A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem

Economic dispatch (ED) plays an important role in power system operation. ED problem is a non-smooth and non-convex problem when valve-point effects of generation units are taken into account. This paper presents an efficient hybrid evolutionary approach for solving the ED problem considering the valve-point effect. The proposed algorithm combines a fuzzy adaptive particle swarm optimization (FAPSO) algorithm with Nelder–Mead (NM) simplex search called FAPSO-NM. In the resulting hybrid algorithm, the NM algorithm is used as a local search algorithm around the global solution found by FAPSO at each iteration. Therefore, the proposed approach improves the performance of the FAPSO algorithm significantly. The algorithm is tested on two typical systems consisting of 13 and 40 thermal units whose incremental fuel cost functions take into account the valve-point loading effects.