Two Black Boxes, One Solver: Encoder Probing and Decoder Attribution for Neural Multi-Attribute VRP under Hard-Mask and Recourse Decoders

2026-07-05

AI Summary

This study addresses the lack of interpretability in existing neural autoregressive solvers for the Multi-Attribute Vehicle Routing Problem (MAVRP), which hinders their utility in supporting dispatch decisions. For the first time, it jointly analyzes the black-box mechanisms of both encoder and decoder components: the encoder’s representation of constraints is examined through linear probing, rank-based richness, and measures of spontaneous organization, while the decoder’s decision logic is interpreted via gradient-based attribution, counterfactual interventions, and contrastive abductive reasoning. The findings reveal that graph inductive bias enhances representational predictability, a Mixture-of-Experts (MoE) architecture enables distributed constraint encoding, and Recourse training substantially improves decoding rationality. Notably, this approach generates feasibility-restoring counterfactual explanations unattainable with Hard-Mask methods, thereby enhancing solution verifiability and operational applicability.

Abstract

Neural autoregressive solvers for the Multi-Attribute Vehicle Routing Problem (MAVRP) reach competitive cost but offer no per-step justification, a problem when dispatchers must validate, accept, or compare them. We open two complementary black boxes in one protocol. On the encoder side, linear probes, spontaneous-organization metrics, rank-based richness measures, and discovered-direction analyses with intervention validation characterize how the latent represents constraint families at the graph, node, and edge level. On the decoder side, three attribution methods (gradient, integrated gradients, DeepLIFT) feed three reading angles: abductive, contrastive against the best feasible alternative, and counterfactual (smallest input change that switches the action or restores feasibility). Explanations are scored on fidelity, concentration, stability, sanity, and actionability. Across six variants combining three encoders (Attention baseline, Unimp, UnimpMoe) with two decoders (Hard-Mask, Recourse), we find that graph inductive bias improves both representational predictability and decoder sanity, that the Mixture-of-Experts encoder represents constraints in a distributed rather than axis-aligned way, and that the Recourse training regime, not merely its softer mask, produces policies that represent infeasibility usefully, exposing make-feasible counterfactuals that Hard-Mask policies fail to produce even when fed infeasible alternatives externally.

Problem

• Multi-Attribute Vehicle Routing Problem
• neural solvers
• interpretability
• explainability
• decision justification

Innovation

• Explainable AI
• Vehicle Routing Problem
• Encoder Probing
• Decoder Attribution
• Counterfactual Explanation