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In this paper, we propose a new method for the visual reorganization of online analytical processing (OLAP) cubes that aims at improving their visualization. Our method addresses dimensions with hierarchically organized members. It uses a genetic algorithm that reorganizes k-ary trees. Genetic operators perform permutations of subtrees to optimize a visual homogeneity function. We propose several ways to reorganize an OLAP cube depending on which set of members is selected for the reorganization: all of the members, only the displayed members, or the members at a given level (level by level approach). The results that are evaluated by using optimization criteria show that our algorithm has a reliable performance even when it is limited to 1 minute runs. Our algorithm was integrated in an interactive 3D interface for OLAP. A user study was conducted to evaluate our approach with users. The results highlight the usefulness of reorganization in two OLAP tasks.