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Air travel demand is a crucial part of planning for airlines and airports. It helps in elaborating decisions and recognizing risks and opportunities. Forecasting air passenger demand is an interesting research study that deserves investigation. This problem requires prediction techniques such that Linear Regression and Neural Network. These techniques are efficient, but they have several parameters that necessitate appropriate values to provide the least error rate of prediction. Some recent air travel demand studies investigated Genetic Algorithms to provide optimal values for these parameters. In this article, we propose to explore the Firefly Algorithm (FA) and Particle Swarm Optimization (PSO) to find the optimal values for Linear Regression (LR) coefficients. This study presents two new hybrid prediction techniques (PSO based LR and FA based LR) to handle airline demand forecasting, which researchers have not previously covered. The results of PSO based LR, FA-based LR and LR are compared to find the best model with the lowest prediction error rate. The results showed that PSO based LR achieved the best prediction results with a lower error rate compared to FA based LR and LR alone. This study is performed using the data of Los Angeles International airport.