Today, due to the lack of fresh water resources and the growing population, pollution of groundwater aquifers has become one of the main concerns of each country. Pumping and purification is one of the most common and effective methods in this regard. Various reasons, including high cost of drilling wells, related facilities and their exploitation, execution time, etc. In this way, researchers have been looking for an optimal design for this cleaning method so that with the lowest The cost, the most pollutant withdrawal from water. In this paper, various methods of optimizing the pumping and purification methods are reviewed. Among the methods presented, the method of congestion of particles and firewall algorithm has been introduced as more effective algorithms for optimizing pumping and purification systems.