Many problems in statistics, finance, biology, pharmacology, physics, mathematics, economics, and chemistry involve determination of the global minimum of multidimensional functions. R packages for different stochastic methods such as genetic algorithms and differential evolution have been developed and successfully used in the R community. Based on Tsallis statistics, the R package GenSA was developed for generalized simulated annealing to process complicated non-linear objective functions with a large number of local minima. In this paper we provide a brief introduction to the R package and demonstrate its utility by solving a non-convex portfolio optimization problem in finance and the Thomson problem in physics. GenSA is useful and can serve as a complementary tool to, rather than a replacement for, other widely used R packages for optimization.