一类新的分式规划问题的全局优化方法

摘要

This paper presents an efficient global optimization method for a class of new fractional programming problem (FP).First,the problem (FP) is transformed into its equivalent problem (EFP).Then,a linear relaxation programming problem (RLP) for (EFP) is established utilizing a linearization technique.Through successive refinements of the feasible region and the solution of a series of the linear programming problems,the upper and lower bounds of the global optimal value for the problem (EFP) are obtained.The theoretical proof and numerical results show that the algorithm can effectively solve the problem (FP).The case of sum of linear ratios is extended.%本文对一类新的分式规划问题(FP)提出了一个有效的全局优化方法.首先将问题(FP)转化为其等价问题(EFP),然后利用线性化技术建立了(EFP)的松弛线性规划问题(RLP),通过对其可行域的细分和求解一系列的线性规划,得到问题(EFP)的全局最优值的上下界.理论证明和数值试验的结果都表明该算法能有效求解问题(FP),推广了线性比式和的情形.