Primal-Optimal-Binding LPNet: Deep Learning Architecture to Predict Optimal Binding Constraints of a Linear Programming Problem

Abstract

Identifying an optimal basis for a linear programming problem is a challenging learning task. Traditionally, an optimal basis is obtained via the iterative simplex method which improves from the current basic feasible solution to the adjacent one until it reaches optimal. The obtained result is the value of the optimal solution and the corresponding optimal basis. Even though learning the optimal value is hard but learning the optimal basis is possible via deep learning. This paper presents the primal-optimal-binding LPNet that learns from massive linear programming problems of various sizes casting as all-unit-rowexcept-first-unit-column matrices. During the training step, these matrices are fed to the special row-column convolutional layer followed by the state-of-the-art deep learning architecture and sent to two fully connected layers. The result is the probability vector of non-negativity constraints and the original linear programming constraints at the optimal basis. The experiment shows that this LPNet achieves 99% accuracy of predicting a single binding optimal constraint on unseen test problems and Netlib problems. It identifies correctly 80% LP problems having all optimal binding constraints and faster than cplex solution time.