  Swarm intelligence has becoming a powerful technique in solving design and
scheduling tasks. Metaheuristic algorithms are an integrated part of this
paradigm, and particle swarm optimization is often viewed as an important
landmark. The outstanding performance and efficiency of swarm-based algorithms
inspired many new developments, though mathematical understanding of
metaheuristics remains partly a mystery. In contrast to the classic
deterministic algorithms, metaheuristics such as PSO always use some form of
randomness, and such randomization now employs various techniques. This paper
intends to review and analyze some of the convergence and efficiency associated
with metaheuristics such as firefly algorithm, random walks, and L\'evy
flights. We will discuss how these techniques are used and their implications
for further research.
