Using electric storage systems (ESSs) is known as a viable strategy to mitigate the volatility and intermittency of renewable distributed generators (DGs) in microgrids (MGs). Among different electric storage technologies, battery energy storage (BES) is considered as the best option. In unit commitment (UC) module, the set of committed dispatchable DGs along with their power, power exported to/imported from macrogrid and status and power of ESS units are determined. In this paper, BES degradation is considered in UC formulation and an efficient particle swarm optimisation with quadratic transfer function is proposed for solving UC in BES-integrated MGs, while the uncertainties of demand, renewable generation and market price are considered and dealt with robust optimisation. UC is formulated as a multi-objective optimisation problem whose objectives are MG operation cost and BES degradation. The resultant multi-objective optimisation problem is converted into a single-objective optimisation problem and the effect of weight factors on MG operation cost and BES lifecycle are investigated. The results show that by consideration of BES degradation in objective function, BES lifecycle increases from 350 to 500 and the minimum depth of charge increases from 5.5% to 34%; however, MG operation cost increases from $8717 to $8910.2. The results also show that by consideration of uncertainties, MG's operation cost increases by 8.22%.