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In this paper, an off-line traffic engineering algorithm is presented that optimizes the single-path routing of Label Switched Paths in a Differentiated Services IP domain by means of explicit, Multi-Protocol Label Switching controlled nonshortest paths. This algorithm allows traffic engineering up to 2500 traffic trunks in flat networks with sizes up to 150 nodes while supporting protection, pre-emption, quality-of-service, oversubscription, and resource class affinity. The algorithm with proper extensions can be applied to hierarchical networks, thus increasing the scalability properties for network size with a factor of about 50. First the single-area algorithm is detailed, then the concept and implementation of hierarchy is introduced for inter-area traffic engineering. These topics are illustrated with simulation results. KEY WORDS: Traffic engineering; hierarchy; differentiated services; quality-of-service; explicit routing. [ABSTRACT FROM AUTHOR]