Since its introduction, mobile wireless communication has grown and changed substantially. This massive growth leads to different levels of complexity, mainly concerned with the assignment of different parameters to radio or base stations. One parameter is the Root Sequence Index (RSI), related to the Physical Random Access Channel (PRACH) preambles, used to allocate uplink channels between the user equipment and the base station. The assignment of RSIs close-in-range to neighbor antennas may cause collisions, which are responsible for failures on service establishment, and therefore, performance degradation. Such allocation problems can be modeled as Graph Coloring Problems, including several additional constraints. However, few studies focus on RSI allocation and collisions from the optimization perspective. The objective of this study is to develop methods for allocating the RSI, trying to lessen the risk of collision, and obeying other constraints. In this study, both exact and heuristics methods are explored and compared. For this, several mathematical models were made, alongside a biased random key genetic algorithm. The results show that the utilization of an allocation strategy based on neighbor relations is efficient for finding good solutions.