Clustering algorithms are an important component of data mining technology which has been applied widely in many applications including those that operate on Internet. Recently a new line of research namely Web Intelligence emerged that demands for advanced analytics and machine learning algorithms for supporting knowledge discovery mainly in the Web environment. The so called Web Intelligence data are known to be dynamic, loosely structured and consists of complex attributes. To deal with this challenge standard clustering algorithms are improved and evolved with optimization ability by swarm intelligence which is a branch of nature-inspired computing. Some examples are PSO Clustering (C-PSO) and Clustering with Ant Colony Optimization. The objective of this paper is to investigate the possibilities of applying other nature-inspired optimization algorithms (such as Fireflies, Cuckoos, Bats and Wolves) for performing clustering over Web Intelligence data. The efficacies of each new clustering algorithm are reported in this paper, and in general they outperformed C-PSO.