Classification vs regression models in a decision tree-based Interactive evolutionary multi-objective optimization algorithm

Multi-objective optimization problems involve conflicting objectives, making it particularly challenging to find a single optimal solution. Instead, their solution methods aim to yield numerous high-quality, non-dominated solutions, each representing different trade-offs among the objectives. Evolutionary multi-objective algorithms (EMOAs) are widely used to generate these diverse sets of non-dominated solutions. However, the sheer number of solutions complicates decision-making by making it difficult to identify the most desirable ones. Additionally, generating a diverse representation of non-dominated solutions becomes increasingly difficult as the number of objectives increases. Interactive EMOAs leverage the decision-maker's (DM) preferences to guide the search towards a smaller subset of preferred non-dominated solutions or even the most preferred one. However, existing methods often lack robustness in learning the DM's preferences under realistic conditions. Recently, the use of decision trees (DTs) for learning DM's preferences has been proposed to enhance the robustness of interactive algorithms. Since the performance of different DT models in preference learning has not been thoroughly analyzed, this study aims to evaluate and compare the effectiveness of DT classification and regression models in learning to rank, which is a crucial element in ranking-based interactive algorithms. The analysis considers different problems with different dimensions and various preference models. The results demonstrate that DT-classification-based preference learning is superior to the DT-regression-based method. Nevertheless, this study discusses an improvement to the regression models that could enhance their performance, paving the way towards the realization of the potential of these models.