Computational complexity of swarm-based algorithms: a detailed analysis

In recent years, swarm-based algorithms have been applied to numerous optimization problems. These algorithms use a set or population of solutions that are updated in an iterative process to obtain an approximate solution to the problem. Many articles use these methods to solve complex problems, but do not include information about how time-consuming the methods are. On the other hand, the literature on swarm-based algorithms does not usually include the analysis of computational complexity of the algorithms. The structure of these algorithms makes them time-consuming, so it is essential to know that cost to assess whether it is appropriate to apply them. This article aims to fill the gap by showing a detailed analysis of the computational complexity of a set of 10 popular swarm-based algorithms (particle swarm optimization, shuffled-frog leaping algorithm, artificial bee colony, firefly algorithm, gravitational search, cuckoo search, bat algorithm, grey wolf optimization, chicken swarm optimization, and whale optimization). The operations associated with each method are described using a homogeneous notation, and then the computational complexity is analyzed. Furthermore, the methods are applied to 20 problems, and statistical tests are performed on the results. Although the algorithms have a common basic structure, it is observed that the computational cost is not the same for all of them. Furthermore, the algorithms that consume the most time are not always the ones that generate the best results, so it is advisable to take this information into account before choosing a specific algorithm to solve a complex problem.