Lagrangean heuristic for primary routes assignment in survivable connection-oriented networks

Abstract

Our discussion in this article centers on the application of a Lagrangean relaxation and a subgradient optimization technique to the problem of primary route assignment (PRA) in survivable connection-oriented networks. The PRA problem consists in a static optimization of primary routes minimizing the Lost Flow in Node (LFN) function. The major contribution of this work is a combination of the Lagrangean relaxation with other heuristic algorithms. We evaluate the performance of the proposed Lagrangean-based heuristic by making a comparison with their counterparts including evolutionary algorithm and GRASP using various network topologies and demand patterns. The results of simulation tests show that the new algorithm provides sub-optimal results, which are better than other heuristics.

Anycasting in connection-oriented computer networks: Models, algorithms and results

“…In order to formulate a dual problem for (1)- (6), we will use the same approach as in (Gavish and Huntler, 1983;Walkowiak, 2007b). First, we transform the problem CFA/DEL into an equivalent formulation, which is better suited for a Lagrangean relaxation procedure.…”

“…More information on these functions and unicast FD algorithms applying these functions can be found in (Walkowiak, 2004;. The method of solving Subproblem 1 for the LFL function is included in (Walkowiak, 2007b).…”

“…Thus all anycast requests can be treated as unicast ones (the server node is constant). Consequently, the routes for both unicast and anycast demands are selected using a traditional unicast version of the Lagrangean relaxation heuristic developed for the DEL, LFL and RCL functions in (Gavish and Huntler, 1983;Walkowiak, 2007b), respectively. For ease of reference, we call these algorithms ULR DEL (Unicast Lagrangean Relaxation with DEL function), ULR LFL and ULR RCL, respectively.…”