Genetic Algorithms (GAs) are general-purpose search and optimization procedures. They were inspired by the biological evolution principle of survival of the fittest. This led to the metaphoric use of terminology borrowed from the field of biological evolution. Another method of optimization, Particle Swarm Optimization (PSO), is able to accomplish the same goal as GA in a new way. The thought process behind the algorithm was inspired by social behavior of animals, such as bird flocking. PSO is similar to the GA in that it begins with a random population, unlike the GA; PSO has no evolution operators such as crossover and mutation.In this thesis, three problems were chosen to compare between GA and PSO performance. These problems are (Solving Linear Algebraic Equations (SLAE), Solving N-Queens problem (SNQP), and Substitution Cipher (SC)). The Solving Linear Algebraic problem is a simple problem with (212) search space to find the solution for linear equations; both GA and PSO consistently find good solutions. The Solving N-Queens problem is the problem of putting n queens on an n×n chessboard with ((n-k)?) search space such that non of them is to be able to attack any other. Eight and sixteen queens were tried in this implementation. Good results are obtained, but the GA performance is better and faster than PSO when the number of queens is increased. Finally, the Substitution Cipher problem is a complete problem, with (26?) search space size the full key space of all possible substitution ciphers was searched, and this implementation was met with limited success.