The aim of this work is to give a review of the division of heuristic methods, to choose three different metaheuristic methods and to carry out the optimization of the problem (objective function) and, finally, to compare and comment on the results. The paper is divided into five chapters. The first chapter introduces the definition of optimization and classification and the comparison of exact and approximate methods. The second chapter gives an overview of heuristic methods, which are divided into heuristics of specific problems and Metaheuristics. After the difference between these two types of heuristic methods has been defined, the paper presents the division in more detail. The third chapter describes some of the most popular local metaheuristic optimization methods, such as local search method, method of simulated annealing, tabu search, GRASP method and Monte Carlo method. The fourth chapter describes some of the most popular global metaheuristic optimization methods, such as genetic algorithm, ant colony optimization, particle swarm optimization and bee swarm optimization. The next chapter (Chapter 5) is the core of this work because it implements metaheuristic methods through software Matlab - trial version. This section consists of a brief explanation of the concept of computed tomography and industrial computed tomography, an illustration and description of the equation objective function and its limitations, implementation of the genetic algorithm, particle swarm optimization and artificial bee colony optimization and by comparing the results obtained.