| 求解二进制二次规划问题的一种连续化方法 |
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| 引用本文： | 李兴斯,谭涛.求解二进制二次规划问题的一种连续化方法[J].工程数学学报,2006,23(3):499-504. |
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| 作者姓名： | 李兴斯 谭涛 |
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| 作者单位： | 大连理工大学工业装备结构分析国家重点实验室,大连,116024;大连理工大学工业装备结构分析国家重点实验室,大连,116024 |
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| 基金项目： | 国家高技术研究发展计划(863计划);南京大学校科研和教改项目 |
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| 摘 要： | 本文提出了一种求解二进制二次规划问题的连续化方法。首先利用NCP函数方法,将二进制变量转化为等价的非光滑方程,再用凝聚函数法对其进行光滑化处理,从而把原来的组合优化问题转化成了一般的可微非线性规划问题。通过对一些标准考题进行计算,表明了该连续化方法的可行性、高效性以及稳定性。
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| 关 键 词： | 二进制规划 连续化方法 NCP函数 非线性规划 凝聚函数法 |
| 文章编号： | 1005-3085(2006)03-0499-06 |
| 收稿时间： | 2004-11-03 |
| 修稿时间： | 2004年11月3日 |
A Continuous Approach to Binary Quadratic Problems |
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| LI Xing-si,TAN Tao.A Continuous Approach to Binary Quadratic Problems[J].Chinese Journal of Engineering Mathematics,2006,23(3):499-504. |
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| Authors: | LI Xing-si TAN Tao |
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| Affiliation: | State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024 |
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| Abstract: | A continuous approach to solving general binary quadratic problems is investigated.With this approach,the original problem is converted into an equivalent continuous optimization problem.In the implementation,each complementary condition is reduced to an equation by means of the so-called NCP function.As such,the binary quadratic problem can be solved by mature optimization technique. To validate the applicability,robustness and solution quality of the approach,computational experience on certain scale problems of up to 1000 variables has been performed.The numerical results show that the proposed approach is both efficient and effective,and could be applied to large scale problems. |
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| Keywords: | binary quadratic program continuous approach NCP function nonlinear programming aggregate function |
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