Parameter sweep applications consist of large sets of independent tasks and arise in many fields of science and engineering. Due to their flexible task synchronization requirements, these applications are ideally suited to large-scale distributed platforms such as the Computational Grid. However, for users to readily benefit from such platforms, it is necessary to provide transparent application deployment and automatic application scheduling. We present here version 2.0 of the AppLeS Parameter Sweep Template (APST) software, an application execution environment which schedules and deploys large-scale parameter sweep applications on Grid platforms. We describe the main principles behind the design of APST, its current implementation, and the services and mechanisms it can leverage to deploy applications. We illustrate APST's usability and explain how its XML-based interface allows users to easily direct Grid resources to run their applications. Finally, we briefly discuss applications that are currently using APST, and we highlight future developments.