Analysis on global convergence and time complexity of fireworks algorithm

Fireworks Algorithm (FWA) is a new proposed optimization technique based on swarm intelligence. In FWA, the algorithm generates the explosion sparks and Gaussian mutation sparks by the explosion operator and Gaussian mutation operator to search the global optimum in the problem space. FWA has been applied in various fields of practical optimization problems and gains great success. However, its convergence property has not been analyzed since it has been provided. Same as other swarm intelligence (SI) algorithms, the optimization process of FWA is able to be considered as a Markov process. In this paper, a Markov stochastic process on FWA has been defined, and is used to prove the global convergence of FWA while analyzing its time complexity. In addition, the computation of the approximation region of expected convergence time of FWA has also been given.