Identifying a multicast label-switched-path (LSP) tree that satisfy a set of traffic-oriented and resource-oriented QoS constraints such as cost, reliability, bandwidth, jitter, and delay, has become an important research issue in the area of multicast routing in MPLS networks. In general, multiconstrained multicast tree-selection is an NP-complete problem. In this survey, QoS-based multicast tree-selection algorithms from the perspective of optimization techniques are evaluated. The existing algorithms are classified into three dimensions: non-MPLS-/MPLS-based, single/multiple QoS constrained, and heuristic-/unicast-/artificial-intelligence optimization techniques. In addition to state-of-the-art review of existing solutions, this article highlights important characteristics of QoS-based MPLS multicast algorithms and discuss important issues that are worthy of investigation in future research activities.