## 1 Introduction  
An energy carrier is a substance--for example, fuel, or sometimes a phenomenon (energy system)--that contains energy, which can be later converted to other forms, such as mechanical work or heat, or operate chemical or physical processes. Today's societies use several energy carriers in the industry, service, residential, and transportation sectors. Among the various energy carriers, oil is of paramount importance, since its price has a considerable effect on economic growth. Besides, neither oil nor any of the fossil fuels such as coal and natural gas have endless sources. The growing demand on the one hand and declining fossil resources, on the other hand, necessitate full consideration for the operation of energy. Therefore, the operation of energy carriers to supply the energy demand, called the Energy Commitment (EC) problem, is studied, in particular from the perspective of an electric power system. Unit Commitment (UC) is a significant study carried out in the operation of the electricity grid. An essential criterion in UC is the supply of power demand with the least fuel cost and optimal combination of different power plants [1]. It forms the basis of energy carrier commitment. The UC issue has been of great interest to researchers as evident from the following representative literature. In [2], uncertainty in the production of virtual power plants is investigated, and transmission line constraints in solving the UC problem for large-scale networks are studied in [3]. The UC problem in the presence of Flexible AC Transmission System (FACTS) devices and energy storage devices is investigated in [4]. To solve the UC problem, a novel annual analysis is proposed for the thermal power generator and pumped storages under a massive introduction of renewable energy sources [5]. Ref. [6], the authors proposed the implementation of the UC in the presence of energy storage systems and its optimal size for a region in northern Chile. Solving the UC problem in the presence of wind, nuclear, and thermal power plants has been studied by considering the security constraints of the transmission line and the influence of wind power uncertainty on the spinning reserve capacity of the system in China [7]. A new method based on the Particle Swarm Optimization (PSO) algorithm, [8], and the solution of the UC problem using genetic algorithm was proposed in [9]. Other algorithms, such as the Gray Wolf Optimizer (GWO) [10], Whale Optimization Algorithm (WOA) [11], simulated annealing [12], and shuffled frog-leaping algorithm [13] have also been suggested to find the solution to the UC problem. In recent years, Multi-Carrier Energy (MCE) systems that improve energy efficiency and reliability have received much attention. Each of the gas, electrical, and heat networks consists of energy sources, several loads, and a set of transmission lines or pipes that supply energy demand through the resources of the system. The flow value of the supply lines of each of these grids can be calculated mathematically by the quantities of those lines [14]. A mathematical model for intelligent loads participation in load response programs in an MCE system management is proposed, [15]. In this model, the optimal operation is performed using an energy storage system. The effects of load response programs on the efficiency and operating costs of MCE systems in the presence and absence of wind energy and energy storage are evaluated and analyzed in [16]. The teaching and learning-based optimization algorithm is applied to optimize the operation of MCE systems in [17]. In general, an Energy Hub (EH) is an interface between the production, consumption, and transmission of different forms of energy. EHs are connected to electric power grids and perform energy conversion operations from one state to another or improve the quality of energy delivered to the load. Thus, the inputs of an EH consist of different forms of energy, and its outputs are systemloads.