This paper proposes a method based on genetic algorithm (GA) for the security-constrained optimal dispatch of integrated natural gas and electricity networks, considering operating scenarios in both energy systems. The mathematical formulation of the optimization problem consists of a multi-objective function which aims to minimize both cost of thermal generation (diesel and natural gas) as well as the production and transportation of natural gas. The joint gas-electricity system is modeled by two separate groups of nonlinear equation, which are solved by the combination of Newton's method with the GA. The applicability of the proposed method is tested in the Belgian gas network integrated with the IEEE 14-bus test system and a 15-node natural gas network integrated with the IEEE 118-bus test system. The results demonstrate that the proposed method provides efficient and secure solutions for different operating scenarios in both energy systems.