Coevolutionary Genetic Algorithm Based on the Augmented Lagrangian Function for Solving the Economic Dispatch Problem

This paper proposes a coevolutionary augmented Lagrangian method (AGCE) for solving the classic economic dispatch problem. This problem becomes non-convex and non-differentiable if valve-point loadings effects are considered in the cost curves of thermal units. In such cases, the evolutionary approaches have proven to be efficient for solving the primal economic dispatch problem; however, the great majority of these methods are not capable of solving the associated dual problem. Furthermore, the solutions obtained by these methods cannot be evaluated concerning their optimality. The AGCE works in the primal-dual subspaces and is able to calculate both primal and dual optimal values. For such a purpose, AGCE processes, in parallel, the evolution of two distinct groups of individuals, associated with primal and dual variables, respectively. The “clouds” of primal and dual points become iteratively denser, and converge to the saddle points associated with the problem, even in the presence of non-differentiability points. Therefore, AGCE makes possible the evaluation of optimality of its solution points. In the results, the AGCE is compared with a traditional interior point method and with a genetic algorithm that works only in the primal subspace.