Abstarct: Location theory is one of the most important topics in optimization and operations research. In location problems, the goal is to find the location of one or more facilities such that some criteria such as transportation costs, customer distance traveled, total service time, and cost of servicing are optimized. In this thesis, we consider the ideal location problems in which the location of a number of customers on a plane is given, and the ideal is locating the facility in the distance Ri, from the i-th client. However, in most instances, the solution of this problem doesn’t exist. Therefore, the minimizing sum of errors is considered. For this purpose, we consider two models of symmetric and asymmetric loss (error) function and use the distance function ℓ p norm to define these loss functions. In order to minimize the symmetric loss function, we use the Weiszfeld like method, Gauss-Newton and Imperialist competitive algorithm (ICA) and compare the numerical results obtained by solving these algorithms. In addition, in another part of this thesis, we consider the asymmetric loss function and explain its interesting features. Using the some modified BFGS methods, Imperialist competitive algorithms, and the Weiszfeld-like algorithm, we minimize this loss function and present the results of the implementation of these algorithms and compare these results with each other. Also, in the final part of this thesis, we seek to solve large-scale problems using stochastic optimization methods. Stochastic optimization methods perform very well in largescale problems by reducing computational cost and achieve less objective function value in less time, which has led to the popularity of these methods among researchers in the field of optimization. We have also solved the problem of ideal location under the symmetric loss function by using Stochastic methods and have obtained very good results, which we have presented and described in the final part of the thesis using various figures and tables.