In order to improve the performance of relational databases, one has to reduce the number of disk accesses necessary to transfer data from disk to main memory. The paper proposes to reduce the number of disk I/O accesses by vertically partitioning relation into fragments and allowing attribute replication to fragments if necessary. When zero-one integer programming model is solved by the branch-and-bound method, it requires much computing time to solve a large sized problem. Therefore, heuristic solutions using genetic algorithm(GA) are presented. GA in this paper adapts a few ideas which are different from traditional genetic algorithms, for examples, a rank-based sharing fitness function, elitism and so on. In order to improve performance of GA, a set of optimal parameter levels is determined by the experiment and makes use of it. As relations are vertically partitioned allowing attribute replications and saved in disk, an attribute replicating vertical partition method by GA can attain less access cost than non-attribute-replication one and require less computing time than the branch-and-bound method in large-sized problems. Also, it can acquire a good solution similar to the optimum solution in small-sized problem.