Grid computing is one of the main paradigms for resource-intensive scientific applications. It enables resource sharing and dynamic allocation of computational resources, thus increasing access to distributed data, promoting operational flexibility and collaboration, and allowing service providers to scale efficiently to meet variable demands. Large-scale grids are complex systems composed of many components from different domains. Quality of service (QoS) in such environments is an important issue due to the distributed nature of the services. In this paper we propose an allocation algorithm for matching service requests of Grid users with Grid services based on a QoS metric using either matchmaking or a well-tested genetic algorithm: NSGA-II. Experiments are performed and results are discussed for both approaches.