## 1 Introduction
The purpose of the EH is to provide the required energy for load demand through its input and internal equipment [18]. The concept of EH has been introduced in various residential, commercial, and other applications. In this regard, economy and energy savings in a hospital have been studied [19], and linear integer programming is presented to improve the performance of an electric micro-grid in the presence of cooling, thermal, and electrical loads [20]. The optimal operation of a residential house as an EH using the PSO algorithm is proposed in [21]. The optimal operation of an EH has been studied considering the energy storage systems in [22]. The EH has also been proposed for economic and reliability purposes in [23] with the aim of proper selection of the internal EH equipment. Furthermore, the energy management of smart hubs is discussed in [24]. As mentioned in the previous subsections, in UC, the goal is to determine the appropriate pattern of power plant production to supply the electrical demand. In an MCE system, gas, electrical, and heat networks are examined, and the purpose of the EH is to supply the required energy demand through its input and internal equipment. Although very valuable studies have been conducted by researchers in the operation of power systems, the operation of an integrated grid called the energy grid and determining the appropriate pattern of use of energy carriers to supply energy demand in this network has been less studied. Therefore, a new study named the Energy Commitment (EC) problem that determines a suitable pattern of energy carriers utilization to supply the energy demand in particular from the perspective of an electric power system is proposed. In the proposed EC study, more details of the network such as the simulation of oil refining and the impact of the imports and exports of energy carriers are considered. The EC problem in a multi-carrier energy system is proposed to be studied using the Following Optimization Algorithm (FOA). Therefore, the optimal operation of energy carriers can be obtained. The proposed study aims to realize the following:  
* Mathematical modeling and formulation for an EC problem. * Objective function is considered as minimizing energy supply costs for the total study period. * The FOA is used to solve the EC problem, which is a constrained optimization problem. * Study the technical aspect of supply energy demand in various sections (with different types of energy carriers). * Applying the proposed study to a standard energy grid that includes different sectors of energy consumption (transportation, agriculture, industrial, residential, commercial, and public). * Studying the simulation of refinery and oil-refining process. * Studying the impact of import and export of energy carriers on EC. * Determining the appropriate pattern for the use of energy carriers to supply energy demand, considering technical and economic constraints. * Increasing the awareness of the importance of an EC study to enhance the operation of energy systems. The introduction and background of the topic are presented in Section 1. The problem definition and problem formulation are described, respectively, in Sections 2 and 3. Application of the proposed study is investigated and discussed in Section 4, while the conclusions are presented in Section 5.