Tchebycheff Fractal Decomposition Algorithm for Bi-objective Optimization Problems

In most of the existing multi-objective metaheuristics based on decomposition, the reference points and the subspaces are statically defined. In this paper, a new adaptive strategy based on Tchebycheff fractals is proposed. A fractal decomposition of the objective space based on Tchebycheff functions, and adaptive strategies for updating the reference points are performed. The proposed algorithm outperforms popular multi-objective evolutionary algorithms both in terms of the quality of the obtained Pareto fronts (convergence, cardinality, diversity) and the search time.