一类优化问题的确定性算法

Deterministic Algorithm for a Class of Optimization Problem

对广泛应用于工程设计中的一类线性比式和问题(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,最终数值实验表明所提方法的可行性.

In this paper a global optimization algorithm is proposed for locating global minimum of a class of sum of linear ratios problem （P）, which can be applied to engineering designs. By utilizing equivalent problem and linearization technique, the relaxation linear programming （RLP） about problem （P） is established, thus the initial nonconvex problem （P）is reduced to a series of linear programmin g （RLP）. The proposed branch and bound algorithm is convergent to the global minimum of problem （P） through the successive refinement of the feasible region and solutions of RLP. And finally the numerical experiment is given to illustrate the feasibility of the presented algorithm.