In the present electricity markets, an algorithm with fast convergence characteristics along with the production of accurate results is more needful in order to improve the profit margins of a utility. In this view, a hybrid algorithm comprising various techniques like gravitational search algorithm (GSA) and fuzzy adaptive particle swarm optimization (FAPSO) is proposed in the present work. The hybridization of the algorithms is done to have combined advantages like local search capability and global search capability of GSA and standard PSO (S-PSO) algorithms, respectively. Furthermore, fuzzy system based dynamic inertia weight is incorporated in the S-PSO algorithm in order to have exact nonlinear search space. The proposed hybrid algorithm is implemented to a complex nonlinear transmission congestion management problem in which the active powers of generators are rescheduled for achieving the congestion-free network lines of a bulk power system. The practical feasibility of the proposed approach is checked by evaluating the congestion cost on various IEEE standard networks. The adaptability of the algorithm is checked by considering various case studies involving congestion due to bilateral, multilateral transactions and line outages on respective test bus system.