A deep learning approach for solving linear programming problems

Abstract

Finding the optimal solution to a linear programming (LP) problem is a long-standing computational problem in Operations Research. This paper proposes a deep learning approach in the form of feed-forward neural networks to solve the LP problem. The latter is first modeled by an ordinary differential equations (ODE) system, the state solution of which globally converges to the optimal solution of the LP problem. A neural network model is constructed as an approximate state solution to the ODE system, such that the neural network model contains the prediction of the LP problem. Furthermore, we extend the capability of the neural network by taking the parameter of LP problems as an input variable so that one neural network can solve multiple LP instances in a one-shot manner. Finally, we validate the proposed method through a collection of specific LP examples and show concretely how the proposed method solves the example.