The aim of this study is to illustrate and compares the use of Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) for multi-objective optimization of two and three dimensional moment resisting steel structures subjected to earthquake loads. For this purpose, steel buildings with different characteristics are designed under earthquakes using the Non-dominated Sorting Genetic Algorithm (NSGA-II) and PSO as a tool to achieve the best structure in terms of: minimize the total structural weight (which is directly related with the costs), control of the maximum inter-story drift, and to satisfy the strength requirements of the AISC-LRFD specification. It is considered that all the steel structures are constituted by elements with W section (256 in total) taken from the LRFD-AISC Database. Although, the GAs and PSO are applied for moment resisting steel structures, the concepts can be extended for other structural systems. It is concluded that the use of NSGA-II and PSO reduce the structural weight and they are a very useful tools to improve the structural performance of the buildings. Finally, the structural buildings obtained via PSO are in general better solutions in comparison with the NSGA-II approach.