非线性大系统多目标优化的交互式满意分解方法
Interactive satisfying decomposition method of multiobjective optimization for nonlinear large-scale systems
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摘要: 本文提出了交互式二级算法,在此基础上又提出了交互式三级算法,统称为交互式满意方法。利用加权切贝雪夫方法,将多目标优化问题化简为单目标优化问题。采用大系统分解协调理论完成了对决策空间的分解,降低了系统的维数。通过引入代值目标完成了对目标空阿的分解,兼顾了系统的整体利益和局部利益。运用希望水平方法实现了人机交互过程。该方法具有一定的智能水平,所需的计算机内存容量较小,收敛速度较快。用数值例子表明了其实用性和有效性。Abstract: An interactive two-level algorithm is presented and an interactive threelevel algorithm is also proposed. They are both called Interactive Satisfying Decomposition Method (ISDM). The problem of multiobjective optimization is simplified to that of scalar objective optimization by weighted Tchebycheff procedure. Decision space is decomposed by the decomposition and coordination method, while objective Space is decomposed by introducing the surrogate worth objective into the subsystems, so that the system dimension is reduced significantly. Both whole benefits and local benefits are considered. Man-machine interaction is realized by the aspiration level method. ISDM has the characteristics of some intelligence, requiring less internal computer memories, but with fast convergence speed. A numerical example is given to show that ISDM is practical and efficient.