使用混合整数规划求解器作为基于对偶分解的混合整数规划启发式算法
Using a MIP Solver as a PDHG-Based MIP Heuristic
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中文总结 AI 辅助
研究能否用对偶分解算法替换现代混合整数规划求解器中的默认线性规划求解器来加速启发式算法，虽有缺点，但多数启发式算法不受影响，能更快找到高质量高精度的混合整数规划问题解。
中文摘要 AI 辅助
对偶分解（PDHG）算法为解决困难的线性规划（LP）问题提供了新能力，即能快速找到低精度解。虽此类解并非适用于LP的所有应用，但可用于加速混合整数规划（MIP）问题可行解的启发式搜索，近似LP解有望引导启发式算法找到准确且高质量的MIP解。本文提出能否用PDHG替换现代MIP求解器中的默认LP求解器以加速多数（或所有）现有启发式算法的问题。结果表明这样做有明显缺点，会妨碍使用一些强大的MIP技术，但多数不受影响，最终得到的启发式算法通常能比当前最先进策略更快找到高质量、高精度解。
英文摘要
The PDHG algorithm provides a new capability for solving difficult linear programming (LP) problems: the ability to find low-accuracy solutions quickly. While such solutions may not be applicable in all applications of LP, one possible use is to accelerate heuristics for finding feasible solutions to Mixed-Integer Programming (MIP) problems, where these approximate LP solutions can hopefully guide a heuristic towards accurate and high-quality MIP solutions. While a monolithic heuristic that exploits PDHG solutions would be useful, we pose a broader question here: could we replace the default LP solver in a modern MIP solver with PDHG to accelerate most (or all) of its existing heuristics? We find that doing so does have some obvious drawbacks, preventing us from using several powerful MIP techniques, but it leaves most others unaffected, ultimately resulting in a heuristic that often finds high-quality, high-accuracy solutions faster than current state-of-the-art strategies.
发表机构
- Gurobi Optimization, LLC（Gurobi优化有限公司）
机构由 AI 辅助整理，请以论文原文为准。
