The bat algorithm (BA) is one of the metaheuristic algorithms that are used to solve optimization problems. The differential evolution (DE) algorithm is also applied to optimization problems and has successful exploitation ability. In this study, an advanced modified BA (MBA) algorithm was initially proposed by making some modifications to improve the exploration and exploitation abilities of the BA. A hybrid system (MBADE), involving the use of the MBA in conjunction with the DE, was then suggested in order to further improve the exploitation potential and provide superior performance in various test problem clusters. The proposed hybrid system uses a common population, and the algorithm to be applied to the individual is selected on the basis of a probability value, which is calculated in accordance with the performance of the algorithms; thus, the probability of applying a successful algorithm is increased. The performance of the proposed method was tested on functions that have frequently been studied, such as classical benchmark functions, small-scale CEC 2005 benchmark functions, large-scale CEC 2010 benchmark functions, and CEC 2011 real-world problems. The obtained results were compared with the results obtained from the standard BA and other findings in the literature and interpreted by means of statistical tests. The developed hybrid system showed superior performance to the standard BA in all test problem sets and produced more acceptable results when compared to the published data for the existing algorithms. In addition, the contribution of the MBA and DE algorithms to the hybrid system was examined.