This article presents a new particle swarm optimization (PSO)-based multi-objective optimization algorithm, named multi-guide particle swarm optimization (MGPSO). The MGPSO is a multi-swarm approach, where each subswarm optimizes one of the objectives. An archive guide is added to the velocity update equation to facilitate convergence to a Pareto front of non-dominated solutions. An extensive empirical and stability analysis of the MGPSO is conducted. The empirical analysis focuses on the exploration behavior of the MGPSO and compares the performance of the MGPSO with that of state-of-the-art multi-objective PSO and evolutionary algorithms. The results show that the MGPSO is highly competitive on a number of benchmark functions. The paper provides a theoretical stability analysis which focuses on the sufficient and necessary conditions for order-1 and order-2 stability of the MGPSO. The paper extends existing work on MGPSO stability analysis by deriving new stability criteria for differing values of the acceleration coefficients used in the velocity update equation.

中文翻译：

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多目标优化的多导粒子群算法：经验和稳定性分析

本文提出了一种新的基于粒子群优化（PSO）的多目标优化算法，称为多向导粒子群优化（MGPSO）。MGPSO是一种多群方法，其中每个子群都优化了一个目标。存档指南已添加到速度更新方程式，以促进收敛到非支配解的Pareto前沿。对MGPSO进行了广泛的经验和稳定性分析。实证分析集中在MGPSO的探索行为上，并将MGPSO的性能与最新的多目标PSO和进化算法进行了比较。结果表明，MGPSO在许多基准功能上具有很高的竞争力。本文提供了理论上的稳定性分析，其重点在于MGPSO的1级和2级稳定性的充分必要条件。通过为速度更新方程中使用的加速度系数的不同值导出新的稳定性标准，本文扩展了MGPSO稳定性分析的现有工作。