Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solver

TL;DR

ICAM introduces an instance conditioned adaptation framework to improve large-scale generalization for RL based neural routing solvers. It leverages a simple adaptation function f(N,d_{ij}) and a lightweight Adaptation Attention Free Module to integrate instance information throughout the solution construction process. The three stage varying scale training and Top-k Elite training further enhance cross scale generalization, delivering state of the art or competitive performance on TSP, CVRP, and ATSP with fast inference times. The approach demonstrates robust cross distribution and benchmark performance, suggesting practical impact for real world large scale routing tasks.

Abstract

The neural combinatorial optimization (NCO) method has shown great potential for solving routing problems of intelligent transportation systems without requiring expert knowledge. However, existing constructive NCO methods still struggle to solve large-scale instances, which significantly limits their application prospects. To address these crucial shortcomings, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) for better large-scale generalization of neural routing solvers. In particular, we design a simple yet efficient instance-conditioned adaptation function to significantly improve the generalization performance of existing NCO models with a small time and memory overhead. In addition, with a systematic investigation on the performance of information incorporation between different attention mechanisms, we further propose a powerful yet low-complexity instance-conditioned adaptation module to generate better solutions for instances across different scales. Extensive experimental results on both synthetic and benchmark instances show that our proposed method is capable of obtaining promising results with a very fast inference time in solving large-scale Traveling Salesman Problems (TSPs), Capacitated Vehicle Routing Problems (CVRPs), and Asymmetric Traveling Salesman Problems (ATSPs). Our code is available at https://github.com/CIAM-Group/ICAM.

Figures (5)

• Figure 1: Comparison of two TSP instances and their optimal solutions with different scales (Left: Instance, Right: Solution). The patterns and geometric structures are quite different for these instances. In this work, we propose a powerful Instance-Conditioned Adaptation Model (ICAM) to leverage these instance-specific patterns to directly generate promising solutions for instances across quite different scales.
• Figure 2: The proposed ICAM. Taking the TSP as an example, comprehensive instance-conditioned information is incorporated into the whole solution construction process. ICAM solves the specific instance by adaptively updating the corresponding adaptation bias matrix. Specifically, we utilize AAFM to replace all MHA operations and combine $f(N,d_{ij})$ with the compatibility calculation.
• Figure 3: The Structure of AAFM.
• Figure 4: The Detailed Calculation Process of AAFM.
• Figure 5: Comparison of cosine similarity between node embeddings generated by the encoders of different models and actual pair-wise distance with different scales. It is noteworthy that darker shades indicate lower similarity. If the node embeddings can successfully capture the instance-specific features, their similarity matrix should share some similar patterns with the normalized inverse distance matrix.