An improved branch‐and‐cut algorithm for mixed‐integer nonlinear systems optimization problem
An improved branch‐and‐cut algorithm for mixed‐integer nonlinear systems optimization problem
复制标题
混合整数非线性系统优化问题的改进分支割算法
DOI：
10.1002/aic.11616
复制
发表时间：
2008
期刊：
影响因子：
3.7
通讯作者：
M. Nakaiwa
中科院分区：
文献类型：
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作者：
Yushan Zhu;Yijiong Hu;Hao Wu;M. Nakaiwa
混合整数系统的全局优化和动态优化的最新进展对混合整数非线性规划(MINLP)问题的高效和稳健的数值算法提出了越来越高的要求。本文利用我们以前对0-1 MINLP的析取割平面的临界发现(朱和库诺，Ind Eng Chem Res.2006；45：187-196)，提出了一种改进的0-1 MINLP问题的分枝割算法。借助于原MINLP问题的混合整数非线性集在每个枚举结点处的多面体外逼近，利用Balas等人关于MILP问题的割集生成、提升和加强方法，生成了一个对原MINLP问题有效且去除了分数阶解的提升和投影割平面.(数学课程。1993年；58：295-324)。讨论了割平面的具体实现问题，并将其融入到分支切割算法的算法开发中。11个系统优化问题的计算结果表明，改进的析取割面算法对实际MINLP问题具有很好的应用前景，因为求解多约束非线性规划问题的内点算法逐渐成熟。美国化学工程师学会AICHE J，2008
Recent advances for global optimization and dynamic optimization of the mixed-integer systems have created an increasing demand for efficient and robust numerical algorithms for mixed-integer nonlinear programming (MINLP) problem. In this article, an improved branch-and-cut algorithm for 0-1 MINLP problems has been proposed by using our former critical finding (Zhu and Kuno, Ind Eng Chem Res. 2006;45:187–196) of the disjunctive cutting plane for 0-1 MINLP. By virtue of the polyhedral outer approximation of the mixed-integer nonlinear set of the original MINLP problem at each enumeration node, a lift-and-project cutting planes that is valid for the original MINLP problem and cuts the fractional solution away can be generated by using the cut generating, lifting, and strengthening approach for MILP problem of Balas et al. (Math Program. 1993;58:295–324). The specific implementation issues of the cutting planes are discussed and incorporated into the algorithmic development of a branch-and-cut algorithm. The efficiency of the improved disjunctive cutting plane is demonstrated by the computational results for 11 systems optimization problems, and it is implied that the proposed branch-and-cut algorithm is very promising for practical MINLP problems as the interior-point solvers for nonlinear programming problems with many constraints are becoming mature gradually. © 2008 American Institute of Chemical Engineers AIChE J, 2008
0-1混合整数凸非线性规划的基于析取割平面的分支割算法
DOI：
--
发表时间：
2006
期刊：
Industrial and Engineering Chemistry Research 45
影响因子：
--
作者：
Y.Zhu;T.Kuno
通讯作者：
T.Kuno