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Flower pollination algorithm is a recent metaheuristic algorithm for solvingnonlinear global optimization problems. The algorithm has also been extended tosolve multiobjective optimization with promising results. In this work, weanalyze this algorithm mathematically and prove its convergence properties byusing Markov chain theory. By constructing the appropriate transitionprobability for a population of flower pollen and using the homogeneityproperty, it can be shown that the constructed stochastic sequences canconverge to the optimal set. Under the two proper conditions for convergence,it is proved that the simplified flower pollination algorithm can indeedsatisfy these convergence conditions and thus the global convergence of thisalgorithm can be guaranteed. Numerical experiments are used to demonstrate thatthe flower pollination algorithm can converge quickly in practice and can thusachieve global optimality efficiently.

Global Convergence Analysis of the Flower Pollination Algorithm: A Discrete-Time Markov Chain Approach