Micro-Grid (MG) with hybrid power resources can supply electric loads independently. In case of surplus power, the neighborhood micro-grids can be integrated together in order to supply the overloaded micro-grid. The challenge is to select the most suitable, optimal and preferable micro-grid within a distributed network, which consists of islanded MGs, to form that integration. This paper presents an intelligent decision-making criteria based on the Weighted Arithmetic Mean (WAM) of different technical indices, for optimal selection of micro-grids integration in case of overloaded event due to either unusual increase in consumed power or any deficiency in power generation. In addition, overloading is expected due to excess increase or decrease in weather temperature. This may lead to extreme increase of load due to increase of air conditioning or heating loads respectively. The proposed arithmetic mean determination based on six multi-objective indices, which are voltage deviation, frequency deviation, reliability, power loss in transmission lines, electricity price and CO2 emission is applied. This work is developed through three main scenarios. The first scenario studies the effect of each index on the integrated micro-grid formation. The second scenario is the biased optimization analysis. In this stage, the optimal micro-grids integration is based on intentionally chosen multi-objective index weights to fulfil certain requirements. The third scenario targets the optimal selection of the multi-objective indices’ effectiveness weights for power system optimum redistribution. The sharing weights of each index will be optimally selected by Water Cycle Optimization Technique (WCOT) and Genetic Algorithm (GA) addressing the system optimal power sharing through optimum micro-grids re-formation (integration). WCOT and GA are simulated using MATLAB (R2017a, The MathWorks Ltd, Natick, MA, USA). The developed work is applied to a distributed network which consists of a five micro-grid tested system, with one overloaded micro-grid. The three modules are utilized for multi-objective analysis of different alternative micro-grids. Both WCOT and GA results are compared. In addition, it is investigated to find and validate the optimum solution. Final decision-making for optimal combination is determined, aiming to reach a perfect technical, economic and environmental solution. The results indicate that the optimal decision may be modified after each individual index weight exceeds a specific limit.