  Nature-inspired swarm-based algorithms have been widely applied to tackle
high-dimensional and complex optimization problems across many disciplines.
They are general purpose optimization algorithms, easy to use and implement,
flexible and assumption-free. A common drawback of these algorithms is
premature convergence and the solution found is not a global optimum. We
provide sufficient conditions for an algorithm to converge almost surely (a.s.)
to a global optimum. We then propose a general, simple and effective strategy,
called Perturbation-Projection (PP), to enhance an algorithm's exploration
capability so that our convergence conditions are guaranteed to hold. We
illustrate this approach using three widely used nature-inspired swarm-based
optimization algorithms: particle swarm optimization (PSO), bat algorithm (BAT)
and competitive swarm optimizer (CSO). Extensive numerical experiments show
that each of the three algorithms with the enhanced PP strategy outperforms the
original version in a number of notable ways.
