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arXiv 1401.3830cs.AI
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基于决策图的交互式成本配置

Interactive Cost Configuration Over Decision Diagrams

Configit A/S;University College Cork(科克大学学院);Technical University of Denmark(丹麦技术大学)

Henrik Reif Andersen, Tarik Hadzic, David Pisinger

摘要:

在许多人工智能领域,如产品配置,用户应该交互式地指定一个解决方案,必须满足一组约束。在这种情况下,离线编译可行的解决方案到一个易于处理的表示是一个重要的方法来提供有效的无回溯的用户交互在线。特别是,二元决策图(BDD)已成功地用作产品和服务配置的编译目标。在本文中,我们将讨论如何扩展BDD为基础的配置方案涉及成本函数,表达用户的喜好。我们首先表明,一个有效的,强大的和易于实现的扩展是可能的,如果成本函数是添加剂,和可行的解决方案表示使用多值决策图(MDDs)。我们还讨论了MDD大小的影响,如果成本函数是非加性的,或者如果它是明确编码到MDD。然后,我们讨论了存在多个成本函数的交互式配置。我们证明,即使在其最简单的形式,多成本配置是NP难的输入MDD。然而,对于解决两个成本配置,我们开发了一个伪多项式计划和一个完全多项式逼近计划。我们的方法的适用性证明了通过实验在现实世界的配置模型和产品目录数据集。响应时间通常在几分之一秒内,即使是非常大的实例。

英文摘要:

In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrack-free user interaction online. In particular,binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDD-based configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multi-valued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is non-additive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiple-cost configuration is NP-hard in the input MDD. However, for solving two-cost configuration we develop a pseudo-polynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over real-world configuration models and product-catalogue datasets. Response times are generally within a fraction of a second even for very large instances.

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。

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