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Plug-in hybrid electric vehicles (PHEVs) and plug-in electric vehicles (PEVs) have gained enormous attention for their ability to reduce fuel consumption in transportation and are, thus, helpful in the reduction of the greenhouse effect and pollution. However, they bring up some technical problems that should be resolved. Due to the ever-increasing demand for these PHEVs, the simultaneous connection of large PEVs and PHEVs to the electric grid can cause overloading, which results in disturbance to overall power system stability and quality and can cause a blackout. Such situations can be avoided by adequately manipulating power available from the grid and vehicle power demand. State of charge (SoC) is the leading performance parameter that should be optimized using computational techniques to charge vehicles efficiently. In this research, an efficient metaheuristic algorithm, accelerated particle swarm optimization (APSO), and its five variants were applied to allocate power to vehicles connected to the grid intelligently. For this, the maximization of average SoC is considered a fitness function, and each PHEV can be connected to the grid once a day so that the maximum number of cars can be charged daily. To statistically compare the performance of these six algorithms, one-way ANOVA was used. Simulation and statistical results obtained by maximizing this highly non-linear objective function show that accelerated particle swarm optimization with Variant 5 achieved some improvements in terms of computational time and best fitness value. The APSO-5 solution has a considerable percentage increase compared with the solution of other variants of APSO for the four PHEV datasets considered. Moreover, after 30 trials, APSO 5 gives the highest possible fitness value among all the algorithms. [ABSTRACT FROM AUTHOR]