Learning to Solve Compositional Geometry Routing Problems

2026-05-18

AI Summary

This work addresses the Combinatorial Geometric Path Planning (CGRP) problem, which involves mixed geometric tasks comprising points, lines, and surfaces and is characterized by asymmetry, strong path coupling, and an enormous action space. To tackle these challenges, the authors propose DiCon, a novel framework that uniquely integrates differential attention mechanisms with dual-level contrastive learning. The differential attention suppresses probabilities of suboptimal actions, while the contrastive learning jointly enhances both global instance-level and geometry-aware representations. DiCon enables unified modeling and efficient solving of complex geometric routing tasks, offering plug-and-play flexibility. Empirical evaluations demonstrate its superior performance, broad applicability, and strong generalization across diverse CGRP instances.

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.

Problem

• Compositional Geometry Routing Problem
• asymmetric routing
• action space explosion
• geometry-aware representation
• hybrid task geometries

Innovation

• differential attention
• contrastive learning
• compositional geometry routing
• representation learning
• asymmetric routing