[1]杨金勇,宋海洲.一类非线性比式和问题的分支定界算法[J].华侨大学学报(自然科学版),2014,35(3):340-343.[doi:10.11830/ISSN.1000-5013.2014.03.0340]
　YANG Jin-yong,SONG Hai-zhou.Branch and Bound Algorithm for a Class of Nonlinear Sum of Ratios Problem[J].Journal of Huaqiao University(Natural Science),2014,35(3):340-343.[doi:10.11830/ISSN.1000-5013.2014.03.0340]
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一类非线性比式和问题的分支定界算法()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第35卷
期数:
2014年第3期
页码:
340-343
栏目:
出版日期:
2014-05-16

文章信息/Info

Title:
Branch and Bound Algorithm for a Class of Nonlinear Sum of Ratios Problem
文章编号:
1000-5013(2014)03-0340-04
作者:
杨金勇;  宋海洲
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
YANG Jin-yong;  SONG Hai-zhou
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
松弛线性规划;  分支定界算法;  区域删减策略;  非线性比式和;  全局优化
Keywords:
relaxed linear programming;  branch and bound;  region-deleting rules;  nonlinear sum of ratios;  global optimization
分类号:
O157
DOI:
10.11830/ISSN.1000-5013.2014.03.0340
文献标志码:
A
摘要:
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.
Abstract:
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 constrains 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 algorithm and the region-deleting rules are feasible.

参考文献/References:

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[8] 申培萍,王俊华.一类带反凸约束的非线性比式和问题的全局优化算法[J],应用数学,2012,25(1):126-130.
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备注/Memo

备注/Memo:
收稿日期: 2012-11-06
通信作者: 宋海洲(1971-),男,教授,主要从事数学模型的研究.E-mail:hzsong@hqu.edu.cn.
基金项目: 华侨大学科研基金资助项目(10HZR26)
更新日期/Last Update: 2014-05-20