Differential evolution based on truncated Lévy-type flights and population diversity measure to solve economic load dispatch problems

Abstract

Economic load dispatch (ELD) is an important constrained optimization task addressing this vital concern for power system operations. ELD problem is the process of allocating generation among available committed generating units such that cost of generation is optimum subject to several equality and inequality constraints. The conventional optimization methods are mainly classical mathematical methods, which include gradient method and Lagrange relaxation method. In recent years, different types of evolutionary algorithms have been used to solve ELD problems. Among the existing evolutionary algorithms, a well-known branch is the differential evolution (DE). The mutation operation of DE applies vector differentials between existing population members for determining both the degree and the direction applied to the individual subject of the mutation operation. With an eye to improve the performance of classical DE, in this paper, a DE algorithm combined with truncated Lévy flight random walks and a population diversity measure (DEL) to improve the crossover and mutation operations is designed to help avoiding premature convergence effectively. A Lévy flight random walks (a sequence of displacements) in which the increments are distributed according to a heavy-tailed probability distribution form the α-stable distribution family. The effectiveness of the proposed DEL is demonstrated for two benchmark ELD problems. In order to evaluate the performance of the proposed DEL, it is applied to benchmark systems consisting of 13 and 140 thermal units. Simulation results reveal that, compared with the classical DE and those other methods reported in literatures recently, the proposed DEL is capable of obtaining better quality solutions with higher efficiency.