This paper describes a solution to the key problem of ensuring high performance behavior of the Grid, namely the scheduling of activities. It presents a distributed, fault-tolerant, scalable and efficient solution for optimizing task assignment. The scheduler uses a combination of genetic algorithms and lookup services built on a multiagent infrastructure for obtaining a scalable and highly reliable optimization tool. The experiments have been carried out on the MonALISA monitoring environment and its extensions. The results demonstrate very good behavior in comparison with other scheduling approaches.