Title: DistrictNet: Decision-aware learning for geographical districting
Venue: NeurIPS 2024
Accepted: yes
Keywords: routing

combinatorial optimization

decision-focused learning
Abstract: Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts. In logistics, it is a major strategic decision determining operating costs for several years. Solving districting problems using traditional methods is intractable even for small geographical areas and existing heuristics often provide sub-optimal results. We present a structured learning approach to find high-quality solutions to real-world districting problems in a few minutes. It is based on integrating a combinatorial optimization layer, the capacitated minimum spanning tree problem, into a graph neural network architecture. To train this pipeline in a decision-aware fashion, we show how to construct target solutions embedded in a suitable space and learn from target solutions. Experiments show that our approach outperforms existing methods as it can significantly reduce costs on real-world cities.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper propose an ML-based method to solve districting problems that are known to be challenging. The core idea is to first convert the districting problem to a simpler capacitated minimum spanning tree problem and then leverage the existing learning to optimize method to perform imitation learning. Such conversion is valuable because the learning to optimize approach requires repeatedly solving the optimization problem of interest. Extensive numerical studies were presented, leading to a rich set of insights. I found the paper inspiring.\n\nSTRENGTHS:\n1. Districting problems are common in practice, so I believe this paper is interesting to a broad community.\n\n2. The mapping from a districting problem to a minimum spanning tree problem is elegant and well justified. \n\n3. The numerical studies were well designed and excuted. I particularly appreciate the analysis related to the model's generalizablity, which we do not see in every learning to optimize paper. \n\n4. The paper was well structed and presented. I found it easy to follow.\n\nWEAKNESSES:\n- The paper focus on a specific problem class (that is of common interest). The paper can benefit from drawing connections to other problem classes. The idea of converting a harder problem to an easier problem to enable the application of learning to optimize techniques is general and has potential. And I believe there should exist many other examples, in transportation and beyond. Conducting additional experiments on other problems is probably out of the scope of this paper, but it'd be great if the author can add more discussions related to its broader applicability. \n\n- Discussion/comparison related to some benchmarks from the OR/optimization community are missing. For example, when the demands are uniformly distributed, I believe the second-stage TSP objective value has some very nice closed-form approximations (see literature related to continuous approximation). Such approximation usually leads to tractable districting problem with good performance. I'd be good to see some comparisons related to that.\n\n- I'm not fully convinced about the generalizability from small instances to larger instances as the size range experimented in this paper is relatively narrow.\n\nQUESTIONS:\n- It is unclear to me what the costs (objective) are in the numerical experiments. \n\n- Related to weakness 1, what is the downside of performing such conversion?\n\nLIMITATIONS:\nDiscussed.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-06-27"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles the problem of geographical districting through decision-aware learning. The problem is challenging due to the large combinatorial number of possible district designs. By generalizing the GNN-based method (similar to [Ferraz et al.2024 arXiv]) based on decision-aware learning through the Fenchel-Young loss, the proposed method showed much better relative performance to the existing methods.\n\nSTRENGTHS:\n- The connection between CMST and the districting problem is utilized for decision-aware learning.\n- Compared with the recent existing work [Ferraz et al. 2024], a more powerful learning methodology through GNN and FY loss was studied and evaluated, demonstrated using real data (i.e., real districts in famous cities).\n- The experimental results show better results than those of existing solvers.\n\nWEAKNESSES:\n- Some unclear explanations of using GNN, compared with the existing work [Ferraz et al. 2024]; some parts just follow [Ferraz et al. 2024]. These points raise the insufficient explanation of the technical contributions.\n- Datasets are not explained semantically (i.e., geographical differences, why these cities are selected, etc.) in the main text: It is important to explain the importance of the task and used datasets (I understand the page limit and appendix).\n\nQUESTIONS:\n- I am not sure why we should evaluate the p-value in this setting. Where does the randomness come from?\n- I understood that the average demands are required. Once BU and average demands are fixed, the solution seems to be (almost) unique. Can we combine some learning-based demand predictors? If the estimation is not correct, how can the districting results be affected? Some questions could be about district costs.\n\n~~~\n\nAfter discussions, I have updated my score.\n\nLIMITATIONS:\nIn my opinion, the authors have addressed the issue adequately and mentioned these points.