In the power system, economic power dispatch is a popular and fundamental optimization problem. In its classical form, this problem only considers thermal generators and does not take into account network security constraints. However, other forms of the problem, such as economic emission dispatch (EED), are becoming increasingly important due to the emphasis on minimizing emissions for environmental purposes. The integration of renewable sources, such as solar, wind, and hydro units, is an important aspect of EED, but it can be challenging due to the stochastic nature of these sources. In this study, a multi-objective algorithm is developed to address the problem of economic emission power dispatch with the inclusion of these renewable sources. To account for the intermittent behavior of solar, wind, and hydro power, the algorithm uses Lognormal, Weibull, and Gumbel distributions, respectively. The algorithm also considers voltage limitations, transmission line capacities, prohibited areas of operation for thermal generator plants, and system restrictions. The multi-objective real coded non-dominated sorting genetic algorithm II (R-NSGA-II) is applied to the problem and includes a procedure for handling system restrictions to meet system limitations. Results are extracted using fuzzy decision-making and are analyzed and discussed. The proposed method is compared to other newer techniques from another study to demonstrate its robustness. The results show that the proposed method despite being older is cost-significant while maintaining the same or lower emissions. These results were observed consistently and did not happen by chance, detailed explanation of why and how is discussed.