With the increasing focus within the commercial aviation industry on fuel-efficient designs, it is imperative for turbofan manufacturers to ensure that their engine designs are well-optimized with respect to a number of objective parameters, including the thrust specific fuel consumption (TSFC). Current research on this problem mainly employs the use of population methods, particularly genetic algorithms, as a means of finding the optimal design point. In this paper, a genetic algorithm is first deployed as an optimization method to minimize the TSFC of a turbofan engine, and its shortcomings faced in solving this particular problem identified. A new population method, the Domain-Shrink method, is introduced. The Domain-Shrink method outperformed the genetic algorithm in minimizing TSFC as evaluated by the metrics of CPU time, consistency, and its ability to reach the global minimum. However, its widespread applicability and suitability remains to be examined.