Ranking-Dominance and Many-Objective Optimization

An alternative relation to Pareto-dominance is studied. The relation is based on ranking a set of solutions according to each separate objective and an aggregation function to calculate a scalar fitness value for each solution. The relation is called as ranking-dominance and it tries to tackle the curse of dimensionality commonly observed in multi-objective optimization. Ranking-dominance can be used to sort a set of solutions even for a large number of objectives when the Pareto-dominance relation cannot distinguish solutions from one another anymore. This permits the search to advance even with a large number of objectives. Experimental results indicate that in some cases the selection based on ranking-dominance is able to advance the search towards the Pareto-front better than the selection based on Pareto-dominance. However, in some cases it is also possible that the search does not proceed into direction of the Pareto-front because the ranking-dominance relation permits deterioration of individual objectives. The results also show that when the number of objectives increases, the selection based on just Pareto-dominance without diversity maintenance is able to advance the search better than with diversity maintenance. Therefore, diversity maintenance connives at difficulties solving problems with a high number of objectives.