This paper demonstrates a hybrid between two optimization methods that are Artificial Immune System (AIS) and Genetic Algorithm (GA). The capability of overcoming the shortcomings of individual algorithms without losing their advantages makes the hybrid techniques superior to the stand-alone ones based on the dominant purpose of hybridization. The improvement of the results that enable to get it if GA and AIS work separately is the main objective of this hybrid. The hybrid includes two processes; firstly, AIS is the attraction among the researchers as the algorithm. This enables it to develop local searching ability and efficiency yet the convergence rate for AIS is preferably not precise compared to the GA. Secondly, a Genetic Algorithm is typically initializing population randomly. The last generation of AIS will be the input to the next process of the hybrid which is the GA in this hybrid AIS-GA. Hybrid makes GA enters the stage of standard solutions more rapidly and more accurate compared with GA initialized population at random. To differentiate between the results in terms of achieving the minimum value for these functions, eight mathematical test functions are being used to make comparison.