随机分形多目标粒子群优化算法及其在鄱阳湖综合承载能力分析中的应用研究

Multi-objective particle swarm optimization (MOPSO) algorithm is one of the effective methods to solve multi-objective optimization problems and has become a research hotspot of multi-objective optimization algorithm. However, the performance of MOPSO still needs to be improved, and the theoretical foundation of MOPSO is still inadequate till now, which restricts the design and application of MOPSO. In this project, based on the deep study on the basic features of MOPSO and the fractal theory, a particle swarm model based on the fractal Brown motion is established and an effective stochastic fractal multi-objective particle swarm optimization algorithm (stochastic fractal MOPSO algorithm) is proposed. The vector optimization theory is employed to analyze the convergence of the general MOPSO, and the global convergence of the stochastic fractal MOPSO algorithm is proved. The convergence speed of the stochastic fractal MOPSO algorithm is measured by the expected convergence time and the convergence order, respectively. Based on the theoretical analysis results of MOPSO, the improved stochastic fractal MOPSO algorithm is applied to the comprehensive carrying capacity of Poyang Lake which is a multi-objective optimization problem. This project not only provides a new method and idea for the design of MOPSO, but also lays the foundation for the theoretical analysis of MOPSO, and provides the theoretical guidance for the design and application of MOPSO.

多目标粒子群优化(MOPSO)算法是解决多目标优化问题的有效方法之一，并成为多目标优化算法的研究热点。但MOPSO算法的性能仍需提高，而且理论基础不完善，制约了算法的设计及应用。本项目深入研究MOPSO算法的基本特征和分形理论，建立基于分形布朗运动的粒子群模型，提出有效的随机分形多目标粒子群优化算法(随机分形MOPSO算法)。利用向量优化理论分析基本MOPSO算法的收敛性，进而证明随机分形MOPSO算法全局收敛,力图利用期望收敛时间和收敛阶衡量随机分形MOPSO算法的收敛速度。基于MOPSO算法的理论分析结果，把改进的随机分形MOPSO算法应用于鄱阳湖综合承载能力多目标优化问题。本项目既为MOPSO算法的设计提供了新的方法和思路且为MOPSO算法的理论分析奠定基础，又为MOPSO算法的设计及应用提供理论指导。

多目标粒子群优化(MOPSO)算法是解决多目标优化问题的有效方法之一，并成为多目标优化算法的研究热点。但MOPSO算法的理论基础不完善，制约了算法的设计及应用。本项目深入研究了MOPSO算法的基本特征，构建了其随机序列模型，利用概率理论证明了基本MOPSO算法以概率收敛，进而证明了MOPSO的改进版本以概率1收敛。基于MOPSO算法的收敛理论成果，把新信息引入MOPSO算法，提出了一种改进的MOPSO算法，实验结果表明提高了MOPSO算法的性能；也提出了几种改进的粒子群优化(PSO)算法，并应用于实际问题，实验结果表明提出的PSO算法性能优良。对本项目还进行了一些延伸研究。本项目通过基于理论分析成果设计的算法应证了理论分析的正确性，既为MOPSO算法的理论分析奠定了基础和MOPSO算法的进一步理论分析提供了新的方法和思路，又为MOPSO算法和PSO算法的设计及应用提供了理论指导。