基于机器学习的混合整数舍入割平面优化分离方法
Machine Learning for Optimization-Based Separation of Mixed-Integer Rounding Cuts
AI总结：
针对约束固定、成本变化的MIP场景，提出结合ML的混合MIR割生成框架，通过ML筛选约束构建简化MIP割生成器，实验验证其在割平面生成各轮次中能更有效强化界，尤其适用于完整分离器难寻强割的实例。
摘要：
混合整数舍入（MIR）割平面（割）可有效提升混合整数线性规划（MIP）问题线性松弛的强度。这类割平面通过聚合约束后对系数舍入推导得到，但要找到最强的MIR割平面，需要在聚合步骤中求解一个计算成本高昂的MIP优化问题，因此实际中常采用启发式策略来分离分数点。我们针对应用中的一类常见场景——约束保持固定而成本系数变化——提出改进MIR割平面生成的方法。我们提出一种混合割平面生成框架，其中训练机器学习（ML）模型，基于问题松弛得到的分数点分类哪些约束会参与生成有效的MIR割平面。在测试阶段，ML模型的预测结果可构建一个简化的基于MIP的MIR割平面生成器。实验中，我们对三个基准MIP实例分别进行细致且高成本的目标系数扰动，构建了一个包含1000个待分离分数点的数据集，所有实例共享同一约束集。结果表明，简化的分离器在每一轮割平面生成中都能更好地强化界，尤其是在完整分离器无法找到强割平面的实例上效果更显著。
英文摘要：
Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then rounding coefficients, but finding the strongest MIR cuts requires optimizing a costly MIP for the aggregation step, so in practice, heuristic strategies for separating fractional points are employed. We propose to improve MIR cut generation in the context of a common scenario in applications, where constraints remain fixed but costs are varied. We present a hybrid cut generation framework in which we train a machine learning (ML) model to classify which constraints are involved in useful MIR cuts based on fractional points from relaxations of the problem. At test time, the predictions of the ML model create a reduced MIP-based generator of MIR cuts. In our experiments, we create an instance family from each of three benchmark MIP instances by performing a careful and costly perturbation of objective coefficients to build a dataset of 1,000 fractional points to be separated over the same constraint set. The results indicate that the reduced separator better strengthens the bound in each round of cut generation, particularly for instances in which the full separator failed to find strong cuts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
