Economic load dispatch is to operate thermal generators economically with fulfilling load demand. This economic dispatch problem becomes highly complex and non-linear after considering various operating constraints like valve-point loading effect, generator operating constraints, and prohibited operating zone. The recently developed physics law-based artificial electric field algorithm has been applied to solve highly complex and non-linear ELD problems. The exploration and exploitation strategy of the algorithm helps to avoid local optimum value, and to get global optimum value in less computation time. The AEFA method has been applied to 10, 13, 15, 40, and large 110 thermal generators to validate the effectiveness of the proposed algorithm. The results obtained by the proposed algorithm have been compared with other recently developed algorithms.