Global Convergence Analysis of the Flower Pollination Algorithm: A Discrete-Time Markov Chain Approach
This work provides a theoretical foundation for the Flower Pollination Algorithm, addressing a gap in convergence analysis for researchers in optimization and metaheuristics, though it is incremental as it builds on existing algorithm extensions.
The authors tackled the problem of proving global convergence for the Flower Pollination Algorithm, a metaheuristic for nonlinear optimization, by using discrete-time Markov chain theory to show it converges to optimal solutions under specific conditions, with numerical experiments demonstrating quick convergence in practice.
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.