SymILO: A Symmetry-Aware Learning Framework for Integer Linear Optimization

TL;DR

SymILO is a novel symmetry-aware learning framework that leverages the intrinsic symmetries of ILPs to improve solution accuracy, outperforming existing methods significantly.

Contribution

The paper introduces SymILO, a new training framework that incorporates ILP symmetries through solution permutation and joint optimization, enhancing learning stability and performance.

Findings

Achieves up to 66.5% average improvement over existing methods.

Effectively incorporates problem symmetries into the learning process.

Demonstrates robustness across various ILP symmetry types.

Abstract

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via supervised learning, with an ILP as the input and an optimal solution as the label. An ILP is symmetric if its variables can be permuted without changing the problem structure, resulting in numerous equivalent and optimal solutions. Randomly selecting an optimal solution as the label can introduce variability in the training data, which may hinder the model from learning stable patterns. In this work, we incorporate the intrinsic symmetry of ILPs and propose a novel training framework called SymILO. Specifically, we modify the learning task by introducing solution permutation along with neural network weights as learnable parameters and then design an alternating algorithm to jointly optimize the loss function. We conduct extensive experiments on ILPs involving different symmetries and the computational results demonstrate that our symmetry-aware approach significantly outperforms three existing methods -- achieving $50.3\%$, $66.5\%$, and $45.4\%$ average improvements, respectively.