Learning to Solve Network Flow Problems via Neural Decoding

TL;DR

This paper introduces a neural decoding approach leveraging LP duality theory to significantly accelerate the solution of large-scale network flow problems, outperforming traditional algorithms in speed and solution quality.

Contribution

It presents a novel neural decoding method that interprets LP solutions as noisy codewords, enabling faster and more accurate solutions for network flow problems.

Findings

Orders of magnitude speedup over iterative solvers

Better feasibility and optimality than end-to-end learning methods

Effective decoding strategy based on LP duality theory

Abstract

Many decision-making problems in engineering applications such as transportation, power system and operations research require repeatedly solving large-scale linear programming problems with a large number of different inputs. For example, in energy systems with high levels of uncertain renewable resources, tens of thousands of scenarios may need to be solved every few minutes. Standard iterative algorithms for linear network flow problems, even though highly efficient, becomes a bottleneck in these applications. In this work, we propose a novel learning approach to accelerate the solving process. By leveraging the rich theory and economic interpretations of LP duality, we interpret the output of the neural network as a noisy codeword, where the codebook is given by the optimization problem's KKT conditions. We propose a feedforward decoding strategy that finds the optimal set of active constraints. This design is error correcting and can offer orders of magnitude speedup compared to current state-of-the-art iterative solvers, while providing much better solutions in terms of feasibility and optimality compared to end-to-end learning approaches.