Particle swarm optimisation and high dimensional problem spaces

Particle Swarm Optimisation (PSO) has been very successful in finding, if not the optimum, at least very good positions in many diverse and complex problem spaces. However, as the number of dimensions of this problem space increases, the performance can fall away. This paper considers the role that the separable nature of the traditional PSO equations may have in this and introduces the ideal of a dynamic momentum value for each dimension as one way of making the PSO equations non-separable. Results obtained using high dimensional versions of a number of traditional functions are presented and clearly show that both the quality of, and the time taken to find, the optimum obtained using variable momentum are better than when using fixed momentum.