Knowing the mobility patterns of citizens using public transportation is an important issue for modern smart cities. Mobility information is crucial for designing and planning an urban transportation system able to provide good service to citizens. We address two relevant problems related to public transportation systems: the analysis of mobility patterns of passengers and the relocation of bus stops in an urban area. For the first problem, a big-data approach is applied to process large volume one space of information. Several relevant metrics are computed and analyzed to characterize the mobility patterns using data from the public transportation system on Montevideo, Uruguay. We obtain user demand and origin-destination matrices by analyzing the tickets sale information and the buses locations. A distributed implementation is proposed, reaching significant execution time improvements (speedup up to 17.10 when using 24 computing resources). For the second problem, a multiobjective evolutionary algorithm is proposed to relocate bus stops in order to improve the quality of service by minimizing the travel time and bus operational costs. The algorithm is evaluated over instances of the problem generated with real data from the year 2015. The experimental results show that the algorithm is able to obtain improvements of up to 16.7 and 33.9% in time and cost respectively, compared to space situation in the year 2015.