Learning to Solve Compositional Geometry Routing Problems

TL;DR

This paper introduces DiCon, a novel differential attention and contrastive learning framework, to effectively solve the complex, diverse Compositional Geometry Routing Problem with improved generalization.

Contribution

The paper presents DiCon, a plug-and-play framework combining differential attention and contrastive learning to address representation and decision-making challenges in CGRP.

Findings

DiCon achieves strong performance across diverse CGRP instances.

DiCon demonstrates broad versatility and superior generalization.

The framework effectively suppresses less relevant actions and promotes robust representations.

Abstract

We study the Compositional Geometry Routing Problem (CGRP), a unified superclass of traditional routing problems that covers point-only, line-only, area-only, and arbitrary hybrid task geometries, providing a broad abstraction for real-world routing scenarios. Beyond standard point-based routing, CGRP with non-point tasks can be inherently asymmetric, tightly coupled travel routes with the intrinsic path, and enlarges the action space with numerous feasible yet often irrelevant options, thereby posing significant challenges for both representation learning and decision-making. To address these challenges, we propose DiCon, a differential attention-assisted solver with contrastive learning, as a plug-and-play framework that tackles the problem from two complementary angles. First, we introduce a differential attention mechanism that actively suppresses the probability mass on less competitive candidate actions. Second, we design a double-level contrastive learning objective to promote robust global instance representations and regularize geometry-aware task representations. Extensive experiments demonstrate that DiCon achieves strong performance, broad versatility, and superior generalization across diverse CGRP instances with different compositions.