Conceptual and numerical comparisons of swarm intelligence optimization algorithms

Swarm intelligence (SI) optimization algorithms are fast and robust global optimization methods, and have attracted significant attention due to their ability to solve complex optimization problems. The underlying idea behind all SI algorithms is similar, and various SI algorithms differ only in their details. In this paper we discuss the algorithmic equivalence of particle swarm optimization (PSO) and various other newer SI algorithms, including the shuffled frog leaping algorithm (SFLA), the group search optimizer (GSO), the firefly algorithm (FA), artificial bee colony algorithm (ABC) and the gravitational search algorithm (GSA). We find that the original versions of SFLA, GSO, FA, ABC, and GSA, are all algorithmically identical to PSO under certain conditions. We discuss their diverse biological motivations and algorithmic details as typically implemented, and show how their differences enhance the diversity of SI research and application. Then we numerically compare SFLA, GSO, FA, ABC, and GSA, with basic and advanced versions on some continuous benchmark functions and combinatorial knapsack problems. Empirical results show that an advanced version of ABC performs best on the continuous benchmark functions, and advanced versions of SFLA and GSA perform best on the combinatorial knapsack problems. We conclude that although these SI algorithms are conceptually equivalent, their implementation details result in notably different performance levels.