The need for integration of applications and services in business processes from enterprises has increased with the advancement of cloud and mobile applications. Enterprises started dealing with high volumes of data from the cloud and from mobile applications, besides their own. This is the reason why integration tools must adapt themselves to handle with high volumes of data, and to exploit the scalability of cloud computational resources without increasing enterprise operations costs. Integration platforms are tools that integrate enterprises’ applications through integration processes, which are nothing but workflows composed of a set of atomic tasks connected through communication channels. Many integration platforms schedule tasks to be executed by computational resources through the First-in-first-out heuristic. This article proposes a Queue-priority algorithm that uses a novel heuristic and tackles high volumes of data in the task scheduling of integration processes. This heuristic is optimized by the Particle Swarm Optimization computational method. The results of our experiments were confirmed by statistical tests, and validated the proposal as a feasible alternative to improve integration platforms in the execution of integration processes under a high volume of data.