The purpose of the present dissertation is not only to introduce different methods for solving optimization problems, but also to expose a new strategy to deal with constrained structural optimization problems which combines modern Artificial Intelligence and machine learning methods. In the first introductory part, the classical resolution methods are exposed mainly focusing on the Lagrange multiplier rule and the most used mathematical programming methods of the past. These approaches, based on the calculation of the gradient of the objective function, usually solve optimization problems in a sequential way. Afterwards, an overview of the most popular modern meta-heuristic approaches to solve optimization problems is presented.