  Many problems in science and engineering can be formulated as optimization
problems, subject to complex nonlinear constraints. The solutions of highly
nonlinear problems usually require sophisticated optimization algorithms, and
traditional algorithms may struggle to deal with such problems. A current trend
is to use nature-inspired algorithms due to their flexibility and
effectiveness. However, there are some key issues concerning nature-inspired
computation and swarm intelligence. This paper provides an in-depth review of
some recent nature-inspired algorithms with the emphasis on their search
mechanisms and mathematical foundations. Some challenging issues are identified
and five open problems are highlighted, concerning the analysis of algorithmic
convergence and stability, parameter tuning, mathematical framework, role of
benchmarking and scalability. These problems are discussed with the directions
for future research.
