1. A method for selecting a traffic engineering (TE) label switched path (LSP) from among a plurality of TE-LSPs, each TE-LSP spanning multiple domains of a computer network from a local domain to a remote domain in order to reach one or more address prefixes within the remote domain, the method comprising: executing a hierarchical selection algorithm at a head-end node of the local domain, the hierarchical selection algorithm based on predetermined TE-LSP attributes of the inter-domain TE-LSPs and configured to select one or more appropriate TE-LSPs for the reachable address prefix by examining attributes in a hierarchical manner by order of predetermined preference for each address prefix reachable by the TE-LSPs, and selecting one or more appropriate TE-LSPs for a preferred TE-LSP attribute to reach the address prefix in the remote domain; and invoking load balancing, in cooperation with the hierarchical selection algorithm, to enable the head-end node to balance traffic loads among the one or more appropriate selected TE-LSPs.