Quadratic Road Intersection (QRI) belongs to the group of traffic intersections with alternative designs, which have become popular due to their ability to alleviate traffic congestion and reduce travel time. A common feature of all alternative intersection designs is their implementation in suburbs, since they require more space compared to traditional intersections. The second common characteristic of the family of alternative intersections is treating left-turning vehicles in an unconventional way. QRI eliminates all left-turn movements at the main intersection, using quadratic bypasses to accommodate the missing turns. This creates two secondary intersections downstream from the main one, typically controlled by traffic lights. There are two phasing schemes that are used to control QRI: with one controller (Reid phases) and with three controllers, one for each intersection. The latter assumes optimization of traffic progression between the separated intersections that the QRI consists of. In this study, the QRI layout from the field is used to investigate control delay discrepancies in the implementation of the two phasing schemes. Moreover, this study develops a unique offset optimization approach, especially suited for QRI. In that endeavour, a swarm optimization technique, Bee Colony Optimization (BCO), is leveraged to optimize traffic control parameters: cycle, splits, and offsets. BCO is a well-known metaheuristic approach, based on the natural process of collecting nectar by honeybees. BCO has already shown high performance in traffic control optimization tasks. Although more complex to implement, the results show that the three-controller phase scheme, with offset optimization, outperforms the Reid phase scheme in terms of control delay as the primary performance measure in traffic signal control optimization problems.