It is well established that formulating an effective constraint model of a
problem of interest is crucial to the efficiency with which it can subsequently
be solved. Following from the observation that it is difficult, if not
impossible, to know a priori which of a set of candidate models will perform
best in practice, we envisage a system that explores the space of models
through a process of reformulation from an initial model, guided by performance
on a set of training instances from the problem class under consideration. We
plan to situate this system in a refinement-based approach, where a user writes
a constraint specification describing a problem above the level of abstraction
at which many modelling decisions are made. In this position paper we set out
our plan for an exploratory reformulation system, and discuss progress made so
far.

通过对训练实例的性能指导，我们计划构建一个探索性重构系统，用于从初始模型出发，通过重构自动化地探索模型空间。

约束模型的探索性重构

Towards Exploratory Reformulation of Constraint Models

Factorio is a 2D construction and management simulation video game about
building automated factories to produce items of increasing complexity. A core
feature of the game is its blueprint system, which allows players to easily
save and replicate parts of their designs. Blueprints can reproduce any layout
of objects in the game, but are typically used to encapsulate a complex
behaviour, such as the production of a non-basic object. Once created, these
blueprints are then used as basic building blocks, allowing the player to
create a layer of abstraction. The usage of blueprints not only eases the
expansion of the factory but also allows the sharing of designs with the game's
community. The layout in a blueprint can be optimised using various criteria,
such as the total space used or the final production throughput. The design of
an optimal blueprint is a hard combinatorial problem, interleaving elements of
many well-studied problems such as bin-packing, routing or network design. This
work presents a new challenging problem and explores the feasibility of a
constraint model to optimise Factorio blueprints, balancing correctness,
optimality, and performance.

Factorio 是一款关于建立自动化工厂以生产日益复杂物品的二维建设与管理模拟游戏，该研究工作提出了一个新的具有挑战性的问题，并探索了使用约束模型优化 Factorio 蓝图的可行性，平衡正确性、最优性和性能。

自动设计 Factorio 蓝图的探索

Towards Automatic Design of Factorio Blueprints

The performance of a constraint model can often be improved by converting a
subproblem into a single table constraint. In this paper we study heuristics
for identifying promising candidate subproblems, where converting the candidate
into a table constraint is likely to improve solver performance. We propose a
small set of heuristics to identify common cases, such as expressions that will
propagate weakly. The process of discovering promising subproblems and
tabulating them is entirely automated in the constraint modelling tool Savile
Row. Caches are implemented to avoid tabulating equivalent subproblems many
times. We give a simple algorithm to generate table constraints directly from a
constraint expression in \savilerow. We demonstrate good performance on the
benchmark problems used in earlier work on tabulation, and also for several new
problem classes. In some cases, the entirely automated process leads to orders
of magnitude improvements in solver performance.

该论文研究 Constraint Model 的性能如何通过将子问题转换为单个表约束来提高，提出了识别有前途的候选子问题的启发式方法，并自动将它们转换为表约束。在 Savile Row 约束建模工具中，完全自动地发现有前途的子问题并将其制表以避免多次制表。通过表述约束表达式的简单算法，我们对早期的制表工作中使用的基准问题表现出良好的表现，对于一些新的问题类别也表现出良好的效果。在某些情况下，完全自动的过程导致求解器性能增长数个数量级。

约束模型中的自动制表

Automatic Tabulation in Constraint Models

Plotting is a tile-matching puzzle video game published by Taito in 1989. Its
objective is to reduce a given grid of coloured blocks down to a goal number or
fewer. This is achieved by the avatar character repeatedly shooting the block
it holds into the grid. Plotting is an example of a planning problem: given a
model of the environment, a planning problem asks us to find a sequence of
actions that can lead from an initial state of the environment to a given goal
state while respecting some constraints. The key difficulty in modelling
Plotting is in capturing the way the puzzle state changes after each shot. A
single shot can affect multiple tiles directly, and the grid is affected by
gravity so numerous other tiles can be affected indirectly. We present and
evaluate a constraint model of the Plotting problem that captures this
complexity. We also discuss the difficulties and inefficiencies of modelling
Plotting in PDDL, the standard language used for input to specialised AI
planners. We conclude by arguing that AI planning could benefit from a richer
modelling language.

介绍了一种约束模型，用于解决将网格减少到给定目标数量或更少的 Plotting 问题，探讨了 AI 规划在建模语言方面的不足，建议富有表达力的建模语言对 AI 规划有益。