Single facility goal location problems with Lp norm

Location theory is an interstice field of optimization and operations research. In the classic location problem, the goal is finding the location of one or more facilities such that some criteria such as transportation cost, the sum of distances passed by clients, total service time and cost of servicing are minimized. In this paper, we consider the goal location problem. In the goal location problem, the ideal is locating the facility in the distances ri, from the i-th client. However, in the most instances, the solution of this problem doesn’t exist. Therefore, we consider the minimizing of distances between clients and ideal point. The minimizing sum of square errors and minimizing absolute errors under Lp norm are considered as the objective function. We use the Weiszfeld like, Gauss-Newton and imperialist competitive algorithms for solving the problem. Then we compare the results which obtained by these methods for some test problems.