Abstarct: Drilling hydrocarbon wells is one of the most expensive operations in the field of oil and gas . One of the most important parameters affecting it is the penetration rate . Penetration rate can be considered as an important factor in cost optimization and minimization as well as progress of drilling operations in a shorter time . With the development of technology , the use of artificial intelligence and machine learning in the field of drilling and especially the estimation of penetration rate has become very important . In this research, machine learning has been used to predict the penetration rate , optimize and find the relationship between it and other data parameters . In order to predict the penetration rate, models are built baxsed on three algorithms : nearest neighbor (KNN) , support vector machine (SVM) and decision tree (DT) . To achieve this goal, the data of  rings of directional drilling wells in the South Pars gas field in the sedimentary part of Zagros , which includes two reservoirs , Kangan and Dalan, have been used as input data. We evaluate three models of prediction algorithms baxsed on several criteria . The accuracy of the built models are compared with each other .  error measurement indicators have been used to check the results. In the next step , the population crowding algorithm or (PSO) is used to optimize the penetration rate. This optimization follows non-linear functions . After entering the data or preprocessing the inputs ,  of the  data is allocated to training,  to the evaluation rate and  to the test. Finally , the cost function that represents the best optimal points is investigated.Correlation matrix has been used to compare the relationship between penetration rate and other data parameters . In all the mentioned cases, there are two types of data , the first data has  entries and the second data has  entries . After entering the software space and normalizing between zero and one , each case is pre-processed according to the codes of each algorithm , and in order to better understand the results , we draw graphs and then interpret each one . In the discussion of forecasting, comparison is made by comparing the results of the error measurement indices of the mentioned algorithms baxsed on the percentages obtained from each case in the form of evaluation tables, and that superior model will be the selected model. In the optimization section , the value of the drilling rate to maximize the  parameters of the evaluation data and the best value of the cost function is equal to . In the last part, the values in the matrix show the relationship between the drilling penetration rate parameter and the existing parameters. If the value obtained between two parameters is positive, it means that the increase in one item causes the increase in the other model .