With the continuously expanding installed capacity of the power system, the ever-increasing short-circuit current hinders its secure operation and further development. Installing fault current limiters to suppress short-circuit current is very effective but expensive. Thus, transmission line switching and unit commitment are considered in operation to reduce the investment cost. This paper establishes the optimal configuration model of fault current limiters considering transmission line switching and unit commitment, which is a complex Mixed-Integer Linear Programming (MILP) problem. To accelerate the solution of the MILP problem, a heuristic decomposition algorithm was proposed based on Analytical Target Cascading (ATC) and a Large Neighborhood Search (LNS) algorithm, which has two stages. In the first stage, the feasible solution is constructed based on the framework of ATC and combines the idea of LNS in ATC to improve the efficiency of constructing feasible solutions. In the second stage, LNS is used to improve the feasible solution based on the decomposed sub-problem. Finally, simulations were conducted on an IEEE 118-bus and 186-branch power system and a real 727-bus and 861-branch power system. The numerical results show that for these IEEE and real systems, compared with GUROBI, the proposed algorithm is 125.7 and 10.6 times faster with only 0.04% and 0.003% higher total cost, respectively; compared with ATC, it is slightly slower with 0.2% and 0.3% lower total cost, respectively.