In this paper; we present a new approach to tackle scheduling problems in manufacturers? assembly line. Former solutions also provide resu..l..ts, yet they turn out to be ineffective or time-consuming. Our approach involves several new schemes in crossover and mutation, which reduce its processing time. In order to avoid premature convergences of the chromosomes, we choose a self-adaptive mutation rate and a Clone-Replacement approach. We then try an alternative called Derivative Tree Crossover. Finally, the paper examines this algorithm?s efficiency, which outperforms the previous methods.