## 2 Literature Review  
The optimization problems for electrical power systems have been studied for more than five decades. A definition of economic dispatch is the operation of generation facilities to produce energy at the lowest cost to reliably serve consumers, recognizing any operational limits of generation and transmission facilities. In the typical unit commitment [1], the problem consists as determining the mix of generators and their estimated output level to meet the expected demand of electricity over a given time horizon (a day or a week) while satisfying the load demand, spinning reserve requirement and transmission network constraints. An electric network consists of many generation nodes with various generating capacities and cost functions, lines of transmission, and nodes of power demand [2]. The application of optimization models for electrical power systems is marked by constant development for new algorithms like exact methods, metaheuristics, and hybrid strategies [3]. Authors such as [PERSON]. [4] show applications of a non-linear economic dispatch problem and its implementation in commercial software for operational and regulatory analyses in Colombia. Other works, such as [PERSON] et al. [5], show the application of an optimization model for hydrothermal coordination and the emission of polluting particles. Recent research integrates various sources of fuel, such as natural gas, in the determination of the optimal generation at the lowest cost, considering wind generation, in addition to considering the model as a bi-level model [6]. [PERSON] et al. [7] shows a dynamic version of the problem of economic dispatch, considering a hybrid energy micro-grid, and adding to the problem a virtual energy storage system. The problem has approached from the perspective of the integration of renewable energies. As well as different methods of solving the optimization problem, such as the case of [PERSON] et al. [8], where the application of multi-objective evolutionary algorithms models is shown for the solution of an environmental-economic dispatch problem. In the same way, different versions of the problem of economic dispatch have been explored through the temporality of the solution. Depending on the demand period that is desired to be planned, in [PERSON] et al. [9], a stochastic version of the problem of economic dispatch is shown, considering wind energy and demand response for scheduling of home energy management. Other authors include in the problem constraints related to the emission of pollutants as well as risk measures in the electrical system. [PERSON] et al. [5] propose a multi-objective model of economic dispatch with restrictions on risks arising from the integration of wind energy into the system. Similarly, economic dispatch models with multiple energy carriers have proposed, in this case, works such as [PERSON] et al. [10], which address the treatment of energy hubs in the operation of integrated systems using a particle-swarm optimization algorithm. The approach to the problem of economic dispatch has multiple aspects, among which the solution method and the characteristics of the analyzed electrical system can highlight. Recent research shows the integration of clean energy as well as energy storage and multiple energy carriers. The problem of economic dispatch is and will continue to be a priority problem in the academic and industrial fields because electrical systems evolve under the availability of energy in the world and with technological development. Along with the development of novel algorithms for solving the problem of economic dispatch in its multiple variants, it is necessary to have test systems to evaluate solution algorithms. The electricity network, as well as the characteristics of the operation of an electrical system, are reserved information. Generally, there are test versions of electrical systems as well as characteristics of the network's demand behavior.