The battery energy storage system (BESS) can accommodate the uncertainties of renewable energy sources (RESs) and load demand. Proper allocation of the BESS in the distribution network (DN) can bring cost-effectiveness and enhance system stability. To realize the reliable and economic operation of BESS in the DN, a multi-objective optimization model for optimal BESS allocation is established, which aims at minimizing the annual overall cost of the whole system, including life cycle cost (LCC), power loss cost, peak-shaving cost, tie-line fluctuation penalty, and voltage deviation penalty. Then, a novel implementation of the improved equilibrium optimizer (IEO) algorithm is proposed to solve the optimal BESS allocation scheme. In order to verify the effectiveness of the proposed method, the simulation experiment based on the IEEE 33-bus test system is performed. Simulation results prove that the IEO algorithm is capable of rapid stable convergence and efficient searching for optimum in the multidimensional space. By the end of the iteration, the annual overall cost of the whole system records a minimum value of $1.8692e+06 every year. A meticulous techno-economic analysis demonstrates that the obtained BESS allocation scheme not only effectively ensures cost-effectiveness of BESS but also significantly reduces power loss, load peak-valley difference, tie-line power fluctuation, and voltage deviation.