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In this paper, a reliable server assignment problem in networks is defined as determining a deployment of identical servers to maximize a measure of service availability, and solved using nature-inspired metaheuristic approaches, namely Ant Colony Optimization, Particle Swarm Optimization, and Clonal Selection Principle of Artificial Immune Systems. In networks, the communication between a client and a server might be interrupted because the server itself is offline or unreachable as a result of catastrophic network failures. Therefore, it is very important to deploy servers at critical network nodes so that the reliability of the system is maximized. A new reliability measure, called critical service rate, is defined to evaluate alternative server assignments with respect to the network's ability to provide services in the case of catastrophic component failures. The structure of the optimal server assignments is studied, and the performances of three nature inspired metaheuristics are investigated in a rigorous experimental study. Based on the computational studies, their advantages and disadvantages are discussed.