Research and Application of Multi-Objective Particle Swarm Optimization Algorithm Based on α-Stable Distribution

基于α-stable分布的多目标粒子群算法研究及应用

School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

Received: 4 April 2018

Abstract

The multi-objective particle swarm optimization algorithm (MOPSO) has been applied and modified for optimal designs in various engineering fields. However, the intimal algorithm is still has the problems of low accuracy and poor diversity of solutions as it is easy to fall into local optimum in the later evolution stage. A new dynamic mutation operator has been established based on the α-stable distribution theory and incorporated with multi-objective particle swarm optimization algorithm(ASMOPSO). By using random Numbers which generated by the α-stable distribution, the population of PSO algorithm was mutated. And this mutate operation increases the diversity of the population. Because the stability coefficient in the ASMOPSO algorithm can change the range and amplitude of the mutation. This operation makes the new algorithm has the ability to balance the calculation accuracy and global optimization. Several benchmark functions test show that the ASMOPSO algorithm has fast global optimization ability. The proposed algorithm is applied to the multi-objective aerodynamic optimization design of RAE2822 transonic airfoil. The comparison results also show that ASMOPSO algorithm is more excellent than the basic MOPSO algorithm.

摘要

多目标的粒子群算法（MOPSO）在各个领域的优化设计中得到了广泛应用及改进，但是目前仍然存在着在进化后期容易陷入局部最优导致收敛精度低、解的多样性差等问题。引入α-stable分布理论，发展建立了一种新的基于α-stable动态变异的多目标粒子群优化算法（ASMOPSO）。通过α-stable分布生成随机数对PSO算法的种群进行变异操作，增加种群的多样性，在算法中动态调整稳定性系数α实现变异范围和幅度的变化，从而使得改进的ASMOPSO算法具有兼顾计算精度和全局寻优的能力。使用ZDT系列无约束函数和带约束的Tanaka及Srinivas函数对改进前后的算法进行了测试，结果显示出了ASMOPSO算法的快速全局寻优性能。将改进后的算法应用到RAE2822跨音速翼型的减阻和力矩绝对值不增大的综合优化中，得到了较好的多目标气动优化结果。