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, including post-processing,
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.

利用变压器模型解决容量限制批量问题，并通过深度学习框架和线性规划解决被认为是 NP - 难的问题，提供了解决时效、优化率和可行性等方面超越当前最先进解法的算法。