A new global particle swarm optimization for the economic emission dispatch with or without transmission losses

A new global particle swarm optimization (NGPSO) algorithm is proposed to solve the economic emission dispatch (EED) problems in this paper. NGPSO is different from the traditional particle swarm optimization (PSO) algorithm in two aspects. First, NGPSO uses a new position updating equation which relies on the global best particle to guide the searching activities of all particles. Second, it uses the randomization based on the uniform distribution to slightly disturb the flight trajectories of particles during the late evolutionary process. The two steps enable NGPSO to effectively execute a number of global searches, and thus they increase the chance of exploring promising solution space, and reduce the probabilities of getting trapped into local optima for all particles. On the other hand, the two objective functions of EED are normalized separately according to all candidate solutions, and then they are incorporated into one single objective function. The transformation steps are very helpful in eliminating the difference caused by the different dimensions of the two functions, and thus they strike a balance between the fuel cost and emission. In addition, a simple and common penalty function method is employed to facilitate the satisfactions of EED's constraints. Based on these improvements in PSO, objective functions and constraints handling, high-quality solutions can be obtained for EED problems. Five examples are chosen to testify the performance of three improved PSOs on solving EED problems with or without transmission losses. Experimental results show that NGPSO is the most efficient approach on solving the single objective optimization (fuel cost or emission minimization) and multi-objective optimization (fuel cost and emission minimizations) problems.