一类非线性比式和问题的分支定界算法

Branch and Bound Algorithm for a Class of Nonlinear Sum of Ratios Problem

针对一类带有常系数的非线性比式和全局优化问题(P),给出求解该问题的分支定界算法.首先,将问题(P)转化为问题(Q),两者的变量个数和约束条件的个数相同.然后,利用不等式放缩的方法,建立问题(Q)的松弛线性规划,并结合分支定界算法求解.最后,在此基础上提出区域删减策略,并进行数值实验.结果表明:本算法和删减策略均是有效的.

For a class nonlinear sum of ratios global optimization problem （P）, the branch and bound algorithm is given. First of all, problem（P） will be transformed into problem （Q）, so that the number of variables and the number of con- strains of the two problems are equal. After that, by using the inequality sacling method, the relaxed linear programming about problem （Q） is established and combined with the branch and bound algorithm for solving. Last, based on these steps, region-deleting rules are put forward and numerical experiments are carried out. The result shows that the algo- rithm and the region-deleting rules are feasible.