The oscillating tailing shape and spectrum of the decelerated finite-energy Airy pulse are influenced by various parameters. This study examined the impacts of peak power, width, initial chirp, truncation coefficient, and distribution factor of the Airy pulse on the generation of rogue waves in a supercontinuum (SC) as well as the SC coherence and stability. The findings reveal that altering these parameters can regulate the rogue waves and affect the SC coherence and stability. Moreover, a multiobjective particle-swarm optimization algorithm is used to simultaneously optimize the five pulse parameters. By using the average peak power of 500 analog output solitons (i.e., twice of that required for generating the rogue waves) and considering the number and distribution of rogue waves among the solitons as optimization objectives, this study identifies optimal parameters for the Airy pulse. These parameters either promote or suppress the generation of rogue waves, enabling controlled manipulation of rogue wave generation within the SC.