VN-Solver: Vision-based Neural Solver for Combinatorial Optimization over Graphs

TL;DR

This paper introduces VN-Solver, a novel vision-based neural approach that interprets graph patterns directly from visual representations to solve combinatorial optimization problems, achieving performance comparable to traditional matrix-based methods.

Contribution

The paper presents a new vision-based neural framework for graph optimization, diverging from conventional adjacency matrix inputs, and demonstrates its competitive effectiveness.

Findings

Vision-based approach achieves comparable results to matrix-based methods.

Graph pattern recognition via vision is a viable alternative for optimization.

Open new avenues for data-driven graph optimization techniques.

Abstract

Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input instances may follow distributions with salient patterns that can be leveraged to overcome the worst-case computational hardness. For optimization problems over graphs, the common practice of neural combinatorial solvers consumes the inputs in the form of adjacency matrices. In this paper, we explore a vision-based method that is conceptually novel: can neural models solve graph optimization problems by \textit{taking a look at the graph pattern}? Our results suggest that the performance of such vision-based methods is not only non-trivial but also comparable to the state-of-the-art matrix-based methods, which opens a new avenue for developing data-driven optimization solvers.