We consider a multi-objective optimization problem with objective functions that are expensive to evaluate. The decision maker (DM) has unknown preferences, and so the standard approach is to generate an approximation of the Pareto front and let the DM choose from the generated non-dominated designs. However, especially for expensive to evaluate problems where the number of designs that can be evaluated is very limited, the true best solution according to the DM's unknown preferences is unlikely to be among the small set of non-dominated solutions found, even if these solutions are truly Pareto optimal. We address this issue by using a multi-objective Bayesian optimization algorithm and allowing the DM to select a preferred solution from a predicted continuous Pareto front just once before the end of the algorithm rather than selecting a solution after the end. This allows the algorithm to understand the DM's preferences and make a final attempt to identify a more preferred solution. We demonstrate the idea using ParEGO, and show empirically that the found solutions are significantly better in terms of true DM preferences than if the DM would simply pick a solution at the end.
翻译:我们认为,一个多目标优化问题,其客观功能是难以评估的。决策者(DM)有未知的偏好,因此标准的方法是使Pareto前线近似,让DM从产生的非主导设计中作出选择。然而,特别是对于评估可以评估的设计数量非常有限的问题来说,如果费用昂贵,根据DM的未知偏好,真正的最佳解决办法不大可能是发现的一小套非主导性解决办法,即使这些解决办法确实是Pareto最佳的。我们通过多目标的Bayesian优化算法来解决这个问题,让DM在算法结束之前从预测的Pareto前线选择一个首选的解决方案,而不是在最后选择一个解决方案。这使得算法能够理解DM的偏好,并最后尝试找到一个更可取的解决办法。我们用ParEGO来证明这一想法,并用经验来表明,找到的解决办法在真正的DM偏好方面比DM最后选择一个解决方案要好得多。