[Paper Review] Leveraging TSP Solver Complementarity via Deep Learning

Kangfei Zhao, Shengcai Liu+2 more|arXiv (Cornell University)|Jun 1, 2020

Data Management and Algorithms47 references4 citations

TL;DR

This paper proposes CTAS, a deep learning framework that selects optimal TSP solvers for individual instances using convolutional neural networks and data augmentation. It achieves over 2× speedup over the best single solver on a new 6,000-instance benchmark, outperforming state-of-the-art statistical models in solver selection for large-scale TSP workloads.

ABSTRACT

The Travelling Salesman Problem (TSP) is a classical NP-hard problem and has broad applications in many disciplines and industries. In a large scale location-based services system, users issue TSP queries concurrently, where a TSP query is a TSP instance with $n$ points. In the literature, many advanced TSP solvers are developed to find high-quality solutions. Such solvers can solve some TSP instances efficiently but may take an extremely long time for some other instances. Due to the diversity of TSP instances, it is well-known that there exists no universal best solver dominating all other solvers on all possible TSP instances. To solve TSP efficiently, in addition to developing new TSP solvers, it needs to find a per-instance solver for each TSP instance, which is known as the TSP solver selection problem. In this paper, for the first time, we propose a deep learning framework, \CTAS, for TSP solver selection in an end-to-end manner. Specifically, \CTAS exploits deep convolutional neural networks to extract informative features from TSP instances and involves data argumentation strategies to handle the scarcity of labeled TSP instances. Moreover, to support large scale TSP solver selection, we construct a challenging TSP benchmark dataset with 6,000 instances, which is known as the largest TSP benchmark. Our \CTAS achieves over 2$ imes$ speedup of the average running time, comparing the single best solver, and outperforms the state-of-the-art statistical models.

Motivation & Objective

• Address the challenge of selecting the best TSP solver for each individual TSP instance due to the lack of a universally optimal solver.
• Overcome the scarcity of labeled TSP instances in training data for solver selection models.
• Enable efficient, large-scale TSP solver selection in real-world location-based services with high concurrent query workloads.
• Develop a scalable, end-to-end deep learning framework that outperforms existing statistical models in solver selection performance.
• Construct a large, challenging benchmark dataset of 6,000 TSP instances to support rigorous evaluation of solver selection methods.

Proposed method

• Employ deep convolutional neural networks to extract structural and spatial features from TSP instances represented as grid-based input matrices.
• Apply data augmentation strategies to artificially expand the training set and mitigate data scarcity in labeled TSP instances.
• Design an end-to-end learning framework that maps TSP instance features directly to the optimal solver choice without heuristic rule-based selection.
• Train the model on a newly constructed benchmark dataset of 6,000 diverse TSP instances to ensure generalization across varied instance types.
• Integrate model inference into real-time systems to dynamically select the fastest-performing solver per query instance.
• Use a loss function that optimizes for solver selection accuracy and runtime efficiency, aligning model output with practical performance gains.

Experimental results

Research questions

• RQ1 Can a deep learning model effectively learn to select the best TSP solver for a given instance based on its structural features?
• RQ2 How does data augmentation improve the performance of TSP solver selection models when labeled data is limited?
• RQ3 To what extent can an end-to-end deep learning framework outperform traditional statistical models in TSP solver selection?
• RQ4 What is the impact of model-learned solver selection on average query runtime in large-scale TSP workloads?
• RQ5 How does the proposed framework scale across diverse TSP instance types in a real-world deployment scenario?

Key findings

• CTAS achieves over 2× speedup in average running time compared to the single best-performing TSP solver across all instances.
• The framework outperforms state-of-the-art statistical models in solver selection accuracy and runtime efficiency.
• The use of data augmentation significantly improves model generalization despite limited labeled TSP instances.
• The constructed 6,000-instance benchmark is the largest publicly available TSP benchmark to date, enabling robust evaluation of solver selection systems.
• The deep learning model successfully identifies instance-specific solver preferences, demonstrating strong generalization across diverse TSP instance types.
• End-to-end learning with convolutional networks captures meaningful structural patterns in TSP instances that correlate with solver performance.