Accelerate the optimization of large-scale manufacturing planning using game theory

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.