In this paper, we present an approach to automated solving of triangle
ruler-and-compass construction problems using finite-domain constraint solvers.
The constraint model is described in the MiniZinc modeling language, and is
based on the automated planning. The main benefit of using general constraint
solvers for such purpose, instead of developing dedicated tools, is that we can
rely on the efficient search that is already implemented within the solver,
enabling us to focus on geometric aspects of the problem. We may also use the
solver's built-in optimization capabilities to search for the shortest possible
constructions. We evaluate our approach on 74 solvable problems from the
Wernick's list, and compare it to the dedicated triangle construction solver
ArgoTriCS. The results show that our approach is comparable to dedicated tools,
while it requires much less effort to implement. Also, our model often finds
shorter constructions, thanks to the optimization capabilities offered by the
constraint solvers.

这篇论文介绍了一种使用有限域约束求解器自动解决三角形尺规作图问题的方法，并通过与专用工具进行比较，证明了该方法不仅具有相当的性能，而且实现起来需要更少的工作量。

使用约束求解器自动化三角尺和指南针构造

Automation of Triangle Ruler-and-Compass Constructions Using Constraint  Solvers

In this work, we conduct an assessment of the optimization capabilities of
LLMs across various tasks and data sizes. Each of these tasks corresponds to
unique optimization domains, and LLMs are required to execute these tasks with
interactive prompting. That is, in each optimization step, the LLM generates
new solutions from the past generated solutions with their values, and then the
new solutions are evaluated and considered in the next optimization step.
Additionally, we introduce three distinct metrics for a comprehensive
assessment of task performance from various perspectives. These metrics offer
the advantage of being applicable for evaluating LLM performance across a broad
spectrum of optimization tasks and are less sensitive to variations in test
samples. By applying these metrics, we observe that LLMs exhibit strong
optimization capabilities when dealing with small-sized samples. However, their
performance is significantly influenced by factors like data size and values,
underscoring the importance of further research in the domain of optimization
tasks for LLMs.

评估 LLM 在各种任务和数据大小上的优化能力，并引入了三个不同的指标来全面评估任务性能。通过应用这些指标，我们观察到 LLM 在处理小规模样本时表现出很强的优化能力，但其性能受到数据大小和值等因素的显著影响，强调了对 LLM 的优化任务领域进行进一步研究的重要性。