In this work, a modified structure of the tilted integral derivative (TID) controller, i.e. an integral derivative-tilted (ID-T) controller, is developed for the load frequency control issue of a multi-area interconnected multi-source power system. Moreover, a new optimization algorithm known as Archimedes optimization algorithm (AOA) is used to fine-tune the proposed ID-T controller parameters. The performance of the proposed ID-T controller based on AOA is evaluated through a two-area interconnected power system, each area containing various conventional generation units (i.e., thermal, gas, and hydraulic power plants) and renewables (wind and solar power). Furthermore, system nonlinearities (i.e., generation rate constraints, governor deadband, and communication time delays), system uncertainties, and load/renewables fluctuations are considered in designing the proposed controller. The effectiveness of the proposed ID-T controller based on AOA is verified by comparing its performance with other control techniques in the literature (i.e. integral controller, proportional integral derivative (PID) controller, fractional-order PID controller, TID controller, and I-TD controller). The AOA's optimization superiority has also been verified against a variety of other sophisticated optimization methods, including particle swarm optimization and whale optimization algorithm. The simulation results exhibit that the proposed ID-T controller based on the AOA presents a great improvement in the system frequency stability under several contingencies of different load perturbations, system uncertainties, physical constraints, communication time delays, high renewables penetration.