基于RBF元模型集的多变量全局优化算法研究

Research of Multivariable Global Optimization Algorithm Based on RBF Meta-model Set

首先提出元模型集的概念,根据RBF函数的特点,将其系数向量转化为系数矩阵,使得多个变量可在同一元模型中进行仿真.其次针对通过采样点计算Pareto适存度矩阵困难的问题,提出了增量迭代式Pareto适存度计算方法,利用上一次迭代产生的适存度值直接更新,减少了计算工作量.最后将元模型集和增量Pareto适存度算法应用到多变量全局优化算法中,并将其应用于数值计算以及五杆平面桁架结构优化设计中.结果表明该方法科学合理,效果明显.

Firstly, the concept of meta-model set was proposed, which utilized the feature of RBF function and converted the coefficient vector into coefficient matrix, and made multiple variables simulating in the same meta-model. Then, to tackle the difficult problems such as calculating Pareto fitness matrix through the sample points, a new incremental iterative Pareto fitness calculation method was proposed to signifi- cantly reduce the calculation by using the fitness value of the previous iteration directly. Finally, a new multivariable optimization algorithm based on meta-model set and incremental Pareto fitness algorithm was applied to numerical computation and design optimization of five-bar plane truss structure. The result showed that the method was scientific and reasonable, and the improvement was obvious.