This paper proposes a Linkage Learning Genetic Algorithm (LLGA) based on the messy Genetic Algorithm (mGA) to optimize the Min-Max fuel controller performance in Gas Turbine Engine (GTE).For this purpose,a GTE fuel controller Simulink model based on the Min-Max selection strategy is firstly built.Then,the objective function that considers both performance indices (response time and fuel consumption) and penalty items (fluctuation,tracking error,overspeed and acceleration/deceleration) is established to quantify the controller performance.Next,the task to optimize the fuel controller is converted to find the optimization gains combination that could minimize the objective function while satisfying constraints and limitations.In order to reduce the optimization time and to avoid trapping in the local optimums,two kinds of building block detection methods including lower fitness value method and bigger fitness value change method are proposed to determine the most important bits which have more contribution on fitness value of the chromosomes.Then the procedures to apply LLGA in controller gains tuning are specified stepwise and the optimization results in runway condition are depicted subsequently.Finally,the comparison is made between the LLGA and the simple GA in GTE controller optimization to confirm the effectiveness of the proposed approach.The results show that the LLGA method can get better solution than simple GA within the same iterations or optimization time.The extension applications of the LLGA method in other flight conditions and the complete flight mission simulation will be carried out in part Ⅱ.