  We reconsider stochastic convergence analyses of particle swarm optimisation,
and point out that previously obtained parameter conditions are not always
sufficient to guarantee mean square convergence to a local optimum. We show
that stagnation can in fact occur for non-trivial configurations in non-optimal
parts of the search space, even for simple functions like SPHERE. The
convergence properties of the basic PSO may in these situations be detrimental
to the goal of optimisation, to discover a sufficiently good solution within
reasonable time. To characterise optimisation ability of algorithms, we suggest
the expected first hitting time (FHT), i.e., the time until a search point in
the vicinity of the optimum is visited. It is shown that a basic PSO may have
infinite expected FHT, while an algorithm introduced here, the Noisy PSO, has
finite expected FHT on some functions.
