3.4. Projection and refinement phases

The projection phase is the opposite process followed during the coarsening phase. The assignment reached at levelmþ<sup>1</sup> is now to be extended on is parent levelm. The extension algorithm is simple; if a cluster which belongs to levelmþ<sup>1</sup> is assigned the value of true, then the grouped pair of clusters that it represents, which belong to levelm, are also assigned the true value (line 10 of Algorithm 1). The evolutionary algorithm explained in the next section is used to improve the assignment during each level. The population reached at levelmþ<sup>1</sup> will serve as the initial population for levelm. The projected population already contains individuals with high fitness value leading MA to converge quicker within a few generations to a better assignment (lines 8 and 11 of Algorithm 1).
