The automated design of meander line RFID antennas is a discrete self-avoiding walk (SAW) problem for which efficiency is to be maximized while resonant frequency is to be minimized. This work presents a novel exploration of how discrete local search may be incorporated into a continuous solver such as differential evolution (DE). A prior DE algorithm for this problem that incorporates an adaptive solution encoding and a bias favoring antennas with low resonant frequency is extended by the addition of the backbite local search operator and a variety of schemes for reintroducing modified designs into the DE population. The algorithm is extremely competitive with an existing ACO approach and the technique is transferable to other SAW problems and other continuous solvers. The findings indicate that careful reintegration of discrete local search results into the continuous population is necessary for effective performance.