On the performance of classification algorithms for learning Pareto-dominance relations

Multi-objective evolutionary algorithms (MOEAs) are often criticized for their high-computational costs. This becomes especially relevant in simulation-based optimization where the objectives lack a closed form and are expensive to evaluate. Over the years, meta-modeling or surrogate modeling techniques have been used to build inexpensive approximations of the objective functions which reduce the overall number of function evaluations (simulations). Some recent studies however, have pointed out that accurate models of the objective functions may not be required at all since evolutionary algorithms only rely on the relative ranking of candidate solutions. Extending this notion to MOEAs, algorithms which can `learn´ Pareto-dominance relations can be used to compare candidate solutions under multiple objectives. With this goal in mind, in this paper, we study the performance of ten different off-the-shelf classification algorithms for learning Pareto-dominance relations in the ZDT test suite of benchmark problems. We consider prediction accuracy and training time as performance measures with respect to dimensionality and skewness of the training data. Being a preliminary study, this paper does not include results of integrating the classifiers into the search process of MOEAs.