With the increase in potential uses of terahertz technology, the need for terahertz transceivers with application-oriented adaptive radiation patterns has emerged. Reconfigurable reflectarrays consisting of actuated sub-wavelength reflectors have been successfully used for terahertz beam steering and beamforming. They do not require a complex feeding network and associated electronics, enabling a compact and power-efficient terahertz beam steering system. However, the current reflectarray-based beam steering is accomplished by forming the reflectarray as a grating structure, which is accompanied by the problems such as grating lobes, limited steering range, and discrete steering angles. Here, we configure a MEMS-based reflectarray with the genetic algorithm to eliminate the grating lobes and open up the possibility of customizing its radiation pattern. We used single- and multi-objective optimization to find the optimal height profile of the reflectarray and verified the results by full-wave electromagnetic simulations. We measured the radiation patterns of four reflectarray phantoms, i.e. reflectarrays without the MEMS actuation systems. The measurement results agree well with the calculated ones, with the main beam deviating at most 2° from the target direction. Our work demonstrates how a genetic algorithm is used to shape a reconfigurable terahertz reflectarray to eliminate the grating lobes and tailor some specific featuress in its radiation pattern.