Emphasis on the use of renewable sources of energy is increasing day by day because of the diminishing fossil fuel reserve and stricter environmental regulations. Distributed Generation (DG) using Renewable Energy Sources (RES) can greatly reduce pollutant emission and improve global energy security. However, a RES requires high capital investment and there are reliability issues. RESs like solar energy and wind energy are weather dependent and precise forecasting is very difficult. As no single source of energy is capable of supplying cost effective, clean, and reliable power, a grid-connected hybrid power system is a promising option. Even though it is relatively inexpensive, there are environmental concerns due to pollutant emission. On the other hand, RES provides clean energy but there is an availability problem at times due to their intermittent nature. That is why, in this study, we have simultaneously optimized cost, availability and pollutant emission of a hypothetical grid-connected hybrid power system in Port Arthur, Texas. The system consists of photovoltaic panels, wind turbine generators, and storage batteries. The historical wind speed and solar irradiance data of Port Arthur have been used for obtaining the optimum design parameters. The design parameters derived here, which make the system feasible for South-East Texas, are wind turbine rotor swept area, PV panel area and storage battery capacity. We have used Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) for solving this problem.