The merits of velocity clamping particle swarm optimisation in high dimensional spaces

Velocity clamping has been used as a means to prevent particles from leaving the search space by preventing the initial velocity explosion. In high dimensional spaces, particle velocities may become very large and particles are prone to leaving the search space, never to return. This paper examines velocity clamping as a possible solution to this problem. Two different mechanisms of velocity clamping are considered: clamping per dimension and clamping based on the magnitude of the velocity vector. The paper finds that the optimal values to which the velocity is clamped depends on the dimensionality of the problem and that these optimal values decrease as problem dimensionality increases. Stricter clamping values force particles to take smaller step sizes, thereby encouraging exploitative behaviour. This is in line with findings from previous studies regarding the benefits of focusing on exploitation in high dimensional problem spaces. The paper also shows that clamping per dimension performs better than clamping based on the velocity's magnitude. Lastly, the paper concludes that velocity clamping alone does not guarantee that particles will stay within the search space and that even if the particles are successfully confined, the result is a rapid decrease in swarm diversity and premature convergence.