A NSGA-II variant for the dynamic economic emission dispatch considering plug-in electric vehicles

The dynamic economic emission dispatch considering plug-in electric vehicles (DEED-PEV) belongs to a nonlinear constrained optimization problem and has the multimodal and discontinuity characteristics. The first characteristic mainly comes from the cost function with valve-point effects, and the second one is associated with the constraints of prohibited operating zones. In this paper, a novel NSGA-II (NNSGA-II) is proposed to deal with DEED-PEV. NNSGA-II replaces the simulated binary crossover operator by the one based on Gaussian distribution, and adaptively adjusts the crossover rate of each individual according to its rank in population. Also, it incorporates a rewarding coefficient into the crowding distance in density estimation, which gives considerations to both density and evenness of solutions. Accordingly, NNSGA-II is able to perform extensive searches in solution space and achieve a series of individuals with high diversity and good evenness. Experimental results suggest that NNSGA-II outperforms the other seven MOEAs for nine DEED-PEV problems with different charging and discharging scenarios of plug-in electric vehicles, and its obtained solutions are superior to those of the other seven MOEAs according to the hypervolume and coverage indicators. In short, NNSGA-II is a potential alternative for minimizing the generation cost and pollutant emission of DEED-PEV.