This paper studies a real-world manufacturing problem, which is modeled as a bi-objective integer programming problem. The variables and constraints involved are usually numerous and dramatically vary according to the manufacturing data. It is very challenging to directly solve such large-scale problems using heuristic algorithms or commercial solvers. Considering that the decision space of such problems is usually sparse and has a block-like structure, we propose to use decomposition methods to accelerate the optimization process. However, the existing decomposition methods require that the problem has strict block structures, which is not suitable for our problem. To deal with problems with such block-like structures, we propose a game theory based decomposition algorithm. This new method can overcome the large-scale issue and guarantee convergence to some extent, as it can narrow down the search space and accelerate the convergence. Extensive experimental results on real-world industrial manufacturing planning problems show that our method is more effective than the world fastest commercial solver Gurobi. The results also indicate that our method is less sensitive to the problem scale comparing with Gurobi.

本文研究了一个实际的制造问题，该问题被建模为双目标整数规划问题。涉及的变量和约束通常很多，并且会根据制造数据而有很大的不同。使用启发式算法或商用求解器直接解决此类大规模问题非常具有挑战性。考虑到此类问题的决策空间通常是稀疏的，并且具有类似块的结构，因此我们建议使用分解方法来加速优化过程。但是，现有的分解方法要求该问题具有严格的块结构，这不适合我们的问题。为了解决此类块状结构的问题，我们提出了一种基于博弈论的分解算法。这种新方法可以缩小搜索空间并加快收敛速度​​，因此可以克服大规模问题并在一定程度上保证收敛。关于现实世界中工业制造计划问题的大量实验结果表明，我们的方法比世界上最快的商业求解器Gurobi更有效。结果还表明，与Gurobi相比，我们的方法对问题规模不那么敏感。