This document describes the development an analysis of the main optimization methods used in flexible manufacturing systems (FMS) problems. The results are obtained from a random sample of more than one hundred documents published from 1986 to 2018 dedicated to the optimization of FMS. These are classified by their applications in the most significant fields of this area in analytical methods and heuristic methods. The discussion is based on the importance of this branch of engineering in the economic activity of a country and is motivation to continue doing research in it. The analysis also addresses some aspects of computational complexity found in ordinary optimization as well as the most common NP-hard problems of the FMS. The statistical results obtained are presented and the virtual future of the FMS is projected as well as the new challenges and opportunities to venture into this important field of human activity.