Paper Info
Title
Can Deep Learning Solve Parametric Mathematical Programming? An Application to 0–1 Linear Programming Through Image Representation
Abstract
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.
Year
DOI
Venue
2022
10.1109/TSMC.2021.3130109
IEEE Transactions on Systems, Man, and Cybernetics: Systems
Keywords
DocType
Volume
0-1 linear programming (LP),deep convolutional neural network (DCNN),deep learning,image representation,mathematical programming,optimization
Journal
52
Issue
ISSN
Citations 
9
2168-2216
0
PageRank 
References 
Authors
0.34
11
4
Name
Order
Citations
PageRank
Zhengxuan Ling100.34
Rui Liu2163.32
Yu Zhang36310.00
Xi Chen433370.76