Interactive Final Solution Selection in Multi-Objective Optimization

Recently, multi-objective evolutionary algorithms (MOEAs) with an unbounded external archive (UEA) have received increasing attention in the evolutionary multi-objective optimization community. Its basic idea is to store all examined solutions during the optimization process and select representative solutions as the final output for the decision-maker (DM). Although many studies have investigated MOEAs with UEA, there is a lack of studies focusing on the final solution selection. Actually, selecting a good solution from UEA that meets the requirements of the DM is a challenging task due to the limited information processing capacity of the human decision-maker. Moreover, in many real-world scenarios, decision-makers often prefer not to evaluate a large number of solutions and may not have clear preferences over objectives. To fill this gap in post-processing for MOEAs with UEA, this paper proposes an interactive final solution selection (IFSS) method for multi-objective optimization. The proposed IFSS method aims to provide a good final solution through several interactions with the DM. In other words, the DM can obtain a satisfying solution after evaluating only a small number of solutions even without providing clearly specific preferences. Furthermore, a calibration strategy is introduced to significantly improve the performance of IFSS by slightly increasing the number of interactions. Extensive experiments are conducted on various test problems to demonstrate the effectiveness of the proposed IFSS method.