Optimal economic dispatch with valve loading effect using self-adaptive firefly algorithm.

Economic dispatch (ED) problem exhibits highly nonlinear characteristics, such as prohibited operating zone, ramp rate limits, and non-smooth property. Due to its nonlinear characteristics, it is hard to achieve the expected solution by the classical methods. To overcome the challenging difficulty, this paper proposes an improved firefly algorithm (FA) to solve economic dispatch (ED) problem. The improved FA employs two strategies to enhance the search ability and avoid the premature usually suffered from in standard FA. The first one is based on the distance information among the fireflies, and it adjusts the light absorption coefficient adaptively. The other one is a decreasing strategy for the randomization parameter. Additionally, a crossover operation is employed to create potential solution with high diversity. The designs are able to enhance the search ability and performance of FA, which have been demonstrated on six benchmark functions. To validate the proposed algorithm, we also use three different systems to demonstrate its efficiency and feasibility in solving ED problem. The experimental results show that the proposed FA method was capable of achieving higher quality solutions in ED problems. [ABSTRACT FROM AUTHOR]