## 1 Introduction  
Economic load dispatch (ELD) is known as a means of lowering fuel costs for electricity generation in thermal power plants. In power system operation, the main purpose of the ELD problem is to allocate the power output of each power plant continuously, while observing the conditions such as fuel consumption characteristics, capacity of each generator, technical requirements in the system, and total demand of all loads. The objective function of this problem is to reduce the values of a quadratic function, a non-convex function, or a non-smooth function as much as possible. So, the complexity of the problem is partially dependent on the complexity level of the objective function. Basically, a solution can be regarded as an acceptable operation method if all constraints are exactly met. Thus, complex of constraints is also a challenge for the complexity level of the ELD problem. Due to these challenges,approximately all studies have focused on the objective function and the considered constraints to demonstrate their method's efficiency. In the later years of the previous century, traditional methods were effectively applied to solve the ELD problem with acceptable results. These methods are the lambda-iteration method (LIM) [1], gradient method (GM) [1], hierarchical method (HM) [2], Lagrange relaxation (LR) [3], linear programming technique (LPT) [4], Newton's method (NM) [1], and fast Newton Raphson method (FNM) [5]. Traditional methods have the advantage of using a small number of iterations, and results are the same for different runs because they are deterministic methods. However, traditional methods have to take the partial derivative in the process of finding solutions. So, these methods have some restrictions if they solve the ELD problem for complex systems, for example, those with non-smooth shape objective functions. Another method group that appeared after these traditional methods and has also been successfully applied to solve the ELD problems is composed of the artificial neural network (ANN)-based methods. This group includes the Hopfield neural network (HNN) [6], adaptive Hopfield neural network (AHNN) [7], new Hopfield model (NHM) [8], enhanced augmented Lagrange Hopfield network (EALHN) [9], and augmented Lagrange Hopfield network (ALHN) [10]. ANN-based methods perform better than traditional methods by combining the Lagrange function and Hopfield network. However, these methods, like traditional methods, struggle with complex objective functions. In contrast to the above methods, evolutionary algorithms (EAs) and improved evolutionary algorithms (IEAs) have been popularly applied to solve the ELD problem with complex systems. These types of algorithms include the improved genetic algorithm (IGA) [11], real-code genetic algorithm (RCGA) [12], new RCGA (NRCGA) [12], evolutionary strategy optimization (ESO) [13], improved differential evolution (IDE) [14], differential evolution (DE) [15], hybrid integer coded differential evolution and dynamic programming (HDE-DP) [16], and stud differential evolution (SDE) [17]. Among these methods, RCGA [12] is the best because it can solve the ELD problem with valve point effects (VPEs), multi fuels (MFs), ramp rate limit (RRL), prohibited operating zones (POZs), and spinning reserve (SR), whereas IDE [14] is the best method in terms of solving problems considering transmission losses.