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Topological optimization of computer networks is concerned with the selection of a subset of the available links such that the reliability and fault-tolerance aspects are maximized while meeting a cost constraint. In this case, the problem is stated as optimizing the reliability and fault-tolerance of a network subject to a maximum cost constraint. Existing iterative-based techniques consider the simple single-objective version of the problem by considering reliability as the only objective. We consider fault-tolerance to be an important network design aspect. We consider the use of three iterative techniques, namely tabu search, simulated annealing, and genetic algorithms, in solving the multiobjective topological optimization network design problem. Experimental results for a set of 10 randomly generated networks using the three iterative techniques are presented and compared. It is shown that improving the fault tolerance of a network can be achieved while optimizing its reliability however at the expense of a reasonable increase in the overall cost of the network.