Evolutionary algorithm solution and KKT based optimality verification to multi-area economic dispatch

Abstract

This paper is aimed at exploring the performance of the various evolutionary algorithms on multi-area economic dispatch (MAED) problems. The evolutionary algorithms such as the Real-coded Genetic Algorithm (RGA), Particle Swarm Optimization (PSO), Differential Evolution (DE) and Covariance Matrix Adapted Evolution Strategy (CMAES) are considered. To determine the efficiency and effectiveness of various EAs, they are applied to three test systems; including 4, 10 and 120 unit power systems are considered. The optimal results obtained using various EAs are compared with Nelder–Mead simplex (NMS) method and other relevant methods reported in the literature. To compare the performances of various EAs, statistical measures like best, mean, worst, standard deviation and mean computation time over 20 independent runs are taken. The simulation experiments reveal that CMAES algorithm performs better in terms of solution quality and consistency. 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 error based stopping criterion is demonstrated.