Penalty parameter-less constraint handling scheme based evolutionary algorithm solutions to economic dispatch

The application and performance comparisons of various evolutionary algorithms ( EA) on economic dispatch (ED) problems with non-smooth cost functions considering valve-point effects and multiple fuel options are presented. The EAs such as the real-coded genetic algorithm, particle swarm optimisation (PSO) and differential evolution ( DE) are considered. New penalty parameter-less constraint-handling scheme is employed to improve the performance of EA. Ten-generator ED test system is taken for simulation purposes. To determine the efficiency and effectiveness of various EAs, two experiments are conducted, considering only multiple fuel options and considering both valve-point and multiple fuel options. The optimal results obtained using various EAs are compared with Nelder-Mead simplex method and previous reported results. To compare the performances of various EAs, statistical measures such as best, mean, worst, standard deviation and mean computation time over 20 independent runs are taken. The simulation experiments reveal that PSO performs better in terms of solution quality and consistency. DE performs better in terms of mean computation time. For the first time, Karush-Kuhn Tucker (KKT) conditions are applied to the solutions obtained using EAs to verify optimality. It is found that the obtained results are satisfying the KKT conditions and confirm the optimality. Also, the effectiveness of KKT-based stopping criteria is clearly demonstrated.