Abstract: Although the particle swarm optimization (PSO) algorithm has demonstrated good performance in solving many optimization problems, maintaining population diversity while ensuring convergence accuracy, preventing the swarm from getting trapped in local optima, and balancing exploration and exploitation remain important research problems for PSO algorithms. In response to these issues, this paper proposes an attention learning particle swarm optimization algorithm guided by aggregation indicator (ALPSO-AI). Firstly, to effectively maintain population diversity, the entire population is divided into equally sized subswarms, which are recombined during the evolution process. In each generation, different particles in the subswarms adaptively select multiple high-quality learning objects based on their performance. An external archive is established to guide the search and evaluate the evolutionary progress of the population. Secondly, an attention mechanism is introduced to assign different attention weights to each learning object based on the difference between its performance and the updated particle??s fitness value. Thus, a high-quality learning prototype is generated for particle updates. Different scales of attention allocation methods are designed to meet the diverse search requirements in the early and late stages of the search process, enabling both global and local search capabilities. Furthermore, an aggregation indicator is introduced to the archive, which assesses the current population??s evolutionary level by examining the similarity of fitness values around the current best particle. When the aggregation indicator reaches a threshold, local search is initiated to enhance the overall convergence capability of the algorithm. Experimental evaluations are conducted on the 28 benchmark functions from the CEC2013 test suite in both 30 and 50 dimensions. ALPSO-AI is compared with five popular PSO variants and other optimization algorithms. Experimental results confirm the superiority of ALPSO-AI. The effectiveness of attention learning and the aggregation indicator is also thoroughly validated.

Key words: particle swarm optimization (PSO), attention mechanism, aggregation indicator, archive, local search

摘要： 尽管目前粒子群优化（PSO）算法在求解很多优化问题上表现出了良好的性能，但如何在保持种群多样性的同时确保收敛精度，防止群体陷入局部最优，平衡勘探与开发之间的矛盾，仍是粒子群优化算法研究需要解决的问题。针对这些问题，提出了一种聚集度指标引导的注意力学习粒子群优化算法（ALPSO-AI）。首先，为了有效保持种群多样性，整个种群被分成若干大小相等的子群，并且在进化过程中重新组合，在每一代中，子群中的不同粒子根据其性能自适应地选择多个优质的学习对象。种群外部设有存档，用于指导种群的搜索并评估进化程度；其次，引入注意力机制，根据每个学习对象与更新粒子适应值的差异，对每个学习对象赋予不同的注意力权重，生成一个高质量的学习榜样，用于粒子的更新。针对搜索前期和后期不同的搜索需求，分别设计不同尺度的注意力分配方式，进行全局搜索和局部搜索；此外，对存档引入聚集度指标，通过判断当前最优粒子周围的适应值相似度，评估当前种群进化水平，当聚集度指标达到阈值时，开启局部搜索，以增强算法的整体收敛能力。实验对CEC2013测试集的28个基准函数在30维和50维的空间分别进行测试，并与主流的5种变体PSO和其他优化算法进行比较，实验结果证明了ALPSO-AI的优越性。此外，注意力学习和聚集度指标的有效性也进行了充分的验证。

关键词: 粒子群优化（PSO）, 注意力机制, 聚集度指标, 存档, 局部搜索