Permutation-based Recombination Operator to Node-depth Encoding

The node-depth encoding is a representation for evolutionary algorithms applied to tree problems. Its represents trees by storing the nodes and their depth in a proper ordered list. The original formulation of the node-depth encoding has only mutation operators as the search mechanism. Although the representation has this restriction, it has obtained good results with low convergence. Then, this work proposes a specific recombination operator to improve the convergence of the node-depth encoding representation. These operators are based on recombination for permutation representations. An investigation into the bias and heritability of the proposed recombination operator shows that it has a bias towards stars and low heritability. The performance of node-depth encoding with the proposed operator is investigated for the optimal communication spanning tree problem. The results are presented for benchmark instances in the literature. The use of the recombination operator results in a faster convergence than with only mutation operators.