将约束传播引入动态规划,显著减少状态搜索量。
Domain-Independent Dynamic Programming with Constraint Propagation
- 在动态规划中嵌入通用约束求解器进行状态剪枝。
- 在三个组合优化问题上,状态扩展数大幅减少。
- 适合需要高效求解约束密集型问题的研究者。
组合优化问题通常采用两种模型范式:基于状态的表示方法(如启发式搜索、动态规划、决策图)和基于约束与域的表示方法(如约束编程、(混合)整数规划、布尔可满足性)。本文通过将约束传播集成到动态规划中,使动态规划求解器能够利用约束传播来剪枝状态和转移。为此,我们在无领域依赖的动态规划框架中使用通用约束求解器实现约束传播,并在三个组合优化问题上评估:带时间窗的单机调度、资源受限项目调度问题(RCPSP)以及带时间窗的旅行商问题(TSPTW)。实验表明,约束传播显著减少了状态扩展次数,使得本方法在单机调度和RCPSP问题上求解了更多实例,对紧密约束的TSPTW实例也表现出类似改进。运行时性能显示,对于约束密集的实例,传播带来的收益超过其开销;进一步降低传播开销有望提升整体性能。该工作为理解约束传播在动态规划求解器中的价值迈出关键一步,提供了一种融合动态规划与约束编程的模型化方法。
原文摘要 · Abstract (English)
There are two prevalent model-based paradigms for combinatorial problems: 1) state-based representations, such as heuristic search, dynamic programming (DP), and decision diagrams, and 2) constraint and domain-based representations, such as constraint programming (CP), (mixed-)integer programming, and Boolean satisfiability. In this paper, we bridge the gap between the DP and CP paradigms by integrating constraint propagation into DP, enabling a DP solver to prune states and transitions using constraint propagation. To this end, we implement constraint propagation using a general-purpose CP solver in the Domain-Independent Dynamic Programming framework and evaluate using heuristic search on three combinatorial optimisation problems: Single Machine Scheduling with Time Windows, the Resource Constrained Project Scheduling Problem (RCPSP), and the Travelling Salesperson Problem with Time Windows (TSPTW). Our evaluation shows that constraint propagation significantly reduces the number of state expansions, causing our approach to solve more instances than a DP solver for Single Machine Scheduling and RCPSP, and showing similar improvements for tightly constrained TSPTW instances. The runtime performance indicates that the benefits of propagation outweigh the overhead for constrained instances, but that further work into reducing propagation overhead could improve performance further. Our work is a key step in understanding the value of constraint propagation in DP solvers, providing a model-based approach to integrating DP and CP.
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