仅随机化一次：在基于约束的程序化内容生成中塑造统计特性
You-Only-Randomize-Once: Shaping Statistical Properties in Constraint-based PCG
AI总结：
本文提出 YORO 预滚动方法，通过为约束求解器设计决策变量排序，在基于约束的程序化内容生成中编码并控制输出统计特性，同时保持全局约束，并以求解器版 WFC 验证了其有效性。
摘要：
在程序化内容生成中，将生成任务建模为约束满足问题使我们能够对生成输出定义局部和全局约束。然而，生成器的感知质量往往涉及统计特性，而不仅仅是硬约束。例如，我们可能希望生成的输出使用与参考设计具有相似分布的设计元素。然而，这种统计特性无法直接表达为对任何单个输出生成的硬约束。相比之下，不使用通用约束求解器的方法，例如 Gumin 对 WaveFunctionCollapse（WFC）算法的实现，可以控制输出统计特性，但约束传播能力有限，且无法表达非局部约束。在本文中，我们引入了 You-Only-Randomize-Once（YORO）预滚动方法，这是一种为约束求解器精心设计决策变量排序的方法，可将期望的统计特性编码到基于约束的生成器中。以基于求解器的 WFC 为例，我们展示了该技术能够有效控制由多个现成 SAT 求解器生成的瓦片网格输出的统计特性，同时仍然对输出强制执行全局约束。我们的方法可立即应用于类似 WFC 的生成问题，并为在其他基于约束的生成器中控制设计元素统计特性提供了一个概念性的起点。
英文摘要：
In procedural content generation, modeling the generation task as a constraint satisfaction problem lets us define local and global constraints on the generated output. However, a generator's perceived quality often involves statistics rather than just hard constraints. For example, we may desire that generated outputs use design elements with a similar distribution to that of reference designs. However, such statistical properties cannot be expressed directly as a hard constraint on the generation of any one output. In contrast, methods which do not use a general-purpose constraint solver, such as Gumin's implementation of the WaveFunctionCollapse (WFC) algorithm, can control output statistics but have limited constraint propagation ability and cannot express non-local constraints. In this paper, we introduce You-Only-Randomize-Once (YORO) pre-rolling, a method for crafting a decision variable ordering for a constraint solver that encodes desired statistics in a constraint-based generator. Using a solver-based WFC as an example, we show that this technique effectively controls the statistics of tile-grid outputs generated by several off-the-shelf SAT solvers, while still enforcing global constraints on the outputs.1 Our approach is immediately applicable to WFC-like generation problems and it offers a conceptual starting point for controlling the design element statistics in other constraint-based generators.
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