ABSTRACT: Topological optimization is a numerical analysis technique used in many applications  such as additive manufacturing, casting, industry, plastic automotive and others. Educational  algorithms have been developed, mostly two-dimensional configuration and with well-defined  domains, which clearly describe the various possibilities of boundary conditions found in  structures. The aim of this study is to evaluate the domains of topological optimization in some  two-dimensional cases and contribute for the training and insertion of students in research  activities. For the optimization of the topology, pre-established educational codes were used, such  as sigmund’s code, the finite element theory to define the meshes and generate the matrix with  displacements and supports, through software such as MATLAB®. From the analysis of these  domains, it was possible to verify that some educational algorithms do not work correctly as they  should. The results of this study provided knowledge about the first optimization algorithms and  the Evolution of their approaches to design the details of the numerical aspects of the code and its  equations. Due to the facts mentioned it is concluded that it is important to know in detail the  domains used in two-dimensional educational algorithms and to what extent each of the algorithms  facilitates work with a specific boundary condition. In addition, the evaluation of two-dimensional  algorithms and optimization of the approaches studied helped to consolidate and expand  knowledge about technological development and software for analysis and simulations.