Simulation of multi-stage flash (MSF) desalination processes that have production capacity range between 50,000 to 75,000 m3/d is an intensive computational problem that requires high computer processing speed despite the availability of advanced processing computer power in hand nowadays. In this work, a comparative study is conducted to explore the performance of different numerical techniques to solve large set of nonlinear equations generated by large scale MSF models. These algorithms can be categorized into three groups namely; conventional numerical approximation methods, multi-objective optimization based methods, and the last group comprises artificial neural networks (ANN) based models and genetic algorithms (GA) based methods. The problem of solving large sets of nonlinear equations with upper and lower constraints is accomplished successfully using all algorithms with different prediction efficiency and speed. The idea of using GA and ANN based algorithms in simulating the MSF model is basically used to generate feasible initial solution estimates that were used as starting guesses for other numerical methods in the former case and to eliminate the step of providing these initial guesses in the later case. Significant reduction of computation effort was attained using ANN-based techniques. The outcome of this work can be utilized to develop new generation of process simulators that are based on well trained ANNs in order to achieve speedup of computations and to generate more reliable predictions without detracting from accuracy.