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In control system design, it is important to determine the controller type and controller parameters appropriately. PID controllers are mostly preferred in many applications. At the same time, it is known that PID controllers are insufficient to control higher order oscillatory systems with time delay. In such systems, PIDA controller is preferred instead of traditional PID controller. This paper presents a hybrid algorithm based optimization method for the control of higher order oscillatory systems with time delay. A hybrid algorithm combining the advantages of firefly and genetic algorithm is used to determine PIDA controller parameters. In the proposed method, a multi-criteria objective function is suggested by taking the settling and rising time, percent overshoot and steady state error criteria from the time response parameters. Two simulation studies are conducted to evaluate the performance of the proposed method, and the results are compared with some studies from the literature. In addition, the parameter uncertainties of the systems are analyzed and the robustness performance evaluations of the designed controllers are made. It is seen from the results obtained that the proposed method improves the transient and steady state response of higher order oscillatory systems with time delay and offers a fast and effective tuning method. [ABSTRACT FROM AUTHOR]