“…Analytical methods [6], a Lagrangian method [7], and the Newton-Raphson method [8] have all been employed as initial approaches. Evolutionary methods have also been employed for this purpose, such as a genetic algorithm [9], particle swarm optimization (PSO) [10], simulated annealing [11], artificial immune system [12], differential evolution [13], and the frog algorithm [14]. In [15], the PSO-SIL algorithm was used to obtain an economical power flow with the optimum costs.…”