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper discusses the development and evaluation of a new method called \nDISTRICTNET for addressing districting and routing problems using neural networks.\nThe approach focuses on minimizing the Fenchel Young loss and generalizing to large \nout-of-distribution instances from training on smaller instances. The method involves \na representation of the instances as a set of graph weights learned by GNN. These weights \nare fed to a CMST algorithm to obtain the spatial partitioning. Comparative \nbenchmarks include linear regression models and graph neural networks trained \nfor cost estimation. Results show that DISTRICTNET can achieve lower costs with \na small number of training examples but benefits from more examples, \nwith diminishing returns.\n\nSTRENGTHS:\nSome key strengths of the research presented in this paper include a structured learning approach to obtain high-quality solutions to large districting problems, the robustness of the approach to changes in problem parameters, and the ability to generalize to out-of-distribution instances.\n\nWEAKNESSES:\nI am not familiar with the routing literature and I had a very hard time to read this paper. The supplementary\nmaterial is essential and the authors should consider if the mathematical treatment \nof several issues that were not relevant for the algorithm proposed should not be moved to \nthe appendix in exchange of bringing some of the appendix to the main paper. For example,\nI was lost about the district demand and cost features along the paper. This is \nexplained in the appendix. \n\nThe datasets are small, with the number of areas varying between 120 and 983.\nThey use an additional set of 27 cities, 25 of them with less than 100 areas and a \nmaxium of 684.  \n\nThe benchmarks did not include what the authors call the quick heuristic methods.\nI also found other recent papers in important venues dealing with this districting \nproblem by partitioning a minimum spanning tree as in the paper and with simpler \nmethods. \nTeixeira, L. V., Assunção, R. M., & Loschi, R. H. (2019). Bayesian space-time partitioning by sampling and pruning spanning trees. Journal of Machine Learning Research, 20(85), 1-35.\nLuo, Z. T., Sang, H., & Mallick, B. (2021). A Bayesian contiguous partitioning method for learning clustered latent variables. Journal of Machine Learning Research, 22(37), 1-52.\nLuo, Z. T., Sang, H., & Mallick, B. (2021). BAST: Bayesian additive regression spanning trees for complex constrained domain. Advances in Neural Information Processing Systems, 34, 90-102.\nMcCartan, C., & Imai, K. (2023). Sequential Monte Carlo for sampling balanced and compact redistricting plans. The Annals of Applied Statistics, 17(4), 3300-3323.\n\nQUESTIONS:\nAdd \"routing\" to the paper title.\n\nEach benchmark method has a different definition of a district cost. The outputs of each of \nthese algorithms are a result of these different cost definitions or are due to their \ndifferent approaches?\n\nLIMITATIONS:\nThis is a theoretical paper with no immediate connection to societal impact.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 1, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors use CMST to solve the problem of districting and routing in large scale scenarios. Finding the relationship between CMST and partitioning is quite beneficial for researchers engaged in related research. \n\nHowever, it is worth noting that the authors only report the performance of the model on the 'cost' metric, and do not investigate the performance of the method on the common metrics of traditional districting task. What's more, they do not discuss the efficiency of the method. I hope that the authors can supplement this. \n\nAnother problem is that the baseline methods compared seem to be relatively old except for PREDGNN. The districting methods I know in terms of road network, such as CCH, have not been used as the baseline method. I hope the author can clarify the criteria for baseline selection.\n\nSTRENGTHS:\nThe authors use CMST to solve the problem of districting and routing in large scale scenarios. Finding the relationship between CMST and partitioning is quite beneficial for researchers engaged in related research.\n\nWEAKNESSES:\nIt is worth noting that the authors only report the performance of the model on the 'cost' metric, and do not investigate the performance of the method on the common metrics of traditional districting task. What's more, they do not discuss the efficiency of the method. I hope that the authors can supplement this. \n\nAnother problem is that the baseline methods compared seem to be relatively old except for PREDGNN. The districting methods I know in terms of road network, such as CCH, have not been used as the baseline method. I hope the author can clarify the criteria for baseline selection.\n\nQUESTIONS:\nPlease see the weaknesses.\n\nLIMITATIONS:\nYes. The authors claim that though the proposed method can be applied to a wide variety of partitioning problems, they only focus on the districting and routing problem in this paper. In fact, I think it's a very valuable question to discuss because the evaluation metric of the partitioning problem and that of the districting and routing problem are different. I think it is necessary for the authors to give more explanation of why their method can be applied to a wider range of partitioning problems.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-13"}