  Flower pollination algorithm is a recent metaheuristic algorithm for solving
nonlinear global optimization problems. The algorithm has also been extended to
solve multiobjective optimization with promising results. In this work, we
analyze this algorithm mathematically and prove its convergence properties by
using Markov chain theory. By constructing the appropriate transition
probability for a population of flower pollen and using the homogeneity
property, it can be shown that the constructed stochastic sequences can
converge to the optimal set. Under the two proper conditions for convergence,
it is proved that the simplified flower pollination algorithm can indeed
satisfy these convergence conditions and thus the global convergence of this
algorithm can be guaranteed. Numerical experiments are used to demonstrate that
the flower pollination algorithm can converge quickly in practice and can thus
achieve global optimality efficiently.
