Advanced digital microfluidic biochips based on technologies such as micro-electrode-dot-array (MEDA) and active matrix (AM) provide enhanced functionality compared to conventional biochips. Owing to the larger ratio of droplet size to electrode size, these platforms allow finer control of droplets and diagonal movement. Additionally, they allow dynamic grouping of micro-electrodes to form subsystems that can perform fluidic operations. Shape morphing is a key feature of MEDA/AM biochips that results in faster fluidic operations, thereby improving the efficiency of bioassays. To establish the benefits of shape morphing, we first numerically simulate the shape morphing operation. We employ a simplified 2-D flow model incorporating interface tracking through a level-set method to numerically simulate shape morphing induced by micro-electrode actuation. We also validate our numerical results with COMSOL simulations and experiments performed on MEDA/AM biochips. The validated shape morphing operations are subsequently used to optimize droplet routing for benchmark bioassays. We propose an algorithm to significantly reduce the size of the routing problem and the time needed to solve it. With the help of this improved approach, we show that droplet morphing operations reduce the time needed to complete bioassays.