Optimal location and sizing of battery energy storage systems (BESSs) in a distribution network (DN) is essential to guarantee their economic and reliable operation. Given this, this paper proposes an optimal siting and sizing method for BESSs. First, the C-mean clustering algorithm is used for typical scene clustering of load curves, and wind and photovoltaic (PV) output curves over a year. Secondly, a multi-objective optimization model for optimal location and sizing is established to minimize the daily cost of BESSs, and voltage and load fluctuation. To obtain the Pareto optimal solution set of BESS location, this paper designs a modified multi-objective mayfly algorithm (MMOMA) to analyze the model. An improved ideal-point-based decision (IIPBD) method is employed to select a compromise solution among the Pareto optimal solution set. Thus the best trade-off of three objectives is achieved. Finally, this paper uses the expanded IEEE33 bus system to validate the proposed method. Simulation results show that MMOMA can obtain a widely spread and well-distributed Pareto front compared with two traditional multi-objective optimization algorithms. The compromise decision scheme obtained by the IIPBD method effectively minimizes the comprehensive cost of BESSs, and significantly reduces voltage and load fluctuation of the DN. This work is supported by the National Natural Science Foundation of China (No. 61963020).