  Metaheuristic algorithms are becoming an important part of modern
optimization. A wide range of metaheuristic algorithms have emerged over the
last two decades, and many metaheuristics such as particle swarm optimization
are becoming increasingly popular. Despite their popularity, mathematical
analysis of these algorithms lacks behind. Convergence analysis still remains
unsolved for the majority of metaheuristic algorithms, while efficiency
analysis is equally challenging. In this paper, we intend to provide an
overview of convergence and efficiency studies of metaheuristics, and try to
provide a framework for analyzing metaheuristics in terms of convergence and
efficiency. This can form a basis for analyzing other algorithms. We also
outline some open questions as further research topics.
