超多目标优化问题广泛存在于科学研究与工程实践中，在决策支持、优化调度、机器学习等方面的应用需求日益突出。然而现有的多目标优化技术大多存在计算复杂度高、可伸缩性差、所得到的近似Pareto最优解分布不均匀以及覆盖不完整等问题。本项目针对超多目标优化问题，基于不同的排序策略，研究更加高效的超多目标粒子群优化算法。具体研究包括：1）利用随机投影、空间映射等，给出超多目标环境下的结合收敛性与多样性的占优框架；2）利用构造的占优机制，给出粒子群算法求解超多目标的实现方法；3）利用随机优化、鞅理论，给出多目标粒子群算法的马尔科夫特性。在此基础上，给出关于设计多目标粒子群算法的理论依据。项目的研究对超多目标优化的理论发展和实际工程应用产生积极的推动作用，对于许多优化问题（如大规模大尺度调度）与前沿研究（如机器学习中参数优化）有较高的应用价值，具有重要的学术意义和工程应用前景。

Many-objective optimization problems exist widely in scientific research and engineering practice, and the application requirements in decision support, optimal scheduling and machine learning have become increasingly prominent. However, most of the existing multi-objective optimization techniques have the problems of high computational complexity, poor scalability, uneven distribution of approximate Pareto optimal solutions and incomplete coverage. Focusing on the many-objective optimization problem, this project intends to study more efficient particle swarm optimization algorithm based on different ranking strategies. Specific research problems include: 1) using random projection, spatial mapping, etc. to give a dominant framework combining convergence and diversity in many-objective environment; 2) using the formulated dominant mechanism to give a particle swarm algorithm for solving the many-objective problems; 3) using the stochastic optimization and martingale theory to gave the Markov characteristic of multi-objective particle swarm optimization. Based on this, the theoretical basis for designing a multi-objective particle swarm optimization algorithm will also be given. The research of this project will play a positive role in promoting the theoretical development and practical application of the many-objective optimization algorithm. It will have a high application value for many optimization problems (e.g., large-scale scheduling) and frontier research (e.g., parameter optimization in machine learning), which has important academic significance and engineering application prospect.