通过结合探测和对偶固定增强混合整数规划中的预求解
Enhancing Presolve in Mixed Integer Programming by Combining Probing and Dual Fixing
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中文总结 AI 辅助
研究如何在混合整数规划求解器中结合探测和对偶固定技术。方法是先将对偶固定嵌入探测框架，再改进对偶固定技术并利用探测框架检测缩减。贡献是在开源求解器HiGHS上通过结合二者提升了性能，在MIPLIB 2017基准实例上有潜力。
中文摘要 AI 辅助
探测和对偶固定是混合整数规划（MIP）求解器中的两种强大预求解技术。探测临时将一些二元变量设为0或1，应用基于线性约束的域传播技术以获得更好的变量边界，并提取有用信息。对偶固定尝试将变量固定到上下界同时确保至少保留一个最优解。本文研究如何在MIP求解器中结合这两种方法以实现更好性能。先将对偶固定嵌入探测框架，再开发改进的对偶固定技术，并用探测框架检测缩减。在MIPLIB 2017基准实例上的计算结果证明了这两种技术在开源MIP求解器HiGHS上结合探测和对偶固定的潜力。
英文摘要
Probing and dual fixing are two powerful presolve techniques in mixed integer programming (MIP) solvers. Probing tentatively sets some binary variables to 0 or 1, applies linear constraint based domain propagation techniques to derive better variable bounds, and extracts useful information such as stronger variable implications and better global variable bounds. Dual fixing attempts to fix variables to lower or upper bounds while ensuring that at least one optimal solution is retained, as long as the problem was feasible. In this paper, we investigate how to combine the two approaches in MIP solvers to achieve a better performance. In particular, we first embed dual fixing into the probing framework, deriving more useful variables' implications for enhancing the capability of probing. Then, we develop an improved dual fixing technique where more variable fixings can be applied, and use the probing framework to detect the reductions. Computational results on the MIPLIB 2017 benchmark instances demonstrate the potential of the two proposed techniques in combining probing and dual fixing on the open-source MIP solver HiGHS.
