The artificial bee colony (ABC) algorithm is a metaheuristic search method inspired by bees' foraging behaviour. With its global search ability in scout bee phase, it can easily escape from local optimum traps in the problem space. Therefore, it is good at exploration. The migrating birds optimization (MBO) algorithm is another recent metaheuristic search method. It simulates birds' V flight formation, which minimizes energy consumption during flight. The MBO algorithm achieves a good convergence to the global optimum by using its own unique benefit mechanism. That is, it has a good exploitation capability. This paper aimed to combine the good exploration property of the ABC algorithm and the good exploitation property of the MBO algorithm via a sequential execution strategy. In the proposed method, firstly, the ABC algorithm runs. This enables solutions to escape from local optimum traps and orientates them to the region in which the global optimum exists. Then the MBO algorithm runs. It performs a good convergence to the global optimum. In the proposed method, some variants of the ABC algorithm and some other well-known optimization algorithms were tested via benchmark functions. It was seen in the experiments that the proposed method gave competitive benchmark test results considering both success rates and convergence performances.