迈向Transformer：用Transformer革新混合整数规划的求解
Toward TransfORmers: Revolutionizing the Solution of Mixed Integer Programs with Transformers
AI总结：
本研究提出首个用Transformer预测混合整数规划二元变量的深度学习框架，用于有容量限制的批量问题，后处理算法在求解时间、最优间隙和不可行性上优于CPLEX和LSTM，并将问题简化为LP实现多项式时间近似求解。
摘要：
在本研究中，我们提出了一种创新的深度学习框架，采用Transformer模型来应对混合整数规划的挑战，特别聚焦于有容量限制的批量问题（CLSP）。据我们所知，我们的方法是首个利用Transformer来预测混合整数规划（MIP）问题中二元变量的方法。具体而言，我们的方法利用了编码器-解码器Transformer处理序列数据的能力，使其非常适合预测CLSP每个时期中指示生产设置决策的二元变量。该问题本质上是动态的，我们需要在约束条件下处理序列决策。我们提出了一种高效算法，其中CLSP的解通过Transformer神经网络进行学习。所提出的后处理Transformer算法在超过24万个基准CLSP实例的测试中，在求解时间、最优间隙和不可行百分比方面均优于最先进的求解器CPLEX和长短期记忆网络（LSTM）。在机器学习模型训练完成后，对模型进行推理，将MIP问题简化为线性规划（LP）问题。这使得基于机器学习的算法结合LP求解器，成为一种多项式时间的近似算法，用于求解一个众所周知的NP难问题，且解的质量几乎完美。
英文摘要：
In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our knowledge, is the first to utilize transformers to predict the binary variables of a mixed-integer programming (MIP) problem. Specifically, our approach harnesses the encoder decoder transformer's ability to process sequential data, making it well-suited for predicting binary variables indicating production setup decisions in each period of the CLSP. This problem is inherently dynamic, and we need to handle sequential decision making under constraints. We present an efficient algorithm in which CLSP solutions are learned through a transformer neural network. The proposed post-processed transformer algorithm surpasses the state-of-the-art solver, CPLEX and Long Short-Term Memory (LSTM) in solution time, optimal gap, and percent infeasibility over 240K benchmark CLSP instances tested. After the ML model is trained, conducting inference on the model, reduces the MIP into a linear program (LP). This transforms the ML-based algorithm, combined with an LP solver, into a polynomial-time approximation algorithm to solve a well-known NP-Hard problem, with almost perfect solution quality.
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。
