Efficient solution to the stagnation problem of the particle swarm optimization algorithm for phase diversity

Qi Xin; Ju Guohao; Xu Shuyan

摘要

The phase diversity (PD) technique needs optimization algorithms to minimize the error metric and find the global minimum. Particle swarm optimization (PSO) is very suitable for PD due to its simple structure, fast convergence, and global searching ability. However, the traditional PSO algorithm for PD still suffers from the stagnation problem (premature convergence), which can result in a wrong solution. In this paper, the stagnation problem of the traditional PSO algorithm for PD is illustrated first. Then, an explicit strategy is proposed to solve this problem, based on an in-depth understanding of the inherent optimization mechanism of the PSO algorithm. Specifically, a criterion is proposed to detect premature convergence; then a redistributing mechanism is proposed to prevent premature convergence. To improve the efficiency of this redistributing mechanism, randomized Halton sequences are further introduced to ensure the uniform distribution and randomness of the redistributed particles in the search space. Simulation results show that this strategy can effectively solve the stagnation problem of the PSO algorithm for PD, especially for large-scale and high-dimension wavefront sensing and noisy conditions. This work is further verified by an experiment. This work can improve the robustness and performance of PD wavefront sensing. (C) 2018 Optical Society of America

机译：相位分比（PD）技术需要优化算法，以最大限度地减少误差度量并找到全局最小值。粒子群优化（PSO）由于其结构简单，快速收敛和全球搜索能力，非常适合PD。然而，传统的PD PSO算法仍然存在停滞问题（早产），这可能导致错误的解决方案。本文首先说明了PD传统PSO算法的停滞问题。然后，提出了一种显式策略来解决这个问题，基于对PSO算法的固有优化机制的深入了解。具体地，提出了一种标准来检测过早收敛;然后提出了一种重新分配机制来防止过早收敛。为了提高该再分配机制的效率，进一步引入随机哈尔顿序列以确保搜索空间中重新分配粒子的均匀分布和随机性。仿真结果表明，该策略可以有效解决PD PSO算法的停滞问题，特别是对于大规模和高维波前感测和嘈杂的条件。通过实验进一步验证了这项工作。这项工作可以提高PD波前感的鲁棒性和性能。（c）2018年光学学会

Efficient solution to the stagnation problem of the particle swarm optimization algorithm for phase diversity

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