This paper presents a multi-swarm PSO algorithm for the Quadratic Assignment Problem (QAP) implemented on the OpenCL platform. Our work was motivated by results of time efficiency tests performed for single-swarm algorithm implementation that showed clearly that the benefits of a parallel execution platform can be fully exploited provided the processed population is large. The described algorithm can be executed in two modes: with independent swarms or with migration. We discuss the algorithm construction as well as we report results of tests performed on several problem instances from the QAPLIB library. During the experiments the algorithm was configured to process large populations. This allowed us to collect statistical data related to values of goal function reached by individual particles. We use them to demonstrate on two test cases that although single particles seem to behave chaotically during the optimization process, when the whole population is analyzed, the probability that a particle will select a near-optimal solution grows.