The traditional economic dispatch (ED) inattention to the fossil fuels emission of thermal power plants no longer satisfies the environmental needs. As a result of the non-convex, non-smooth fuel cost functions in addition to the nonlinearity of the emission modelling. These make the combined economic and emission dispatch (CEED) a highly nonlinear optimization problem. Furthermore, different operation process constraints should be taken into account, such as loss in electrical networks and power balance of unit operation. These constraints increase the difficulty of obtaining the global optimal solution based on traditional methods. Recently, meta-heuristic population-based algorithms have successfully become a beneficial technique for solving nonlinear optimization problems. The major contribution in this work is presenting a recent meta-heuristic approach known as Mayfly algorithm (MA) for solving nonlinear and complex CEED problem. The numerical results are compared with results obtained from modern meta-heuristic algorithms like Jellyfish Search (JS) optimizer, Dwarf mongoose optimization (DMO), Tunicate swarm algorithm (TSA), Red deer algorithm (RDA), Tuna Swarm Optimization (TSO), Golden Eagle Optimizer (GEO) and Bald eagle search Optimization algorithm (BES). The standard IEEE 30-bus test system is used in this article. The simulation results are done using MATLAB environment. The results approve the reliability, stability, and consistency of the proposed approach. The proposed technique gives reliable, robust, and high-quality solution with faster computational time. Moreover, MA is more suitable for solving nonlinear CCED problem because it has a considerable convergence feature.