Multi-objective particle swarm optimization algorithms encounter significant challenges when tackling many-objective optimization problems. This is mainly because of the imbalance between convergence and diversity that occurs when increasing the selection pressure. In this paper, a novel adaptive MOPSO (ANMPSO) algorithm based on R2 contribution and adaptive method is developed to improve the performance of MOPSO. First, a new global best solutions selection mechanism with R2 contribution is introduced to select leaders with better diversity and convergence. Second, to obtain a uniform distribution of particles, an adaptive method is used to guide the flight of particles. Third, a re-initialization strategy is proposed to prevent particles from trapping into local optima. Empirical studies on a large number (64 in total) of problem instances have demonstrated that ANMPSO performs well in terms of inverted generational distance and hyper-volume metrics. Experimental studies on the practical application have also revealed that ANMPSO could effectively solve problems in the real world.

多目标粒子群优化算法在处理多目标优化问题时遇到了重大挑战。这主要是因为增加选择压力时会出现收敛性和多样性之间的不平衡。在本文中，开发了一种基于R2贡献和自适应方法的新型自适应 MOPSO（ANMPSO）算法，以提高 MOPSO 的性能。一、新的全球最佳解决方案选择机制与R2贡献被引入以选择具有更好多样性和融合性的领导者。其次，为了获得粒子的均匀分布，采用自适应方法引导粒子飞行。第三，提出了一种重新初始化策略，以防止粒子陷入局部最优。对大量（总共 64 个）问题实例的实证研究表明，ANMPSO 在反向代际距离和超容量指标方面表现良好。实际应用的实验研究也表明，ANMPSO 可以有效地解决现实世界中的问题。