Optimization of the sizing and operation strategy of a complex energy system requires a large computational burden because of the non-linear nature of the mathematical problem. Accordingly, using a conventional numerical method with only a physics-based model for complete optimization is impractical. To resolve this problem, this paper adopted an optimization method of using an artificial intelligence scheme that combines an artificial neural network (ANN) and a genetic algorithm (GA). Especially, the ANN was constructed based on results from a physics-based model to obtain a large amount of accurate simulation data in a short time frame. A distributed generation (DG) system based on a gas turbine (GT) and renewable energy (RE) was simulated to demonstrate the usefulness of the optimization method. In consideration of the capacity and partial load performance of the GT, the optimization of the sizing and operation strategy of the DG system was performed for three system design scenarios. The optimization criteria were cost-effectiveness and eco-friendliness. The method reduced the calculation time by more than three orders of magnitude while maintaining the same accuracy as the physics-based model. The approach and methodology are expected to be applicable to accurate and fast optimization of various sophisticated energy systems.