具闭凸集约束选址问题的简捷算法

Simple Algorithm for Single Location in a Closed Convex Domain

对具闭凸集约束的建造发电厂、仓库、炼油厂、飞机维修厂、商业大厦等的选址问题 ,原有的算法或当在迭代过程中遇极点时不能继续进行 ,或算法形式复杂。针对较 Fermat场址问题更一般的单场址问题 ,给出一种具有全局收敛性的简捷算法。该算法本质上属梯度法 ,但克服了原先梯度法在遇极点时迭代不能继续的缺陷 ,且一般不需做线性搜索 ,同时算法具有较快的收敛速度。

For building a power plant, a storehouse, an oil refining factory or a trade mall, it is important to choose a location in a closed covex domain. The original methods for Fermat location either are ineffective when an iterative point is an extreme point or are very complex. For very general single location in a closed convec domain, a simple algorithm with global convegence has been proposed. The algorithm belongs to the gradient methods, but it overcomes the drawback that the original gradient methods are ineffective when an iterative point is an extreme point, and may need not a linear search.The convergence rate of the algorithm is faster than the rate of the original gradient methods.