Can Deep Learning Solve Parametric Mathematical Programming? An Application to 0–1 Linear Programming Through Image Representation.

Deep learning has been widely applied in many fields. Efficient optimization algorithms contribute a lot to the enhancement of deep learning. However, reverse studies on how deep learning can solve optimization problems, especially mathematical programming, are relatively scarce. In this work, we aim to initiate a discussion on using deep learning to solve parametric mathematical programming, which can be converted to find a mapping from parameter space to solution space. Given that deep convolutional neural networks (DCNNs) have been successfully applied in the field of computer vision, converting a mathematical programming problem into an image representation may provide the solution. This work takes the 0–1 knapsack problem (KP) as an example to build an original image representation method. After modifying the image details, the proposed method is extended to the general 0–1 linear programming (LP) problem, and a deep learning architecture is designed to solve the transferred computer vision problem. The efficiency of the proposed DCNNs method is validated on a large number of problems, and results show that this method can solve the 0–1 LP accurately and efficiently without iteration. The solution speed is 20 times faster than that of traditional optimization solvers. [ABSTRACT FROM AUTHOR]