With the rapid proliferation of residential rooftop photovoltaic (PV) systems, current and voltage unbalance issues have become a matter of great concern in low voltage (LV) distribution feeders. To overcome the issues, this study proposes a model to optimally rephase customers and PVs among the three phases via static transfer switches (STSs). The optimal STS placement is also considered in the model to achieve a cost effective solution with optimum number and location of STSs. The objective is to minimise total energy losses caused by current unbalance, minimise the number of STSs, and keep voltage unbalance along the feeder within the acceptable range. The model is solved via a non-dominated sorting genetic algorithm-II (NSGA-II) which provides a Pareto front. A fuzzy decision-making approach is then applied to choose the final solution among the Pareto front points. The proposed model is simulated on the IEEE 123-Node Test Feeder. The simulations are conducted in MATLAB where the COM interface capability is used to call OpenDSS to evaluate NSGA-II populations. According to the achieved results, the proposed model can effectively and affordably apply STSs to mitigate unbalance issues in LV feeders hosting high penetration of rooftop PVs.