Variable (feature) selection is a key component in artificial intelligence. One way to perform variable selection is to solve the information-criterion-based optimization problems. These optimization problems arise from data mining, genomes analysis, machine learning, numerical simulations, and others. Particle Swarm Stepwise Algorithm (PaSS) is a stochastic search algorithm proposed to solve the information-criterion-based variable selection optimization problems. It has been shown recently that the PaSS outperforms several existed methods. However, to solve the target optimization problems remains a challenge due to the large search spaces. We tackle this issue by proposing a parallel version of the PaSS on clusters equipped with CPU and GPU to shorten the computational time without compromise in solution accuracy. We have successfully achieved near-linear scalability on CPU with single to 64 threads and gained further 7X faster timing performance by using GPU.