Abstract
The Vehicle Routing Problem (VRP) is a widely studied combinatorial optimization problem and has been applied to various practical problems. While the explainability for VRP is significant for improving the reliability and interactivity of practical VRP applications, it remains unexplored. In this paper, we propose RouteExplainer, a post-hoc explanation framework that explains the influence of each edge in a generated route. Our framework realizes this by rethinking a route as the sequence of actions and extending counterfactual explanations based on the action influence model to VRP. To enhance the explanation, we additionally propose an edge classifier that infers the intentions of each edge, a loss function to train the edge classifier, and explanation-text generation by Large Language Models (LLMs). We quantitatively evaluate our edge classifier on four different VRPs. The results demonstrate its rapid computation while maintaining reasonable accuracy, thereby highlighting its potential for deployment in practical applications. Moreover, on the subject of a tourist route, we qualitatively evaluate explanations generated by our framework. This evaluation not only validates our framework but also shows the synergy between explanation frameworks and LLMs. See https://ntt-dkiku.github.io/xai-vrp for code, appendices, and demo.
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Notes
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We call “vertices” for nodes in a DAG and “nodes” for nodes in a VRP instance.
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Our code is publicly available at https://github.com/ntt-dkiku/route-explainer.
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- 5.
EC\(^{\text {--dec}}_{\text {cbce}}\) employs CBCE instead of SCBCE since MLP does not consider sequence.
References
Bach, S., Binder, A., Montavon, G., Klauschen, F., Müller, K.R., Samek, W.: On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PLoS ONE 10(7), 1–46 (2015)
Balas, E.: The prize collecting traveling salesman problem and its applications. In: Gutin, G., Punnen, A.P. (eds.) The Traveling Salesman Problem and Its Variations. Combinatorial Optimization, vol. 12, pp. 663–695. Springer, Boston (2007). https://doi.org/10.1007/0-306-48213-4_14
Bello, I., Pham, H., Le, Q.V., Norouzi, M., Bengio, S.: Neural combinatorial optimization with reinforcement learning (2017)
Cui, Y., Jia, M., Lin, T.Y., Song, Y., Belongie, S.: Class-balanced loss based on effective number of samples. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9260–9269 (2019)
Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. 6(1), 80–91 (1959)
Dumas, Y., Desrosiers, J., Gelinas, E., Solomon, M.M.: An optimal algorithm for the traveling salesman problem with time windows. Oper. Res. 43(2), 367–371 (1995)
Fong, R.C., Vedaldi, A.: Interpretable explanations of black boxes by meaningful perturbation. In: 2017 IEEE International Conference on Computer Vision, pp. 3449–3457 (2017)
Halpern, J.Y., Pearl, J.: Causes and explanations: a structural-model approach. Part I: causes. Br. J. Philos. Sci. 56(4), 843–887 (2005)
Helsgaun, K.: An extension of the Lin-Kernighan-Helsgaun TSP solver for constrained traveling salesman and vehicle routing problems: Technical report (2017)
Hinterreiter, A., et al.: ConfusionFlow: a model-agnostic visualization for temporal analysis of classifier confusion. IEEE Trans. Vis. Comput. Graph. 28(2), 1222–1236 (2022)
Hopfield, J., Tank, D.: Neural computation of decisions in optimization problems. Biol. Cybern. 52, 141–152 (1985)
Joshi, C.K., Laurent, T., Bresson, X.: An efficient graph convolutional network technique for the travelling salesman problem (2019)
Kool, W., van Hoof, H., Gromicho, J., Welling, M.: Deep policy dynamic programming for vehicle routing problems (2021)
Kool, W., van Hoof, H., Welling, M.: Attention, learn to solve routing problems! In: International Conference on Learning Representations (2019)
Li, S., Yan, Z., Wu, C.: Learning to delegate for large-scale vehicle routing. In: Thirty-Fifth Conference on Neural Information Processing Systems (2021)
Lopez, L., Carter, M.W., Gendreau, M.: The hot strip mill production scheduling problem: a Tabu search approach. Eur. J. Oper. Res. 106(2–3), 317–335 (1998)
Lundberg, S.M., Lee, S.I.: A unified approach to interpreting model predictions. In: Advances in Neural Information Processing Systems, vol. 30 (2017)
Madumal, P., Miller, T., Sonenberg, L., Vetere, F.: Explainable reinforcement learning through a causal lens. In: AAAI Conference on Artificial Intelligence (2019)
OpenAI: GPT-4 technical report (2023)
Pessoa, A.A., Sadykov, R., Uchoa, E., Vanderbeck, F.: A generic exact solver for vehicle routing and related problems. Math. Program. 183, 483–523 (2020)
Saeed, W., Omlin, C.: Explainable AI (XAI): a systematic meta-survey of current challenges and future opportunities. Knowl. Based Syst. 263, 110273 (2023). https://www.sciencedirect.com/science/article/pii/S0950705123000230
Vaswani, A., et al.: Attention is all you need. In: Advances in Neural Information Processing Systems, vol. 30 (2017)
Vinyals, O., Fortunato, M., Jaitly, N.: Pointer networks. In: Advances in Neural Information Processing Systems, vol. 28 (2015)
Xin, L., Song, W., Cao, Z., Zhang, J.: NeuroLKH: combining deep learning model with Lin-Kernighan-Helsgaun heuristic for solving the traveling salesman problem. In: Advances in Neural Information Processing Systems, vol. 34 (2021)
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Kikuta, D., Ikeuchi, H., Tajiri, K., Nakano, Y. (2024). RouteExplainer: An Explanation Framework for Vehicle Routing Problem. In: Yang, DN., Xie, X., Tseng, V.S., Pei, J., Huang, JW., Lin, J.CW. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2024. Lecture Notes in Computer Science(), vol 14647. Springer, Singapore. https://doi.org/10.1007/978-981-97-2259-4_3
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