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Web service composition (WSC) is the task of combining a chain of connected single services together to create a more complex and value-added composite service. Quality of service (QoS) has been mostly applied to represent nonfunctional properties of web services and differentiate those with the same functionality. Many research has been done on QoS-aware service composition, as it significantly affects the quality of a composite service. However, existing methods are restricted to predefined workflows, which can incur a couple of limitations, including the lack of guarantee for the optimality on overall QoS and for the completeness of finding a composite service solution. In this paper, instead of predefining a workflow model for service composition, we propose a novel planning-based approach that can automatically convert a QoS-aware composition task to a planning problem with temporal and numerical features. Furthermore, we use state-of-the-art planners, including an existing one and a self-developed one, to handle complex temporal planning problems with logical reasoning and numerical optimization. Our approach can find a composite service graph with the optimal overall QoS value while satisfying multiple global QoS constraints. We implement a prototype system and conduct extensive experiments on large web service repositories. The experimental results show that our proposed approach largely outperforms existing ones in terms of solution quality and is efficient enough for practical deployment.