# Genetic Algorithm with Radial Basis Mapping Network for the Electricity Consumption Modeling
## 1 Introduction  
Across the world, populations in cities have been growing. To avoid overcrowding and the accompanying decrease in quality of life, it is essential to introduce some research. To improve the efficiency, the electricity consumption of the city may use the modeling as one alternative to conduct the data analysis for understanding its behavior. Then, the investigation of approaches that allow the electricity consumption modeling becomes transcendent. The modeling of events requires a meticulous study of past events and the relationships between them, and from there, it tries to extrapolate a present event. The modeling has many applications, such as prediction [1; 2; 3; 4], pattern recognition [5; 6; 7; 8], detection [9; 10; 11], and classification [12; 13; 14]. The backpropagation is a supervised algorithm was used in a radial basis mapping (RBM) network for the modeling; the value of the scale parameters was adjusted according to a cost [15; 16; 17]. Later, one modified backpropagation algorithm based on the backpropagation with momentum [18; 19; 20; 21] was used for the parameter updating of a RBM network; it requires the best hyper-parameters for a more precise modeling. Seeking of the best hyper-parameters in a model it is not an easy task. There are plenty of options to evaluate it; grid search or random search are common practices, but thesealgorithms present the disadvantage that the user has to pick the correct options. Hence, we use a genetic algorithm as the best alternative to seek these values. Genetic algorithms are frequently used for the modeling. The optimization with genetic algorithms is studied in [22; 23; 24; 25]. In [26; 27; 28; 29], the genetic algorithm for path planning is discussed. The fuzzy systems with genetic algorithms are addressed in [30; 31; 32; 33]. In [34; 35; 36; 37], the neural networks with genetic algorithms are introduced. Since the genetic algorithms are highly utilized in the modeling, it is attractive to use a genetic algorithm to seek the best hyper-parameters for more precise modeling. In this article, a genetic algorithm is used to seek the best hyper-parameters in the modified backpropagation for the parameters updating of a RBM network, and this RBM network is used for more precise electricity consumption modeling in a city. The suggested approach is called genetic algorithm with a RBM network. The approach was developed based on the next steps:  
1. The modified backpropagation. We use the momentum to update the parameters' velocities. The momentum encourages the movements in the correct direction, with the advantage of a velocity increasing in the convergence. Using the momentum, the trajectory has a smooth behavior. We use the modified backpropagation for the modeling. 2. The genetic algorithm. The genetic algorithm is a strategy of searching based on the natural selection and genetic laws. It combines the survival principle of the best solutions for an issue; with the interchange of random information, it forms a searching algorithm capable of exploring the promising areas of historic information in the solutions set. We seek the hyper-parameters to be updated for a more precise modeling. 3. The combination of the genetic algorithm with modified backpropagation is called the genetic algorithm with a RBM network for more precise modeling. First, we seek the hyper parameters and find their best values by the genetic algorithm. Second, we use the modified backpropagation with the best hyper-parameters for the modeling. Finally, since the suggested approach called genetic algorithm with an RBM network starts from the modified backpropagation, we compare both approaches for the electricity consumption modeling in a city. The remainder of this article is organized in as follows. Section 2 presents the RBM network and the modified backpropagation. The genetic algorithm with an RBM network is explained in Section 3.