关于惩罚函数中惩罚系数的讨论

Penalty parameter of the penalty function method

对惩罚函数法中的惩罚系数进行了系统分析和讨论.首先,针对Deb基于可行性规则对约束违反相同情况下的比较没有具体说明的现状,提出一种改进的Deb基于可行性规则.在此基础上,证明了惩罚系数过大或者过小均不会影响排序的结论,并给出了惩罚系数影响排序的上下边界.实例分析表明了所得结论的有效性,为基于惩罚系数的算法设计提供了依据.

The penalty parameter of penalty function method is systematically analyzed and discussed. For the problem that Deb’s feasibility-based rule doesnot give the detailed instruction as how to rank two solutions when they have the same constraint violation, an improved Deb’s feasibility-based rule is presented, which can be seen as a reference standard. And based on this, the upper and lower boundary of penalty parameter that affects the ranking is obtained. The example verifies the effectiveness of the systematical analysis, which provides a basis for the future algorithm design based on the penalty parameters.