Bilevel optimization deals with nested problems in which a leader takes the
first decision to minimize their objective function while accounting for a
follower's best-response reaction. Constrained bilevel problems with integer
variables are particularly notorious for their hardness. While exact solvers
have been proposed for mixed-integer linear bilevel optimization, they tend to
scale poorly with problem size and are hard to generalize to the non-linear
case. On the other hand, problem-specific algorithms (exact and heuristic) are
limited in scope. Under a data-driven setting in which similar instances of a
bilevel problem are solved routinely, our proposed framework, Neur2BiLO, embeds
a neural network approximation of the leader's or follower's value function,
trained via supervised regression, into an easy-to-solve mixed-integer program.
Neur2BiLO serves as a heuristic that produces high-quality solutions extremely
fast for the bilevel knapsack interdiction problem, the "critical node game"
from network security, a donor-recipient healthcare problem, and discrete
network design from transportation planning. These problems are diverse in that
they have linear or non-linear objectives/constraints and integer or
mixed-integer variables, making Neur2BiLO unique in its versatility.

通过使用神经网络近似技术，我们提出了一个名为 Neur2BiLO 的框架，用于解决具有整数变量的约束双层问题。Neur2BiLO 能够快速产生高质量的解决方案，适用于多种具有线性或非线性目标 / 约束和整数或混合整数变量的问题。

Neur2BiLO: 神经双层最优化

Neur2BiLO: Neural Bilevel Optimization

Constraint Programming (CP) is a useful technology for modeling and solving
combinatorial constrained problems. On the one hand, on can use a library like
PyCSP3 for easily modeling problems arising in various application fields
(e.g., scheduling, planning, data-mining, cryptography, bio-informatics,
organic chemistry, etc.). Problem instances can then be directly generated from
specific models and data. On the other hand, for solving instances (notably,
represented in XCSP3 format), one can use a constraint solver like ACE, which
is presented in this paper. ACE is an open-source constraint solver, developed
in Java, which focuses on integer variables (including 0/1-Boolean variables),
state-of-the-art table constraints, popular global constraints, search
heuristics and (mono-criterion) optimization.

该研究论文介绍了使用约束编程技术建模和解决组合约束问题的方法，其中提到了 PyCSP3 建模库和 ACE 约束求解器，ACE 是一个基于 Java 开发的开源约束求解器，重点关注整数变量、状态最新技术的表约束和常见全局约束、搜索启发式和单准则优化。