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Traffic engineering is an important mechanism for Internet network providers seeking to optimize network performance and traffic delivery. Routing optimization plays a key role in traffic engineering, finding efficient routes so as to achieve the desired network performance. In this survey we review Internet traffic engineering from the perspective of routing optimization. A taxonomy of routing algorithms in the literature is provided, dating from the advent of the TE concept in the late 1990s. We classify the algorithms into multiple dimensions: unicast/multicast, intra-/inter- domain, IP-/MPLS-based and offline/online TE schemes. In addition, we investigate some important traffic engineering issues, including robustness, TE interactions, and interoperability with overlay selfish routing. In addition to a review of existing solutions, we also point out some challenges in TE operation and important issues that are worthy of investigation in future research activities.