| 多约束非线性整数规划的一种改进的算法 |
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| 引用本文： | 陈娟,钱静静,刘常丽.多约束非线性整数规划的一种改进的算法[J].数学的实践与认识,2011,41(23). |
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| 作者姓名： | 陈娟 钱静静 刘常丽 |
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| 作者单位： | 泰山医学院信息工程学院,山东泰安,271000 |
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| 摘 要： | 多约束非线性整数规划是一类非常重要的问题,非线性背包问题是它的一类特殊而重要的问题.定义在有限整数集上极大化一个可分离非线性函数的多约束最优化问题.这类问题常常用于资源分配、工业生产及计算机网络的最优化模型中,运用一种新的割平面法来求解对偶问题以得到上界,不仅减少了对偶间隙,而且保证了算法的收敛性.利用区域割丢掉某些整数箱子,并把剩下的区域划分为一些整数箱子的并集,以便使拉格朗日松弛问题能有效求解,且使算法在有限步内收敛到最优解.算法把改进的割平面法用于求解对偶问题并与区域分割有效结合解决了多约束非线性背包问题的求解.数值结果表明了改进的割平面方法对对偶搜索更加有效.
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| 关 键 词： | 非线性整数规划 非线性背包问题 拉格朗日对偶 改进的割平面方法 |
An Improving Algorithm for Multi-Dimensional Nonlinear Integer Programming Problems |
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| CHEN juan,QIAN Jing-jing,LIU Chang-li.An Improving Algorithm for Multi-Dimensional Nonlinear Integer Programming Problems[J].Mathematics in Practice and Theory,2011,41(23). |
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| Authors: | CHEN juan QIAN Jing-jing LIU Chang-li |
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| Institution: | CHEN juan~1,QIAN Jing-jing~2,LIU Chang-li~3 (School of Information Engineering,Taishan Medical University,Taian 271000,China) |
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| Abstract: | Multi-dimensional nonlinear integer programming problem is a very important, nonlinear knapsack problem is a bounded nonlinear integer programming problem that maximizes a separable nonlinear function subject to multiple separable nondecreasing constraints. This problem is often encountered in resource allocation,industrial planning and computer network.In this paper,a new convergent Lagrangian dual method was proposed for solving this problem,the improving cutting plan method was used to solve the dual pro... |
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| Keywords: | nonlinear integer programming nonlinear knapsack problem Lagrangian relaxation improving cutting plane |
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