An evolutionary and discrete variant of the Bat Algorithm (EDBA) is proposed for solving the Vehicle Routing Problem with Time Windows, or VRPTW. The EDBA developed not only presents an improved movement strategy, but it also combines with diverse heuristic operators to deal with this type of complex problems. One of the main new concepts is to unify the search process and the minimization of the routes and total distance in the same operators. This hybridization is achieved by using selective node extractions and subsequent reinsertions. In addition, the new approach analyzes all the routes that compose a solution with the intention of enhancing the diversification ability of the search process. In this study, several variants of the EDBA are shown and tested in order to measure the quality of both metaheuristic algorithms and their operators. The benchmark experiments have been carried out by using the 56 instances that compose the 100 customers Solomon’s benchmark. Two statistical tests have also been carried out so as to analyze the results and draw proper conclusions.