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Yaoxin Wu

Yaoxin Wu contributes to research discovery and scholarly infrastructure.

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Artificial Intelligence Machine Learning

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preprint2026arXiv

A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention

Mixed-integer linear programming (MILP), a widely used modeling framework for combinatorial optimization, are central to many scientific and engineering applications, yet remains computationally challenging at scale. Recent advances in deep learning address this challenge by representing MILP instances as variable-constraint bipartite graphs and applying graph neural networks (GNNs) to extract latent structural patterns and enhance solver efficiency. However, this architecture is inherently limited by the local-oriented mechanism, leading to restricted representation power and hindering neural approaches for MILP. Here we present an attention-driven neural architecture that learns expressive representations beyond the pure graph view. A dual-attention mechanism is designed to perform parallel self- and cross-attention over variables and constraints, enabling global information exchange and deeper representation learning. We apply this general backbone to various downstream tasks at the instance level, element level, and solving state level. Extensive experiments across widely used benchmarks show consistent improvements of our approach over state-of-the-art baselines, highlighting attention-based neural architectures as a powerful foundation for learning-enhanced mixed-integer linear optimization.

preprint2026arXiv

Adversarial Instance Generation and Robust Training for Neural Combinatorial Optimization with Multiple Objectives

Deep reinforcement learning (DRL) has shown great promise in addressing multi-objective combinatorial optimization problems (MOCOPs). Nevertheless, the robustness of these learning-based solvers has remained insufficiently explored, especially across diverse and complex problem distributions. In this paper, we propose a unified robustness-oriented framework for preference-conditioned DRL solvers for MOCOPs. Within this framework, we develop a preference-based adversarial attack to generate hard instances that expose solver weaknesses, and quantify the attack impact by the resulting degradation on Pareto-front quality. We further introduce a defense strategy that integrates hardness-aware preference selection into adversarial training to reduce overfitting to restricted preference regions and improve out-of-distribution performance. The experimental results on multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) verify that our attack method successfully learns hard instances for different solvers. Furthermore, our defense method significantly strengthens the robustness and generalizability of neural solvers, delivering superior performance on hard or out-of-distribution instances.

preprint2026arXiv

Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty

Two-Stage Robust Optimization (2RO) with discrete uncertainty is challenging, often rendering exact solutions prohibitive. Scenario reduction alleviates this issue by selecting a small, representative subset of scenarios to enable tractable computation. However, existing methods are largely problem-agnostic, operating solely on the uncertainty set without consulting the feasible region or recourse structure. In this paper, we introduce PRISE, a problem-driven sequential lookahead heuristic that constructs reduced scenario sets by evaluating the marginal impact of each scenario. While PRISE yields high-quality scenario subsets, each selection step requires solving multiple subproblems, making it computationally expensive at scale. To address this, we propose NeurPRISE, a neural surrogate model built on a GNN-Transformer backbone that encodes the per-scenario structure via graph convolution and captures cross-scenario interactions through attention. NeurPRISE is trained via imitation learning with a gain-aware ranking objective, which distills marginal gain information from PRISE into a learned scoring function for scenario ranking and selection. Extensive results on three 2RO problems show that NeurPRISE consistently achieves competitive regret relative to comprehensive methods, maintains strong calability with varying numbers of scenarios, and delivers 7-200x speedup over PRISE. NeurPRISE also exhibits strong zero-shot generalization, effectively handling instances with larger problem scales (up to 5x), more scenarios (up to 4x), and distribution shifts.

preprint2026arXiv

Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Prediction

Neural policies have shown promise in solving vehicle routing problems due to their reduced reliance on handcrafted heuristics. However, current training paradigms suffer from a fundamental limitation: they primarily focus on next-node prediction for solution construction, resulting in myopic decision-making that undermines long-horizon planning capacity. To this end, we introduce Multi-node Lookahead Prediction (MnLP), a novel training strategy that extends the supervised learning paradigm to predict multiple future nodes simultaneously. We incorporate causal and discardable MnLP modules that operate exclusively during training, facilitating models to anticipate multi-step decisions while preserving inference-time efficiency. By incorporating multi-depth auxiliary supervision into the loss function, MnLP equips neural policies with the ability of long-range contextual understanding. Experimentally, MnLP outperforms existing training methods, improving the generalization capability of neural policies across various problem sizes, distributions, and real-world benchmarks. Moreover, MnLP can be seamlessly integrated into diverse neural architectures without introducing additional inference overhead.

preprint2022arXiv

Learning to Solve Routing Problems via Distributionally Robust Optimization

Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust optimization (group DRO) to tackle this issue, where we jointly optimize the weights for different groups of distributions and the parameters for the deep model in an interleaved manner during training. We also design a module based on convolutional neural network, which allows the deep model to learn more informative latent pattern among the nodes. We evaluate the proposed approach on two types of well-known deep models including GCN and POMO. The experimental results on the randomly synthesized instances and the ones from two benchmark dataset (i.e., TSPLib and CVRPLib) demonstrate that our approach could significantly improve the cross-distribution generalization performance over the original models.

preprint2020arXiv

Learning Improvement Heuristics for Solving Routing Problems

Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a solution. However, classic improvement heuristics are all guided by hand-crafted rules which may limit their performance. In this paper, we propose a deep reinforcement learning framework to learn the improvement heuristics for routing problems. We design a self-attention based deep architecture as the policy network to guide the selection of next solution. We apply our method to two important routing problems, i.e. travelling salesman problem (TSP) and capacitated vehicle routing problem (CVRP). Experiments show that our method outperforms state-of-the-art deep learning based approaches. The learned policies are more effective than the traditional hand-crafted ones, and can be further enhanced by simple diversifying strategies. Moreover, the policies generalize well to different problem sizes, initial solutions and even real-world dataset.

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