具有性能约束布局问题的优化理论及双层规划模型的启发式并行算法

项目名称： 具有性能约束布局问题的优化理论及双层规划模型的启发式并行算法

项目编号： No.11301051

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 张旭

作者单位： 大连理工大学

项目金额： 22万元

中文摘要： 本项目研究一类具有性能约束的布局优化问题，目标是克服该类问题优化变量的时断时续性，并且解决组合优化计算量过大的难题。主要研究内容是以卫星舱布局为背景，建立双层规划模型。上层规划对不同构的布局方案进行优化，是有限多个离散变量优化问题；下层规划在同构的布局方案中寻求最优解，是连续变量的不可微非线性约束规化问题。上层规划的不同构布局方案等价类的数量随着图元个数增加呈指数型增长，可以制定启发式删减原则，将尽可能多的不合理的布局等价类删掉，对保留下的布局方案等价类拟采用并行算法求解；下层规划中，拟利用不可微优化理论中的方向可微、半方向可微、不变凸性和预不变凸性等研究最优性条件，结合邻域搜索机制给出可行的下降方向，进一步构造优化算法，最终在并行机上进行数值计算。

中文关键词： 双层规划；半无限优化；并行优化算法；；

英文摘要： The project will reaearch a kind of packing optimization problem with performance constraints. The main object of this item is to overcome optimization variables'on-off nature and to solve the difficulty of enormous calculation work for combinatorial optimization problem. The main research contents is to build a bilevel programming model based on satellite module layout problem. Firstly, upper level programming chooses the suitable packing schemes in the nonisomorphic items. It is a combinatorial optimization with limit discrete variables. Secondly, lower level programming is to find out local optimal solutions in the isomorphic items which is a indifferentiable nolinear constraint optimization with continuous variants. In the upper level programming, the number of nonisomorphic packing schemes equivalence classes is increasing by exponent, we will give a heuristic cutting rules to get rid of unreasonable equivalence classes and construct the parallel algorithm to solve the remained items. For the lower level programming, we will study its optimal conditions by directionally differentiable， semi-directionally differentiable，invexity and pre-invexity,etc. Combining feasible decreasing direction with neighborhood search mechanism, optimization algorithm will be done and numerical computation will be completed

英文关键词： Bi-level progamming；semi-infinite optimization；parallel optimization algorithm；；