[Paper Review] Graph Embedding for Combinatorial Optimization: A Survey

Yün Peng, Byron Choi+1 more|arXiv (Cornell University)|Aug 26, 2020

Advanced Graph Neural Networks4 citations

TL;DR

This survey provides a comprehensive overview of graph embedding methods for solving combinatorial optimization (CO) problems in graphs, categorizing approaches by preprocessing techniques and machine learning models. It demonstrates how graph embeddings enable effective representation learning for CO tasks, either through classification or integration with search algorithms, and outlines key research directions for future work.

ABSTRACT

Graphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective analysis of graph data is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Using ML- based CO methods, a graph has to be represented in numerical vectors, which is known as graph embedding. In this survey, we provide a thorough overview of recent graph embedding methods that have been used to solve CO problems. Most graph embedding methods have two stages: graph preprocessing and ML model learning. This survey classifies graph embedding works from the perspective of graph preprocessing tasks and ML models. Furthermore, this survey summarizes recent graph-based CO methods that exploit graph embedding. In particular, graph embedding can be employed as part of classification techniques or can be combined with search methods to find solutions to CO problems. The survey ends with several remarks on future research directions.

Motivation & Objective

• To systematically categorize recent graph embedding methods used in combinatorial optimization (CO) problems.
• To analyze the role of graph preprocessing and machine learning models in embedding-based CO solutions.
• To summarize how graph embeddings are applied in classification and search-based CO frameworks.
• To identify gaps and propose future research directions in embedding-driven CO.

Proposed method

• The survey classifies graph embedding works based on graph preprocessing tasks, such as node feature engineering and graph structure modification.
• It organizes machine learning models into categories including deep autoencoders, graph neural networks, and traditional ML models applied to handcrafted features.
• The methodology involves analyzing how embeddings are generated and used in CO pipelines, particularly in reducing NP-hard problems to learnable representations.
• The survey integrates findings from multiple domains, including e-commerce, social networks, and bioinformatics, to illustrate real-world applicability.
• It examines embedding integration with search-based CO methods, such as reinforcement learning or heuristic search, to guide solution exploration.
• The analysis is structured around two-stage workflows: preprocessing followed by model learning, with emphasis on end-to-end optimization.

Experimental results

Research questions

• RQ1 How do different graph preprocessing techniques influence the quality of embeddings for CO problems?
• RQ2 Which machine learning models are most effective in learning embeddings that support CO task performance?
• RQ3 In what ways can graph embeddings be integrated with search algorithms to solve NP-hard CO problems?
• RQ4 How do embedding-based methods compare to traditional CO approaches in terms of scalability and accuracy?
• RQ5 What are the key challenges and open research directions in embedding-driven combinatorial optimization?

Key findings

• Graph embedding methods significantly improve the representation of complex graph structures, enabling more effective modeling of CO problems.
• The two-stage pipeline of preprocessing followed by machine learning model training is the dominant framework in current embedding-based CO research.
• Graph neural networks and autoencoders are among the most effective models for learning task-specific embeddings.
• Embeddings are successfully used both as input features for classification and as policy representations in reinforcement learning for CO.
• Integration of embeddings with heuristic or metaheuristic search methods enhances solution quality and convergence speed in NP-hard problems.
• Despite progress, challenges remain in interpretability, generalization across domains, and scalability to large-scale graphs.