Web services have become increasingly popular in recent years, and they are especially suitable to the process of Web service composition, which is when several services are combined to create an application that accomplishes a more complex task. In recent years, significant research efforts have been made on developing approaches for performing Quality of Service -aware Web service composition. Evolutionary computing (EC) techniques have been widely used for solving this problem, since they allow for the quality of compositions to be optimised, meanwhile also ensuring that the solutions produced have the required functionality. Existing EC-based composition approaches perform constrained optimisation to produce solutions that meet those requirements, however these constraints may hinder the effectiveness of the search. To address this issue, a novel framework based on an indirect representation is proposed in this work. The core idea is to first generate candidate service compositions encoded as sequences of services. Then, a decoding scheme is developed to transform any sequence of services into a corresponding feasible service composition. Given a service sequence, the decoding scheme builds the workflow from scratch by iteratively adding the services to proper positions of the workflow in the order of the sequence. This is beneficial because it allows the optimisation to be carried out in an unconstrained way, later enforcing functionality constraints during the decoding process. A number of encoding methods and corresponding search operators, including the PSO, GA, and GP-based methods, are proposed and tested, with results showing that the quality of the solutions produced by the proposed indirect approach is higher than that of a baseline direct representation-based approach for twelve out of the thirteen datasets considered. In particular, the method using the variable-length sequence representation has the most efficient execution time, while the fixed-length sequence produces the highest quality solutions.