Graph Neural Network Training for Large-Scale Combinatorial Optimization

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Solution Overview

Problem

Existing methods for solving large-scale combinatorial optimization problems face challenges in achieving high solution accuracy and reducing calculation time, particularly when using Ising machines and quantum computers, due to limitations in the number of variables that can be handled.

Innovation Solution

The method involves creating subgraphs from a main graph, training sub-GNNs using solutions from a mathematical optimization solver as labeled data, and assigning feature vectors to a main GNN to solve the combinatorial optimization problem, utilizing the high accuracy of mathematical optimization solvers.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Loss of time

If the main graph is downscaled to create subgraphs, then the calculation time is reduced, but the solution accuracy may deteriorate

Engineering Contradiction:

Improvecalculation timeVSAvoidsolution accuracy

Core Design Contradiction:

Loss of timeVSMeasurement precision

Solution Approach 1:

The main graph is divided into multiple subgraphs, allowing the large-scale optimization problem to be broken down into smaller, more manageable subproblems that can be solved independently and then combined

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

A graph neural network serves as an intermediary that learns the mapping between graph structures and optimization solutions. The GNN is trained on subgraph solutions and then applied to the main graph, bridging the gap between downscaled problems and the original problem

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If partial solutions are combined by transmitting and receiving between subproblems, then the complete solution is constructed, but the number of repetition times increases and calculation time increases

Engineering Contradiction:

Improvesolution completenessVSAvoidcalculation time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The graph neural network is trained in advance on solutions from mathematical optimization solvers. This preliminary training enables the GNN to directly generate high-quality solutions without requiring iterative transmission and combination of partial solutions

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The mechanical iterative process of transmitting and combining partial solutions is replaced by a machine learning-based direct solution generation approach, where the trained GNN predicts solutions directly from the graph structure

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS20260080030A1Information Processing Apparatus and Information Processing Method

Publication Date: 2026.03.19 HITACHI LTD

AI summary

An information processing apparatus 100 for processing a combinatorial optimization problem includes: a graph creation unit 112 configured to create one or more subgraphs from a main graph; a mathematical optimization unit 115 configured to solve a combinatorial optimization problem for each of the subgraphs by a mathematical optimization solver; a machine learning unit 117 configured to train a sub-GNN corresponding to each of the subgraphs such that an output of the sub-GNN is approximate to a solution of the mathematical optimization solver; a feature vector assignment unit 118 configured to assign a feature vector at each vertex of the sub-GNN obtained as a result of the training to each corresponding vertex of a main GNN corresponding to graph data of the main graph as an input of a feature vector of the main GNN; and a solution output unit 119 configured to output a solution obtained as a result of the machine learning unit 117 training the main GNN by setting a loss function to solve the combinatorial optimization problem for the main graph.