<p>Large-scale integration of renewable energy sources into the power grid has created a multi-energy system with electricity, heat, and natural gas. These systems must work well to meet goals like reducing operating expenses and greenhouse gas emissions. This study proposes a Stackelberg strategy for game-based multi-energy hub operation a competitive context. Multi-energy hub leads in Stackelberg’s game, and the followers are the consumers. The leaders possess the best multi-energy hub process strategy, whereas followers imitate in changing their energy demand. The hybrid frog-leaping algorithm is introduced for optimization. The optimizing technique employed in this meta-heuristic approach has its origins in frogs’ social behavior. This paper uses the mixed frog leaping technique to find the followers’ and leaders’ decision variables’ optimal values, which are the multi-energy hub’s energy usage, storage, and production and followers’ demand. The proposed method was implemented on a system of three energy hubs. The energy hubs of this 3-hub system use the same technology, supply loads independently, and are separately connected to upstream networks. The results show that the proposed method reduces multi-energy hub (EH) operation expenses and increases renewable energy (RE) source usage. The existing method also allows for various energy carriers and participants to work together in a competitive market to produce more efficient and sustainable energy systems. Generally, Stackelberg game-based strategy and hybrid frog-leap optimization algorithm provide an efficient multi-energy system optimization method. This approach can be adapted to address more sophisticated energy systems and players and to make maximum utilization of renewable energy or minimize greenhouse gases emitted.</p>