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Cloud computing has emerged as a powerful computing paradigm that enables users to access computing services anywhere on demand. It provides a flexible way to implement computation-intensive workflow applications on a pay-per-use basis. Since users are more concerned on the satisfaction of Quality of Service (QoS) in cloud systems, the cloud workflow scheduling problem that addresses different QoS requirements of users has become an important and challenging problem for workflow management in cloud computing. In this paper, we tackle a cloud workflow scheduling problem which enables users to define various QoS constraints like the deadline constraint, the budget constraint, and the reliability constraint. It also enables users to specify one preferred QoS parameter as the optimization objective. A set-based PSO (S-PSO) approach is proposed for this scheduling problem. As the allocation of service instances can be regarded as the selection problem from a set of service instances, it is found the set-based representation scheme in S-PSO is natural for the considered problem. In addition, the S-PSO provides an effective way to take advantage of problem-based heuristics to further accelerate search. We define penalty-based fitness functions to address the multiple QoS constraints and integrate the S-PSO with seven heuristics. A discrete version of the comprehensive learning PSO (CLPSO) algorithm based on the S-PSO method is implemented. Experimental results show that the proposed approach is very competitive especially on the instances with tight QoS constraints.