This paper presents a Hybrid Nelder–Mead – Fuzzy Adaptive Particle Swarm Optimization (HNM-FAPSO) for a Multi-Line Congestion Management (MLCM) problem. MLCM is a nonlinear optimization problem in deregulated power system. The generators which are sensitive to the congested lines are selected based on the novel Apparent Power Sensitivity Factor (APSF) and are rescheduled by using the HNM-FAPSO algorithm. The objective of hybridizing the Nelder–Mead (NM), Fuzzy adaptive Particle Swarm Optimization (FAPSO) is to blend their unique advantages as well as their efficacy. The NM method is a very efficient local search procedure and is used to initialize the population for Particle Swarm Optimization (PSO) which is used to search global best value. But PSO has a problem of premature convergence due to linear variation of its internal parameter i.e. inertia weight. To overcome this, a fuzzy inference system is used to dynamically update the inertia weight. The feasibility and performance of the HNM-FAPSO algorithm is demonstrated on the standard IEEE 30-bus system and IEEE 118-bus system. A comparison of simulation results and statistical analysis reveal optimization efficacy of the HNM-FAPSO algorithm over other algorithms like FAPSO, NM, Simple Bacterial Foraging (SBF), adaptive bacterial foraging algorithm with Nelder–Mead (ABFNM), Genetic Algorithm (GA) and PSO available in literature. The main outcome of the proposed algorithm in solving MLCM is reduction in congestion cost, rescheduled real power, power loss and computational time. 
Managing multi-line power congestion by using Hybrid Nelder–Mead – Fuzzy Adaptive Particle Swarm Optimization (HNM-FAPSO)