarm optimization algorithm and improve the accuracy of the solution. The ASPSO algorithm is compared with several improved particle swarm optimization algorithms and differential evolution algorithm. The benchmark function results show that the new ASPSO algorithm greatly improves the convergence speed and accuracy of the algorithm. Finally, both PSO and ASPSO algorithms were applied to a minimal drag optimization design of the RAE2822 airfoil and compared. The comparisons show that the ASPSO algorithm achieves a lower drag in a faster rate which lifts and pitching moment is well constrained.