Gilmore-Gomory算法避免產生循環的迭代規則

Pivoting Rules for Avoiding Cycles in the Gilmore-Gomory Algorithm

摘要: 分式規劃在管理模型中時常遇到,而且在一般情況下變量個數很多。Gilmore和Gomory提出一種算法1,將分式規劃用變形的單純形法來求解。
本文論述了Gilmore—Gomory算法在迭代過程中有可能產生死循環,從而造成計算失敗。為克服這個缺陷,本文給出了一種避免死循環的迭代規則,使該算法臻于完善。

Abstract: Fractional programming appears often in the management model. It can be Solved by the Gilmore-Gomory algorithm.
In our paper. we have constructed counterexample Showing that the Gilmore-Gomory algorithm may produce cycles, so that the computation is impossible. In this paper. we also give new finite pivoting rules and show that using this new pivoting rules cycles are avoided.