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Learning to Solve Compositional Geometry Routing Problems

NeurIPS 2026 · Point clouds › Point cloud classification · approach: Equivariant point cloud networks · 0 citations (OpenAlex)

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Proposes DiCon, a plug-and-play addition to neural routing solvers (POMO, RELD) for the Compositional Geometry Routing Problem, combining differential attention in the decoder with double-level (instance and intra-task) contrastive learning.

Problem

Neural solvers struggle with CGRP, where point, line, area, and hybrid tasks create asymmetric costs, coupled entry-exit selection, and a large set of feasible but weak candidate actions, especially under compositional generalization.

Approach

Adds a differential attention mechanism (difference of two softmax attention maps) to the decoder to suppress weak candidate actions, and a SimSiam-style double-level contrastive objective (instance-level across rotated views and intra-task across same-task entry-exit candidates) to improve representations, trained jointly with REINFORCE.

Key results

• On CGRP300, DiCon-R reaches objective 15.702 (3.54% gap to LKH3) vs. RELD 15.839 (4.45%) and POMO 16.344 (7.78%) at greedy decoding.
• With augmentation, DiCon-R-Aug attains gap 0.10% on CGRP100 (8.363) and 0.57% on CGRP200, vs. RELD-Aug 0.23% and 1.07%.
• DiCon-R-Aug reaches the optimal objective on Point20 and Line20 (3.918, 4.339), matching Gurobi's exact values.

Surprising findings

• Inter-task contrastive learning (pulling same-type tasks together) degraded performance on CGRP-100, which the authors attribute to over-clustering.
• DiCon-R-Aug is slightly better than LKH3 on Line100 (-2.10% gap) and Area20 despite LKH3 being the reference baseline.

Limitations

• Single-agent routing without operational constraints such as time windows or capacity limits.
• Area tasks use zigzag coverage paths with fixed omega candidates in training; real-world evaluation is zero-shot with a different coverage routine.
• Gains over strong backbones at small sizes are modest (often under 0.5% gap).

Experimental setup

Datasets: synthetic CGRP instances (mixed composition, sizes 20-100)

Benchmarks: CGRP20 CGRP100 CGRP200 CGRP300 Point20 Point100 Line20 Line100 Area20 Area100 Area20+Line30 Area20+Line80

Metrics: objective (tour length) gap (%) to LKH3 runtime

Baselines: LKH3 Google OR-Tools ALNS Gurobi POMO RELD

Builds on: POMO RELD SimSiam Differential Transformer

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