In this paper, the Forward-Backward (FB) strategy has been developed to solve the load flow (LF) problem of a large-scale multi-carrier network. The Teaching–Learning-Based Optimization (TLBO), as a powerful heuristic tool, has been used for the optimization of the proposed LF. For this purpose, a large-scale unbalanced multi-carrier energy system (MCES) including an IEEE 33-bus system, a natural gas network with 25 nodes, and a heat network with 20 nodes have been considered to ascertain the applicability of the proposed FB-based machine learning strategy. By minimizing an objective function of the MCES system under unequal constraints, the TLBO tries to solve the optimization problem of MCES. The unbalanced current and voltage performance of the MCES system has been investigated by employing the current unbalance index (CUI) and voltage unbalance index (VUI). The numerical analysis with the application of the current unbalance index and voltage unbalance index has been studied to appraise the efficiency of the proposed optimal strategy to solve the LF problem of the MCES system. Manuscript profile