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In this paper we suggest an evolutionary computational approach by applying a combination of a genetic algorithm and a tabu search to obtain a good solution for relatively large unidirectional automated guided vehicle flowpath design problems. Unidirectional flowpaths are used to lessen the traffic control loads for large fleets of vehicles and to increase the efficiency in use of space. The flow path design is one of the most important steps in efficient vehicle systems design. We use an genetic algorithm to obtain partially directed networks, which are then completed and afterwards improved by a tabu search. A set of computational experiments is conducted to show the efficiency of the proposed solution procedure and the results are reported.