efficient methods for goal square weber location problem

in this paper, we consider a special case of weber location problem which we call goal location problem. the weber location problem asks to find location of a point in the plane such that the sum of weighted distances between this point and n existing points is minimized. in the goal location problem each existing point pi has a relevant radius ri and it’s ideal for us to locate a new facility on the distance ri from pi for i = 1, ..., n. since in the most instances there does not exist the location of a new facility such that its distance to each point pi be exactly equal to ri. so we try to minimize the sum of the weighted square errors. we consider the case that the distances in the plane are measured by the euclidean norm. we propose a weiszfeld like algorithm for solving the problem and also we use two modifications of particle swarm optimization method for solving this problem. finally the results of these algorithms are compared with results of bsss algorithm.