A modified particle swarm optimization for economic dispatch with non-smooth cost functions

This paper presents a new approach to economic dispatch (ED) problems with non-smooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints, which makes the problem of finding the global optimum difficult when using any mathematical approaches. Since, standard PSO may converge at the early stage, in this paper, a modified P50 (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. To validate the results obtained by MPSO, standard particle swarm optimization (PSO) and guaranteed convergence particle swarm optimization (GCPSO) are applied for comparison. Also, the results obtained by MPSO, PSO and GCPSO are compared with the previous approaches reported in the literature. The results show that the MPSO produces optimal or nearly optimal solutions for the study systems. (C) 2010 Elsevier Ltd. All rights reserved.