Most of the world's oil reserves are in carbonate rocks. In recent years, studies of low-salinity water injection have demonstrated that the salinity of injected water affects increasing oil production. However, optimizing well operating conditions during low-salinity water injection is a major challenge due to the complexity of the process and the time-consuming simulations. Unlike previous studies, this study used a combination of a surrogate model based on machine learning with a multi-objective genetic algorithm to simultaneously model and optimize well operating constraints, including maximum oil production rate, minimum bottom hole pressure, water injection rate, and open and closed perforation conditions. The high-accuracy surrogate model (R-squared value of 0.989 for training data and 0.984 for testing) accelerated the simulation process. Then, considering the net present value, oil recovery factor, and water cut as target parameters, a set of optimal solutions on the Pareto front was obtained. The results showed that choosing the optimal operating conditions could increase the net present value of $135 million and the oil recovery factor up to 65.54%.