发表机构
Koç University; University of Augsburg; University of Michigan; Vienna University of Economics and Business; Johannes Kepler University Linz（博阿兹奇大学; 奥格斯堡大学; 密歇根大学; 维也纳经济与商业大学; 林茨约翰·开普勒大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对整数双层优化中追随者目标为非凸二次的问题，提出基于改进方向的析取割方法，在分支-割算法中排除不可行解，并显著优于现有最先进方法。
AI 中文摘要
本文研究了一类双层优化问题，其中所有变量均为整数，所有约束和领导者目标函数均为线性，而追随者目标函数为非凸二次函数。基于由改进方向导出的无双层可行解集合，我们开发了一种析取割方法，以在分支-割算法中排除双层不可行解。我们证明了我们的析取割可以通过求解一个割生成线性规划来获得。此外，我们讨论了允许减少割生成线性规划中析取项数量的条件，并提出了几种策略来高效地识别改进方向和生成析取割。我们在来自文献的符合我们设置的凸实例以及新的非凸实例上评估了所提出的分支-割算法的各个方面，并将我们最佳方法的性能与现有的最先进方法进行了比较，我们显著优于这些方法。
英文摘要
In this work, we study bilevel optimization problems where all variables are integer, all constraints and the leader objective function are linear, and the follower objective function is non-convex quadratic. Relying on bilevel-free sets derived from improving directions, we develop a disjunctive cut approach to exclude bilevel-infeasible solutions within a branch-and-cut algorithm. We show that our disjunctive cuts can be obtained by solving a cut generating linear program. Furthermore, we discuss conditions that allow the number of disjuncts in the cut generating linear program to be reduced, and we propose several strategies to identify improving directions and generate disjunctive cuts efficiently. We evaluate various aspects of the proposed branch-and-cut algorithm on both convex instances from the literature that fit our setting and new non-convex instances and compare the performance of our best approach with existing state-of-the-art approaches, which we significantly outperform.
