A micro-grid (MG) is regarded as a localized small-scale power supply system designed for providing electrical power for a remote community, which may be connected to the grid. The paper considers six participants’ sites in a remote community. The peak energy consumption patterns for these participants must be different to ensure coalition for mutual benefits and this would facilitate efficient utilization of energy resources. This community concerned may include rural communities having participants such as schools, housing estates, industrial sites, etc. The propose approach would ensure that many participants and their needs are captured and optimized profit of the participants would ensure mutual benefits. In islanded MG, most of the cost/profit distributions in energy trading problems are done based on the self-interest of the participants. Some consider a fair (acceptable or reasonable) cost/profit distribution using the cooperative game theory (CGT) based on the Nash bargaining solution (NBS). However, this method leads to a high degree of dissatisfaction. To improve the fairness and mutual benefits for all MG participants, a new flexible approach is developed. Specifically, CGT which uses a generalized NBS (GNBS) has been proposed, which relaxes certain axiom of the NBS to ensure that fairness of game theory is achieved. The approach allows the profit of the MG participants to be shared using a mechanism based on the negotiation power (i.e. weighted fairness) so that the MG would attain an improved economic outcome. Empirical evaluation of the approach indicates that overall profits using CGT is higher when compared with an independent approach. Moreover, different in negotiation power is achieved in which higher profit is allocated to any participant based on participant's mutual agreement in achieving fair profit distribution. A robust optimization algorithm called Teaching-Learning-Based-Optimization (TLBO) is developed to obtain optimal results. The heuristics algorithms are used in testing the effectiveness of TLBO, which confirm that the TLBO is indeed powerful and robust enough to give quality solutions in solving energy-trading problems.