Web service combinatorial optimisation is an NP problem (that is, characterised by a nondeterministic polynomial time solution), based on the logical relationship between each service pair. As a consequence, obtaining the best Web service composition scheme is typically a complex task. In this article, we propose the the Predatory Search-based Chaos Turbo Particle Swarm Optimization (PS-CTPSO) algorithm, a chaotic particle swarm optimisation algorithm based on the predatory search strategy, which has significant potential to enhance the overall performance of the Autonomous Cloud. This is achieved by integrating a predatory search and cotangent sequence strategies with the particle swarm optimisation algorithm. More specifically, the PS-CTPSO algorithm identifies a feasible service via a global search, and subsequently, it obtains suitable candidate services within the corresponding chain. The different Web services are grouped into the same class, depending on whether they have the same input and output sets, thus reducing the number of combinations and improving the searching efficiency. In the initialisation phase, the PS-CTPSO component introduces the cotangent method, rather than a ran