We focus on solving integer linear programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic or complete approaches and their software implementations.

Traveling Salesman Problem (TSP) is a classic NP-hard problem that has garnered significant attention from both academia and industry. While neural-based methods have shown promise for solving TSPs, they still face challenges in scaling to larger instances, particularly in memory constraints associated with global heatmaps, edge weights, or access matrices, as well as in generating high-quality initial solutions and insufficient global guidance for efficiently navigating vast search spaces. To address these challenges, we propose a Hyper Tour Guided Neighborhood Search (HyperNS) method for large-scale TSP instances. Inspired by the ``clustering first, route second" strategy, our approach initially divides the TSP instance into clusters using a sparse heatmap graph and abstracts them as supernodes, followed by the generation of a hyper tour to guide both the initialization and optimization processes. This method reduces the search space by focusing on edges relevant to the hyper tour, leading to more efficient and effective optimization. Experimental results on both synthetic and real-world datasets demonstrate that our approach outperforms existing neural-based methods, particularly in handling larger-scale instances, offering a significant reduction in the gap to the optimal solution.

We study last-mile delivery with one truck and one drone under explicit battery management: the drone flies at twice the truck speed; each sortie must satisfy an endurance budget; after every delivery the drone recharges on the truck before the next launch. We introduce a hybrid reinforcement learning (RL) solver that couples an ALNS-based truck tour (with 2/3-opt and Or-opt) with a small pointer/attention policy that schedules drone sorties. The policy decodes launch-serve-rendezvous triplets with hard feasibility masks for endurance and post-delivery recharge; a fast, exact timeline simulator enforces launch/recovery handling and computes the true makespan used by masked greedy/beam decoding. On Euclidean instances with $N{=}50$, $E{=}0.7$, and $R{=}0.1$, the method achieves an average makespan of \textbf{5.203}$\pm$0.093, versus \textbf{5.349}$\pm$0.038 for ALNS and \textbf{5.208}$\pm$0.124 for NN -- i.e., \textbf{2.73\%} better than ALNS on average and within \textbf{0.10\%} of NN. Per-seed, the RL scheduler never underperforms ALNS on the same instance and ties or beats NN on two of three seeds. A decomposition of the makespan shows the expected truck-wait trade-off across heuristics; the learned scheduler balances both to minimize the total completion time. We provide a config-first implementation with plotting and significance-test utilities to support replication.

Large Neighborhood Search (LNS) is a common heuristic in combinatorial optimization that iteratively searches over a large neighborhood of the current solution for a better one. Recently, neural network-based LNS solvers have achieved great success in solving Integer Linear Programs (ILPs) by learning to greedily predict the locally optimal solution for the next neighborhood proposal. However, this greedy approach raises two key concerns: (1) to what extent this greedy proposal suffers from local optima, and (2) how can we effectively improve its sample efficiency in the long run . To address these questions, this paper first formulates LNS as a stochastic process, and then introduces SPL-LNS, a sampling-enhanced neural LNS solver that leverages locally-informed proposals to escape local optima. We also develop a novel hindsight relabeling method to efficiently train SPL-LNS on self-generated data. Experimental results demonstrate that SPL-LNS substantially surpasses prior neural LNS solvers for various ILP problems of different sizes.

This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer linear programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic or complete approaches and their software implementations. We show that one can learn a good neighborhood selector using imitation and reinforcement learning techniques. Through an extensive empirical validation in bounded-time optimization, we demonstrate that our LNS framework can significantly outperform compared to state-of-the-art commercial solvers such as Gurobi.

We thank the reviewers for their valuable comments. We want to first globally address the concern on novelty in the paper. Next, we address individual comments from each reviewer. This is an important question to answer for practical relevance. Please see the general comment above.

In this research, we propose an iterative learning hybrid optimization solver developed to strengthen the performance of metaheuristic algorithms in solving the Capacitated Vehicle Routing Problem (CVRP). The iterative hybrid mechanism integrates the proposed Node-Destroyer Model, a machine learning hybrid model that utilized Graph Neural Networks (GNNs) such identifies and selects customer nodes to guide the Large Neighborhood Search (LNS) operator within the metaheuristic optimization frameworks. This model leverages the structural properties of the problem and solution that can be represented as a graph, to guide strategic selections concerning node removal. The proposed approach reduces operational complexity and scales down the search space involved in the optimization process. The hybrid approach is applied specifically to the CVRP and does not require retraining across problem instances of different sizes. The proposed hybrid mechanism is able to improve the performance of baseline metaheuristic algorithms. Our approach not only enhances the solution quality for standard CVRP benchmarks but also proves scalability on very large-scale instances with up to 30,000 customer nodes. Experimental evaluations on benchmark datasets show that the proposed hybrid mechanism is capable of improving different baseline algorithms, achieving better quality of solutions under similar settings.