XU Zhenxing1， ZHU Shuiran2
（1. School of Management Science and Engineering, Anhui University of echnology, Ma’anshan 243032， China； 2. School of Electrical and Information Engineering， Tianjin University， Tianjin 300072， China）
Abstract： To improve the convergence and distributivity of multi-objective particle swarm optimization, we propose a method for multi-objective particle swarm optimization by fusing multiple strategies (MOPSO-MS), which includes three strategies. Firstly, the average crowding distance method is proposed, which takes into account the influence of individuals on the crowding distance and reduces the algorithm’s time complexity and computational cost, ensuring efficient external archive maintenance and improving the algorithm’s distribution. Secondly, the algorithm utilizes particle difference to guide adaptive inertia weights. In this way, the degree of disparity between a particle’s historical optimum and the population’s global optimum is used to determine the value of w. With different degrees of disparity, the size of w is adjusted nonlinearly, improving the algorithm’s convergence. Finally, the algorithm is designed to control the search direction by hierarchically selecting the globally optimal policy, which can avoid a single search direction and eliminate the lack of a random search direction, making the selection of the global optimal position more objective and comprehensive, and further improving the convergence of the algorithm. The MOPSO-MS is tested against seven other algorithms on the ZDT and DTLZ test functions, and the results show that the MOPSO-MS has significant advantages in terms of convergence and distributivity.
Key words： multi-objective particle swarm optimization (MOPSO)； spatially crowding congestion distance； differential guidance weight； hierarchical selection of global optimum
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多策略融合改进的多目标粒子群算法
许振兴1， 祝水然2
（1. 安徽工业大学 管理科学与工程学院， 安徽 马鞍山 243032； 2. 天津大学 电气自动化与信息工程学院， 天津 300072）
摘要:为了提升多目标粒子群算法的收敛性和分布性， 提出了一种多策略融合改进的多目标粒子群优化算法（Multi-objective particle swarm optimization by fusing multiple strategies， MOPSO-MS）。 首先， 设计了空间平均拥挤距离法， 在全面考虑个体对拥挤距离的影响且降低算法时间复杂度和计算成本的基础上， 确保外部档案维护的高效性并提升了算法的分布性。 其次， 算法利用粒子差值指导自适应惯性权重， 以粒子的历史最优与种群最优粒子的差距程度来指导w取值， 随差距程度的不同非线性地调整w的大小， 可提升算法的收敛性。 最后， 设计分层选取全局最优策略， 以确定全局最优位置来控制搜索方向， 从而避免了搜索方向单一及搜索方向随机性不足， 使得全局最优位置选取更客观全面， 进一步提升了算法的收敛性。 该算法与另外8种算法在ZDT测试函数和DTLZ测试函数上进行对比试验， 结果表明， 该算法在收敛性和分布性上具有显著优势。
关键词:多目标粒子群算法； 空间平均拥挤距离； 差值指导； 分层选取全局最优
引用格式： XU Zhenxing， ZHU Shuiran． Multi-objective particle swarm optimization by fusing multiple strategies． Journal of Measurement Science and Instrumentation， 2022， 13（3）： 284-299. DOI： 10．3969／j．issn．1674-8042．2022．03．005
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