Genetic Algorithm based on the Lagrange Method for the Non-Convex Economic Dispatch Problem

This paper considers the non-convex Economic Dispatch Problem (EDP) with power losses, prohibited operating zones, and generation cost functions modeling both valve-point loading effects and multiple fuel options. This constrained problem is stated as an unconstrained problem by using the augmented Lagrange formulation, while introducing Lagrange multipliers and penalty parameters. Then, a genetic algorithm (GA) relying on two iterative loops is described: the inner loop executes a GA with fixed penalty parameters and Lagrange multipliers, while the outer loop updates such parameters when required. The effects of four different mutation operators based on the Gaussian and Cauchy distributions is also investigated. Finally, the effectiveness of the proposed approach is shown by numerical simulations on two practical test systems.