Network Location Theory

网络定位问题涉及在网络上定位一个或多个新设施，例如运输网络，当产生某种成本时，这种成本与网络上新设施和现有设施之间的网络旅行距离成正比，也可能与新设施之间的距离成正比。新设施将设在网络上，以尽量减少目标函数。过去，当问题是连续的（考虑到每条链路上所有可能的位置），解决这类问题的主要方法是利用网络结构。最近已经证明，许多这样的连续问题可以公式化为数学规划问题（定义良好的数学优化问题）。本研究将著重于利用数学规划的连结来解决连续网路定位问题。由于后一个领域相当发达，提高我们解决网络定位问题的能力的机会显得非常有希望。

Network location problems involve locating one or more new facilities on a network, such as a transport network, when costs of some sort are incurred which are proportional to network travel distances between new facilities and existing facilites on the network, as well as possibly to distances between new facilities. The new facilities are to be located on the network so as to minimize an objective function. The principal approach to solving such problems in the past, when the problems have been continuous (considering all possible locations on every link) has been to exploit network structure. Recently it has been shown that many such continuous problems may be formulated as mathematical programming problems (well-defined mathematical optimization problems). This research will focus on solving continuous network location problems by exploiting connections with mathematical programming. Since the latter field is quite highly developed, the opportunities for improving our ability to solve network location problems appear very promising.