In recent years, energy consumption has notably been increasing. This poses a challenge to the power grid operators due to the management and control of the energy supply and consumption. Here, energy commitment is an index criterion useful to specify the quality level and the development of human life. Henceforth, continuity of long-term access to resources and energy delivery requires an appropriate methodology that must consider energy scheduling such as an economic and strategic priority, in which primary energy carriers play an important role. The integrated energy networks such as power and gas systems lead the possibility to minimize the operating costs; this is based on the conversion of energy from one form to another and considering the starting energy in various types. Therefore, the studies toward multi-carrier energy systems are growing up taking into account the interconnection among various energy carriers and the penetration of energy storage technologies in such systems. In this paper, using dynamic programming and genetic algorithm, the energy commitment of an energy network that includes gas and electrical energy is carried out. The studied multi-carrier energy system has considered defending parties including transportation, industrial and agriculture sectors, residential, commercial, and industrial consumers. The proposed study is mathematically modeled and implemented on an energy grid with four power plants and different energy consumption sectors for a 24-h energy study period. In this simulation, an appropriate pattern of using energy carriers to supply energy demand is determined. Simulation results and analysis show that energy carriers can be used efficiently using the proposed energy commitment method.