This paper presents a mete-heuristic approach using a genetic algorithm (GA) to optimize reliability of computer communication networks considering cost. When a network topology is known, the problem of choosing the types of links and computer systems among alternatives which have different reliability and cost to optimize system reliability is an NP-hard combinatorial problem. If there are m alternative links and k alternative computer systems, the search space for a known network topology with \L\ links and \N\ nodes is m(\L\). k(\N\). The heuristic is shown to be effective and computationally efficient compared to optimal solutions on a suite of test problems.