Transportation plays a significant role in the gross domestic product and oil consumption of every nation. In our country, a combination of recent sanctions and underdeveloped rail, air, and sea transportation systems has led to an increased reliance on road transport. Unfortunately, road transport contributes significantly to the emission of greenhouse gases, particularly carbon dioxide. Nevertheless, transportation is a vital aspect of logistics, and addressing pollution in vehicle routing stands as a paramount concern within this realm.This paper introduces a model aimed at optimizing fuel consumption costs, considering various factors such as vehicle load, speed, pollution, as well as parameters like fuel and engine efficiency, incline, traffic density, wind speed and direction, air temperature, asphalt quality, and driver remuneration. Additionally, this mathematical linear mixed-integer model incorporates probabilistic demand and a distribution system involving both delivery and pickup processes, all geared towards cost minimization.By employing this model, organizations can achieve more precise cost estimates, enhanced analysis, and improved planning. Given the NP-hard nature of the problem, its resolution involves the amalgamation of two meta-heuristic algorithms: Extreme Learning Machine (ELM) and Genetic Programming (GP). Experimental results indicate that the developed hybrid algorithm offers highly accurate estimations in a remarkably short time span when compared with similar algorithms.