Following the rapidly increasing global demand for natural gas, many countries are launching projects to expand gas pipeline networks (GPNs). As a result, more cyclic GPNs are under construction with more rigorous physical constraints required, bringing new challenges to GPN optimization. This paper proposes a novel nonconvex mixed-integer nonlinear programming (MINLP) formulation for operational optimization of the cyclic GPN with simultaneous consideration of thermal hydraulics and flow direction reversibility, which has not been explored in the literature. To solve the proposed MINLP model, a three-level decomposition algorithm is proposed to generate an approximate solution, from which the flow direction is extracted and used to fix all discrete variables in the original MINLP model to construct two-stage NLP models. The NLP models are then solved to improve solution feasibility and quality. The computational results show that the proposed approach outweighs several state-of-the-art commercial MINLP solvers with better solutions and shorter computational time.