Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the computation of the entire Pareto front can become prohibitively expensive, both in terms of computational resources and time, particularly when dealing with a large number of objectives. In practical applications, decision-makers (DMs) will select a single solution of the Pareto front that aligns with their preferences to be implemented; thus, traditional multi-objective algorithms invest a lot of budget sampling solutions that are not interesting for the DM. In this paper, we propose two novel algorithms that employ Gaussian Processes and advanced discretization methods to efficiently locate the most preferred region of the Pareto front in expensive-to-evaluate problems. Our approach involves interacting with the decision-maker to guide the optimization process towards their preferred trade-offs. Our experimental results demonstrate that our proposed algorithms are effective in finding non-dominated solutions that align with the decision-maker's preferences while maintaining computational efficiency.

翻译：多目标优化是工程、金融等多个领域中广泛研究的问题，旨在寻找一组非支配解，这些解在相互冲突的目标之间提供最优权衡。然而，计算整个帕累托前沿可能变得异常昂贵——无论是计算资源还是时间成本——尤其是在目标数量较多时。实际应用中，决策者（DM）会从帕累托前沿中选择一个符合其偏好的单一解来实施；因此，传统的多目标算法会投入大量预算采样那些对决策者无意义的解。本文提出了两种新颖算法，采用高斯过程与先进离散化方法，在评估代价高昂的问题中高效定位帕累托前沿的最优偏好区域。我们的方法通过与决策者交互，引导优化过程朝向其偏好的权衡方向。实验结果表明，所提算法能在保持计算效率的同时，有效找到符合决策者偏好的非支配解。