| 具有性能约束布局问题的优化算法及收敛性 |
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| 引用本文： | 张旭,冯恩民.具有性能约束布局问题的优化算法及收敛性[J].大连理工大学学报,2005,45(5):766-771. |
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| 作者姓名： | 张旭 冯恩民 |
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| 作者单位： | 大连理工大学,应用数学系,辽宁,大连,116024;大连理工大学,应用数学系,辽宁,大连,116024 |
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| 摘 要： | 研究了二维布局优化问题,建立了具有性能约束的二维布局半无限优化模型.应用图论、群论等,把该问题分解为有限多个子问题,在每个子问题中克服了优化变量的时断时续性质,并将子问题松弛化,利用极大极小函数给出了松弛子问题的最优性函数,该函数在其零点使松弛子问题的一阶必要条件成立.利用最优性函数构造了松弛子问题的优化算法,并证明了算法的收敛性.
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| 关 键 词： | 二维布局 半无限优化 最优性函数 优化算法 收敛性 |
| 文章编号： | 1000-8608（2005）05-0766-06 |
| 收稿时间： | 2004-05-27 |
| 修稿时间： | 2004-05-272005-06-11 |
Algorithm of layout optimization problem with performance constraints and its convergence |
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| ZHANG Xu,FENG En-min.Algorithm of layout optimization problem with performance constraints and its convergence[J].Journal of Dalian University of Technology,2005,45(5):766-771. |
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| Authors: | ZHANG Xu FENG En-min |
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| Institution: | Dept. of Appl. Math. , Dalian Univ. of Technol. , Dalian 116024, China |
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| Abstract: | The two-dimensional layout optimization problem is studied.A semi-infinite optimization model with performance constraints is presented.The layout problem is partitioned into finite subproblems by virtue of graph theory,the action of group on set,orbits and so on,so that each subproblem can overcome the onoff nature of optimal variable.Each subproblem is relaxed and the optimality function is presented by using the minimax function.The fast order necessary optimality condition of the relaxed subproblem is satisfied at a point if and only if the point is a zero of the optimality function.The optimization algorithm for the relaxed subproblem is constructed by virtue of the optimality function and the convergence is proved. |
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| Keywords: | two-dimensional layout semi-infinite optimization optimality function optimization algorithm convergence |
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