Growing interest in the smart grid, increasing use of distributed generation, and classical distribution system reconfiguration (DSR) and restoration problems have led to the search for efficient distribution automation tools. One such tool, the improved Fast Nondominated Sorting Genetic Algorithm (FNSGA), not only is effective in finding system configurations that are optimal with respect to voltages, currents, and losses, but also considered parametric study to determine minimum values of N and Gen. In this paper, the essential spanning tree concept is expanded to improve the computational efficiency of the algorithm. Results of the study show that for relatively small test systems, optimum system configurations are obtained using values of N and Gen that require very small CPU times. In larger systems, optimum values of N and Gen requiring reasonable CPU times can also be found, provided that certain carefully chosen branches are removed from the pool of possibilities when producing the initial population in the algorithm. By using essential trees, the efficiency of the calculation is improved.