Nowadays, renewable energy sources in a micro‐grid (MG) system have increased challenges in terms of the irregularly and fluctuation of the photovoltaic and wind turbine units. It is necessary to develop battery energy storage. The MG central controller is helping to develop it in the MG system for improving the time of availability. Thus, reducing the total energy expenses of MG and improving the renewable energy sources (battery energy storage) are considered together with the operation management of the MG system. This study proposes fitness‐based modified game particle swarm optimisation (FMGPSO) algorithm to optimise the total costs of operation and pollutant emissions in the MG and multi‐MG system. The optimal size of battery energy storage is also considered. A non‐dominated sorting genetic algorithm‐III, a multi‐objective covariance matrix adaptation evolution strategy, and a speed‐constrained multi‐objective particle swarm optimisation are compared with the proposed FMGPSO to show the performance. The results of the simulation show that the FMGPSO outperforms both the comparison algorithms for the minimisation operation management problem of the MG and the multi‐MG system.