Research Article Earthquake Design of Reinforced Concrete Buildings Using NSGA-II Herian A. Leyva, 1 Ed´ enBoj´ orquez , 1 Juan Boj´ orquez, 1 Alfredo Reyes-Salazar , 1 Jos´ e H. Castorena, 2 Eduardo Fern´ andez, 1 and Manuel A. Barraza 1 1 Facultad de Ingenier´ ıa, Universidad Aut´ onoma de Sinaloa, Culiac´ an, Mexico 2 Facultad de Ingenier´ ıa, Universidad Aut´ onoma de Sinaloa, Mochis, Mexico Correspondence should be addressed to Ed´ en Boj´ orquez; eden@uas.edu.mx Received 5 July 2018; Revised 19 September 2018; Accepted 22 October 2018; Published 27 November 2018 Academic Editor: Eric Lui Copyright © 2018 Herian A. Leyva et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the present study, the optimal seismic design of reinforced concrete (RC) buildings is obtained. For this purpose, genetic algorithms (GAs) are used through the technique NSGA-II (Nondominated Sorting Genetic Algorithm), thus a multiobjective procedure with two objective functions is established. e first objective function is the control of maximum interstory drift which is the most common parameter used in seismic design codes, while the second is to minimize the cost of the structure. For this aim, several RC buildings are designed in accordance with the Mexico City Building Code (MCBC). It is assumed that the structures are constituted by rectangular and square concrete sections for the beams, columns, and slabs which are represented by a binary codification. In conclusion, this study provides complete designed RC buildings which also can be used directly in the structural and civil engineering practice by means of genetic algorithms. Moreover, genetic algorithms are able to find the most adequate structures in terms of seismic performance and economy. 1. Introduction e scientific advances in technology and computation resources have allowed the development of new optimiza- tion procedures in recent years, such as the genetic algo- rithms optimization method. is approach was initially discussed and proposed by Holland, and it is based on the natural selection theory established by Charles Darwin [1, 2]. e main characteristic of GAs is the survival, adaptation, crossing, and mutation of species through time. e in- dividuals with best adaptive capacity have more likelihood of surviving and obtaining descendants. For this reason, the genetic code of the best individuals is maintained, to obtain descendants with equal or better adaptation capacity, thus the species evolve. Mathematically, the GAs technique consists in the generation of an initial population (usually random) of possible solutions represented by binary codification. e weakest or most misfit individuals are eliminated, and the strongest survive and are reproduced. e adaptation level of each individual is measured with a value assigned in one objective function [3]. A typical genetic algorithm uses three basic operators: selection, crossing, and mutation: (i) Selection of individuals: it is based on qualifying each individual according to their adaptation and determining which ones survive and pass to the next generation. (ii) Crossing: the aim of the crossing is to create new individuals with the exchange of genetic in- formation (usually binary codification) among those most adapted, similar to that used by a natural organism in sexual reproduction. (iii) Mutation: it is used to introduce random changes in the population of a generation. e mutation may be beneficial as it allows introducing diversity in a population. Once the previous steps are completed, a new generation is obtained, and the process is repeated until reaching the Hindawi Advances in Civil Engineering Volume 2018, Article ID 5906279, 11 pages https://doi.org/10.1155/2018/5906279