WEBER'S PROBLEM WITH ATTRACTION AND REPULSION*
研究了平面中带正负权重的韦伯问题，将其转化为凸函数差规划，通过外逼近和顶点枚举求解，并扩展到设施厌恶度指数衰减的情形，测试了n达1000的算例。
ABSTRACT. Weber's problem consists of locating a facility in the plane in such a way that the weighted sum of Euclidean distances to n given points be minimum. The case where some weights are positive and some are negative is shown to be a d.‐c. program (i.e., a global optimization problem with both the objective function and constraint functions written as differences of convex functions), reducible to a problem of concave minimization over a convex set. The reduced problem is then solved by outer‐approximation and vertex enumeration. Moreover, locational constraints can be taken into account by combining the previous algorithm with an enumerative procedure on the set of feasible regions. Finally, the algorithm is extended to solve the case where obnoxiousness of the facility is assumed to have exponential decay. Computational experience with n up to 1000 is described.