Artificial neural networks or ANN for short, which have shown their high value in many applications today, were created based on the biological model of the human brain. The concept of artificial neural network, which is actually one of the most important branches of artificial intelligence, is actually a simple sampling of the human nervous system crystallized in the form of a mathematical model. Artificial neural networks have features that distinguish them in some applications such as function estimation, prediction, pattern recognition, control, robotics and generally wherever there is a need to learn a linear or non-linear mapping. . Among these features, we can mention the ability to learn, the ability to generalize, parallel processing and being resistant. The diversity of neural network models and their learning algorithms provides the possibility of different applications for them. Each artificial neural network, or neural network for short, consists of a set of small data processing components called artificial neuron or neuron, each neuron to other neurons through a directional relationship that has its own weight. , is related. The following assumptions are considered in neural networks: • The information processing process takes place in simple units called neurons. These neurons are actually a very simple example of brain neurons. Information is exchanged in communication paths between neurons. • Each of the communication lines between neurons has a weight. • Each neuron uses an operational function (usually non-linear) to produce a specific output by applying it to the input of the neuron (sum of weighted information). Neural networks can be used in various cases, including storing and retrieving data, grouping shapes, performing a general mapping from an input set to an output set, grouping and classifying similar data, optimization and Forecast used. In this research, some of the works done in the field of artificial neural network have been reviewed, in which several heuristic and meta-heuristic algorithms such as: gravitational search algorithm, backpropagation algorithm, differential evolutionary algorithm, particle mass algorithm, ant colony algorithm, genetic algorithm have been used. And the colonial competition algorithm is used.