This study proposes a novel method to optimally allocate capacity for a stand-alone microgrid system (SAMS). An SAMS is usually found on offshore islands or in the areas, where electricity cannot be delivered by utility companies. With the continuing development of renewable energy, the photovoltaic (PV) plant, wind turbine generator and battery energy storage system are integrated into an SAMS to reduce generation cost, mitigate environmental damage and increase generation efficiency. In terms of the uncertainty of renewable generation and to allow optimal capacity allocation for an SAMS, a combination of a Monte Carlo simulation, an enhanced charged system search algorithm and a Pareto-based fuzzy decision-making method is used in this study. The objectives considered are the minimisation of both the levelised cost of energy (LCOE) and the expected energy not supplied. An efficient scheme that reduces the convergence time is also developed. The proposed method is tested using an SAMS that is located on an offshore island of Taiwan. Testing results show that the proposed method produces more stable convergence, lower LCOE value, smaller PV capacity and lower power curtailment than those for the differential evolution and particle swarm optimisation methods.