无需逆向优化：基于Transformer模型的直接解预测
Inverse Optimization Without Inverse Optimization: Direct Solution Prediction with Transformer Models
AI总结：
本文提出基于Transformer模型的直接解预测方法，用于解决具有未知组件的组合优化问题，通过约束推理模块整合已知约束，生成结构相似且满足约束的解，展现出在复杂问题中优于LSTM和逆向优化的性能。
摘要：
我们提出了一种端到端框架，用于生成具有未知组件的组合优化问题的解，使用基于Transformer的序列到序列神经网络。我们的框架直接从过往解中学习，并通过约束推理模块整合已知组件，如硬约束，从而得到一种受约束的学习方案。训练后的模型生成新的解，这些解在结构上与以往的解相似，并且保证尊重已知的约束。我们将我们的方法应用于三个具有未知组件的组合优化问题：具有未知奖励函数的背包问题、具有未知目标函数的二分图匹配问题，以及具有释放时间和未知优先级约束的单机调度问题，目标是最小化平均完成时间。我们证明Transformer模型在性能上表现极为出色，通常能在几秒钟内生成接近最优的解。相比于基于LSTM的替代方案和逆向优化，它们在更复杂的底层目标函数和未知隐式约束存在时表现尤为有效。
英文摘要：
We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and incorporates the known components, such as hard constraints, via a constraint reasoning module, yielding a constrained learning scheme. The trained model generates new solutions that are structurally similar to past solutions and are guaranteed to respect the known constraints. We apply our approach to three combinatorial optimization problems with unknown components: the knapsack problem with an unknown reward function, the bipartite matching problem with an unknown objective function, and the single-machine scheduling problem with release times and unknown precedence constraints, with the objective of minimizing average completion time. We demonstrate that transformer models have remarkably strong performance and often produce near-optimal solutions in a fraction of a second. They can be particularly effective in the presence of more complex underlying objective functions and unknown implicit constraints compared to an LSTM-based alternative and inverse optimization.
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。
