The Job Shop Scheduling Problem (JSP) is an example of a combinatorial optimization problem that has interested researchers for several decades. In this paper we confront an extension of this problem called JSP with Sequence Dependent Setup Times (SDST-JSP). The approach extends a genetic algorithm and a local search method that demonstrated to be efficient in solving the JSP. For local search, we have formalized neighborhood structures that generalize three well-know structures defined for the JSP. We have conducted an experimental study across conventional benchmark instances showing that the genetic algorithm exploited in combination with the local search, considering all three neighborhoods at the same time, provides the best results. Moreover, this approach outperforms the current state-ofthe-art methods.