This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are introduced in the paper by employing two different random walk generators for diffusion process in which SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from three test system. These systems with 6, 10, and 20 units with different objective function forms and different constraints are inspected. Numerical result comparison can confirm that the applied approach has better solution quality and fast convergence time when compared with some recently published standard, modified, and hybrid methods. This elucidates that the two SFS methods are very favorable for solving the ELD problem.