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This paper proposes a modeling of data networks with delay, packet loss ratio and network cost and an optimization of them using genetic algorithm. The network delay is expressed in terms of three delays such as propagation delay, transmission delay and queuing delay of links. The packet loss ratio is defined as the ratio of successful packet transmission to total transmission over a link and the network cost includes the link cost, nodal cost, amplifier cost and other associated costs of the network. For this, we develop three objective functions and three constraints and use multi-objective genetic algorithm for optimized solution as the design of computer networks with multi-choice and multi-constraint are known to be NP-complete. In addition to the multiple objective optimization, the optimized topological design and the source-terminal pair route has been found by assigning a weight factor on each link, where either one or zero weight has been used in the later case. The proposed methodology is run using MATLAB on a set of data networks and satisfactory results have been obtained. For clarity, the detail simulation output of one network is given in this paper.