答案集编程中按最优性进行解枚举
Solution Enumeration by Optimality in Answer Set Programming
AI总结：
本文提出答案集编程中按最优性顺序枚举答案集（ASEO）的通用算法，支持最佳k个或无限枚举，并展示其在优化问题次优解访问和贝叶斯网络采样中的应用。
摘要：
给定一个组合搜索问题，除了找到一个解或证明不存在解之外，枚举其（所有）解可能非常有用。如果提供了目标函数，最优解的情况也是如此。这项工作超越了单纯枚举最优解，解决了按最优性进行解枚举（SEO）的计算任务。该任务在答案集编程（ASP）的背景下进行研究，其中问题的（最优）解通过编码该问题的逻辑程序的答案集来捕获。现有的答案集求解器已经支持枚举所有（最优）答案集。然而，在这项工作中，我们将最优答案集的枚举推广到超越严格最优的答案集，从而产生了按最优性顺序枚举答案集（ASEO）的想法。这种方法适用于最佳k个答案集，或在无限设置中，这相当于基于目标函数对答案集进行排序的过程。作为这项工作的主要贡献，我们提出了针对上述答案集枚举任务的第一个通用算法。此外，我们展示了ASEO的潜在用例。首先，我们研究了在多个已在ASP中形式化和解决的优化问题中，如何高效地访问次优解。其次，我们表明ASEO为我们提供了一种有效的贝叶斯网络采样技术。
英文摘要：
Given a combinatorial search problem, it may be highly useful to enumerate its (all) solutions besides just finding one solution, or showing that none exists. The same can be stated about optimal solutions if an objective function is provided. This work goes beyond the bare enumeration of optimal solutions and addresses the computational task of solution enumeration by optimality (SEO). This task is studied in the context of Answer Set Programming (ASP) where (optimal) solutions of a problem are captured with the answer sets of a logic program encoding the problem. Existing answer-set solvers already support the enumeration of all (optimal) answer sets. However, in this work, we generalize the enumeration of optimal answer sets beyond strictly optimal ones, giving rise to the idea of answer set enumeration in the order of optimality (ASEO). This approach is applicable up to the best k answer sets or in an unlimited setting, which amounts to a process of sorting answer sets based on the objective function. As the main contribution of this work, we present the first general algorithms for the aforementioned tasks of answer set enumeration. Moreover, we illustrate the potential use cases of ASEO. First, we study how efficiently access to the next-best solutions can be achieved in a number of optimization problems that have been formalized and solved in ASP. Second, we show that ASEO provides us with an effective sampling technique for Bayesian networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
