  All swarm-intelligence-based optimization algorithms use some stochastic
components to increase the diversity of solutions during the search process.
Such randomization is often represented in terms of random walks. However, it
is not yet clear why some randomization techniques (and thus why some
algorithms) may perform better than others for a given set of problems. In this
work, we analyze these randomization methods in the context of nature-inspired
algorithms. We also use eagle strategy to provide basic observations and relate
step sizes and search efficiency using Markov theory. Then, we apply our
analysis and observations to solve four design benchmarks, including the
designs of a pressure vessel, a speed reducer, a PID controller and a heat
exchanger. Our results demonstrate that eagle strategy with L\'evy flights can
perform extremely well in reducing the overall computational efforts.
