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One of the important issues in the planning stage of active distribution networks (ADNs) is the optimal design of microgrids (MGs). The design, as a multi-MG system, is comprehensively investigated in this study. In this way, the allocation of energy storage systems (ESSs) and partitioning of ADN are simultaneously performed in order to minimise the cost and maximise the self-adequacy and the reliability considering the uncertainty of load and renewable energy resources. In this study, two approaches are considered. In approach I, the cost, reliability and self-adequacy objectives are taken into account whereas, in approach II, a new probabilistic index representing the ratio of load to storage capacity is also added to mentioned objectives. The proposed multi-objective problem is solved with non-dominated sorting genetic algorithm-II (NSGA-II) as a well-known algorithm based on a probabilistic approach using the Monte-Carlo simulation method (MCSM) and in each approach, several Pareto optimal solutions are evaluated. To simulate and validate the effectiveness of the proposed method, two benchmark distribution networks (the 33-bus and the 119-bus) are used.