论文标题
订购目标和帕累托有效解决方案的方法
An Approach to Ordering Objectives and Pareto Efficient Solutions
论文作者
论文摘要
由于缺乏单个目标的有序性，通常无法比较或有序的多目标优化问题解决方案。此外，经常使决策者认为可以比较规模的目标。这是一个谬论，因为解决方案的空间实际上是不均匀的，而没有线性权衡。我们提出了一种使用概率积分转换的方法，以将问题的目标映射到共享相同范围的分数中。在分数空间中，我们可以了解哪些权衡实际上是可能的，并开发了将所需的权衡取回偏好空间的方法。我们的结果表明，可以使用单个目标的低或偏见聚合来订购帕累托有效解决方案。当在优化过程中使用得分而不是原始目标时，该过程允许获得更接近表达偏好的权衡。使用非线性映射将得分空间中的所需解决方案转换为所需的优先偏好，从而更加明显地改善了这一点。
Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be compared. This is a fallacy, as the space of solutions is in practice inhomogeneous without linear trade-offs. We present a method that uses the probability integral transform in order to map the objectives of a problem into scores that all share the same range. In the score space, we can learn which trade-offs are actually possible and develop methods for mapping the desired trade-off back into the preference space. Our results demonstrate that Pareto efficient solutions can be ordered using a low- or no-preference aggregation of the single objectives. When using scores instead of raw objectives during optimization, the process allows for obtaining trade-offs significantly closer to the expressed preference. Using a non-linear mapping for transforming a desired solution in the score space to the required preference for optimization improves this even more drastically.
