一类比式问题的求解算法

An Algorithm for Solving a Class of Fractional Problem

对一类的线性比式和问题(P)提出了一确定性全局优化算法。利用等价问题和新的线性化技术给出了问题(P)的松弛线性规划(RLP),通过对RLP可行域的细分以及一系列RLP的求解过程,提出了分枝定界算法收敛到问题(P)的全局最优解,最终数值实验表明了提出方法的可行性。

In this paper a deterministic global optimization algorithm is proposed for locating global minimum of a class of sum of linear ratios problem （P）. By utilizing equivalent problem and linearization technique, the （P）is reduced to a series of relaxation linear programming（RLP）. The proposed branch and bound algorithm is convergent to the global minimum of the （P） through the successive refinement of the feasible region and solutions of a series of RLP. And finally the numerical experiment is given to illustrate the feasiblity of the presented algorithm.