Detection of Hidden Objectives and Interactive Objective Reduction

Abstract: In multi-objective optimization problems, there might exist hidden objectives that are important to the decision-maker but are not being optimized. On the other hand, there might also exist irrelevant objectives that are being optimized but are of less importance to the DM. The question that arises here is whether it is possible to detect and reduce irrelevant objectives without deteriorating the quality of the final results? In fact, when dealing with multi-objective problems, each objective implies a significant cost best avoided if possible. However, existing methods that pertain to the reduction of objectives are computationally intensive and ignore the preferences of the decision-maker. In this paper, we propose an approach to exploit the capabilities of interactive evolutionary multi-objective optimization algorithms (EMOAs) and the preference information provided by the decision-maker, to detect and eliminate the irrelevant objectives during the optimization process and replace them with hidden ones, if any. The proposed method, which is based on univariate feature selection, is computationally effective and can be integrated into any ranking-based interactive EMOA. Using synthetic problems developed in this study, we motivate different scenarios in the experiments and prove the effectiveness of the proposed method in improving the computational cost, the total number of objective evaluations, and the quality of the final solutions.