Abstarct: Drilling represents a time-intensive, financially burdensome, and inherently risky endeavor that is essential for the exploration and development of oil resources. Within this operation, the penetration rate is defined as the quantity of area drilled per unit of time, with the enhancement of this rate being a primary objective. Investigating the values of controllable parameters for the optimization of the rate of penetration (ROP) constitutes a significant challenge for drilling engineers. The methodologies employed for estimating and optimizing ROP are categorized into two principal types: analytical methods and machine learning techniques. Analytical methods, often referred to as traditional approaches, possess inherent limitations in their capacity to yield accurate and rapid solutions. A notable constraint of these methods is their inability to calculate the response of a model across multiple wells. Conversely, machine learning techniques, identified as modern methods, offer superior accuracy and speed; however, they too are not devoid of limitations and lack comprehensiveness. In light of these constraints, hybrid methods that amalgamate analytical and machine learning approaches have gained substantial prominence in contemporary practice. These hybrid methodologies first establish a relationship to model the response and subsequently resolve the pertinent model using optimization algorithms. This strategy minimizes error while maximizing the efficiency of the optimization process. In this thesis, following the introduction of a novel analytical relationship, the modeling process for infiltration rate has been executed utilizing the rain mextaheuristic optimization algorithm. The outcomes have been juxtaposed with two conventional analytical models and two optimization methods, namely genetic algorithms and particle swarm optimization. An investigation was conducted utilizing data from two selected wells within an oil field located in southwestern Iran. The findings indicated that the proposed model exhibited superior performance compared to the two conventional analytical models in terms of modeling the infiltration rate within the study area. Furthermore, the rain optimization algorithm demonstrated greater efficacy than both genetic algorithms and particle swarm optimization.