区间多目标粒子群优化算法及其应用

提出了一种区间多目标粒子群优化(IMOPSO)算法，用于解决多目标下区间变量的优化问题.基于区间可信度定义两个区间解的占优关系，通过归一化方法和区间拥挤度距离对Pareto最优解排序，并设立归档机制，利用外部存储器保存Pareto最优解集.针对有界误差系统的建模问题，提出了基于IMOPSO算法训练区间神经网络(INN)模型参数的建模方法，解决了误差界已知和误差界未知两种情况下的有界误差系统建模问题.最后，以一阶不确定系统为例，利用所提算法进行了建模仿真，验证了建模方法的有效性.

Interval Multi-objective Particle Swarm Optimization Algorithm and Its Application

An interval multi-objective particle swarm optimization(IMOPSO)algorithm was proposed to solve the optimization problem of interval variables under multi-objectives. A dominant relationship between two intervals was defined based on interval credibility. Normalization method and interval crowding distance were used to sort the Pareto-optimal solutions. And an archiving mechanism was set up to save the Pareto optimal set in the external memory. Then， an interval neural network(INN)employing the IMOPSO to train was proposed for the unknown-but-bounded(UBB)errors modeling problem， which can be suited for the two situations of the error bounds that is either known or unknown. The first-order uncertain system was taken as an example to verify the proposed method， and the simulation results validated the effectiveness.