The boiler combustion optimization has attracted growing research interest of more and more researchers in thermal energy engineering field. To achieve combustion optimization objective, the combustion characteristics model of the boiler needs to be built, and the efficient optimization algorithm also needs to be found. Therefore, in this study, a logic self-map chaos and Lévy flight Vortex Search (I-VS) algorithm is proposed. Then, comparative study between the I-VS algorithm and some other state-of-the-art optimization algorithms is performed. Next, the combustion efficiency model is built based on fast learning network (FLN). The I-VS algorithm is used to optimize FLN, and then an I-VS-FLN model is built for predicting NOx emissions of a boiler. Experimental results show that the I-VS-FLN model has better generalization ability than five other models. Finally, the I-VS algorithm is used to tune the operating parameters of the boiler based on the FLN model and the I-VS-FLN model to achieve the combustion optimization objective.