In this paper, we study a single-machine scheduling problem with deteriorating processing time of jobs and multiple rate-modifying activities which reset deteriorated processing time to the original processing time. In this situation, the objective function is to minimize total completion time. First, we formulate an integer programming model. Since the model is difficult to solve as the size of real problem being very large, we design an improved genetic algorithm called adaptive genetic algorithm (AGA) with spontaneously adjusting crossover and mutation rate depending upon the status of current population. Finally, we conduct some computational experiments to evaluate the performance of AGA with the conventional GAs with various combinations of crossover and mutation rates.