Lévy-Flights for Particle Swarm Optimisation Algorithms on Graphical Processing Units

Particle Swarm Optimisation (PSO) is a powerful algorithm for space search problems such as parametric optimisation. Particles with Lévy-Flights have a long-tailed probability of outlier jumps in the problem space that provide a good compromise between local space exploration and local minima avoidance. Generating many particles and their trajectories with Lévy-random deviates is computationally expensive, however. We present a data-parallel algorithmic implementation of Lévy-flighted particle swarm optimisation and show how it makes use of accelerators such as graphical processing units (GPUs). We discuss the computational tradeoffs, performance achievable using GPUs, and the scalability of such an approach using various uni-modal and multi-modal test functions in a range of dimensions.