Gas lift is one of the most commonly used artificial lift method in oil-producing wells. However, the technique requires constant optimization of gas allocation to maximize profit. The Gas Lift Performance Curves (GLPC) are the main design element that is used for optimized injection. Several authors have proposed models to fit the GLPC. These curves are generated by modeling wells in a multiphase steady-state simulator. Once the model is built, a sensitivity analysis is run, and the curves are generated. In this work, The common workflow to generate GLPC was followed. Then, a new correlation for GLPC was suggested. The correlation outperforms all the models in the literature in terms of R-score and root mean square error. The correlation was then used to formulate a case study for four wells located in North Africa. First, the wells and PVT models were used to create a simulation. Once the simulation was calibrated, a sensitivity analysis of the gas lift injection rate was run. The new correlation was used to fit the GLPC. The optimization problem was mathematically formulated, and stochastic optimization techniques were used, noting Grey Wolf Optimization (GWO) Algorithm and Genetic Algorithm (GA) to obtain the global optimum of the distribution of a limited gas lift quantity. Both algorithms’ results were compared. GWO slightly outperformed GA. The advantages of GWO over GA were discussed, and the optimum gas allocation was obtained.