Abstract:

The firefly algorithm has been widely concerned and applied because of its characteristics of simple structure, few control parameters and easy implementation, but it is easy to fall into local optimum, which leads to premature convergence and affects the optimization accuracy. To solve this problem, this paper adds a random factor into the individual location update rule to improve search capabilities, and the redundant random items are eliminated. To maintain the diversity of the population and enhance the capabilities of the algorithm to jump out of the local optimum, a position substitution mutation strategy and an optimal mutation strategy which come from the differential evolution algorithm are introduced. The Markov process is used to theoretically analyze the improved algorithm, and it is proved that the algorithm converges to the global optimum with probability of 1. The improved algorithm is simulated and tested using classic benchmark functions and the bin packing problem. Simulation results show that the improved algorithm can effectively jump out of the local optimum and find the theoretical optimal solution for all the given problems with better optimization accuracy and success rate.

Key words: firefly algorithm, stochastic disturbance, mutation strategy, Markov process, function optimization, bin packing problem