Desalination of sea water involving multiple-effect evaporator (MEE) is commonly used in industry, especially with the introduction of the low temperature MEE. Parallel/cross feed flow sequence is one of the most commonly used configurations on account of its high gain output ratio (GOR). GOR is defined as the ratio of the distillate produced to the mass of the steam supplied and it measures the energy intensity of a desalination process. Generally, for parallel/cross flow MEE the feed flow rate is same for all the effects. However, the equal feed flow rate may not guarantee an energy optimal solution. A new methodology, based on the principle of process integration combined with mathematical optimization, is developed in this paper to determine the optimal feed flow rate to each effect. MEE is represented as a Grand Composite Curve (GCC) for understanding energy integration and providing better insight of the overall problem. Through an illustrative example, it is shown that the GOR for 12-effect MEE can be increased by 11% with optimized feed flow rate. Sensitivity analysis is carried out for calculating the optimal operating parameters. Finally, it is proposed to design MEE with high temperature driving force for reduction in capital cost as well as specific energy consumption. (C) 2016 Elsevier Ltd. All rights reserved.