Hub location problems are widely used for network designing. Many variations of these problems can be found in the literature. In this paper we deal with the uncapacitated multiple allocation hub location problem (UMAHLP). We propose a genetic algorithm (GA) for solving UMAHLP that uses binary encoding and genetic operators adapted to the problem. Overall performance of GA implementation is improved by caching technique. We present the results of our computational experience on standard ORLIB instances with up to 200 nodes. The results show that GA approach quickly reaches all optimal solutions that are known so far and also gives results on some large-scale instances that were unsolved before.