The growing utilization of planning tools in practical scenarios has sparked an interest in generating multiple high-quality plans. Consequently, a range of computational problems under the general umbrella of top-quality planning were introduced over a short time period, each with its own definition. In this work, we show that the existing definitions can be unified into one, based on a dominance relation. The different computational problems, therefore, simply correspond to different dominance relations. Given the unified definition, we can now certify the top-quality of the solutions, leveraging existing certification of unsolvability and optimality. We show that task transformations found in the existing literature can be employed for the efficient certification of various top-quality planning problems and propose a novel transformation to efficiently certify loopless top-quality planning.

翻译：实际场景中规划工具的使用日益增长，激发了对生成多个高质量规划方案的需求。因此，在短期内出现了一系列统称为"最优质量规划"的计算问题，每种问题都有其自身定义。在本工作中，我们证明基于支配关系可将现有定义统一为一个。不同的计算问题因此仅对应不同的支配关系。基于这一定义，我们可以借助现有的不可解性认证与最优性认证技术，对解的最优质量进行认证。我们证明现有文献中的任务转换方法可用于高效认证各类最优质量规划问题，并提出了一种新颖的转换方法以实现无环最优质量规划的高效认证。