arXiv subjects

Wen Song

Publications and source records attributed to Wen Song.

At least 19 recordsLinked to original sources

arXiv2026

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 17-200x 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.

cs.AI↗

arXiv2026

ORSMT: Unleashing the Potential of Satisfiability Modulo Theories for Semantic Verification and Repair in LLM-Based Optimization

Large language models increasingly automate optimization modeling from natural language problems, producing written mathematics, solver code and a returned report. Verifying one optimization problem across these artifacts requires semantic comparison: unequal models can attain the same objective, equivalent models can use different auxiliary variables, and mutually consistent artifacts can omit the same source requirement. ORSMT provides a typed semantic interface and exact SMT relation queries. It aligns observable decisions, projects auxiliary variables, proves or refutes feasible region and objective relations, localizes refutations to implicated rows or domains and links source texts when available. It then reconstructs one artifact from another, and each adopted candidate passes the required relation checks. Across 3,034 problems and six generator sizes, ORSMT improves the model-code match rate in all 72 benchmark and generator combinations before selection. Protected selection raises the aggregate rate from 43.2% to 88.2% and the share that are both correct and matched from 25.2% to 40.2%. On the 1,905 refuted outputs, certified voting under the shared fallback makes 50.9% of outputs correct and matched, compared with 44.8% for ReLoop and 49.4% for Opt-Verifier. A separate one-round source revision followed by exact reconstruction restores a model-code match for 84.4% of the refuted pairs.

math.OC↗

arXiv2026

Autoresearch in Mixed-Integer Linear and Nonlinear Programming

Despite recent progress in autoresearch, applying it to practical operations research problems, typically formulated as NP-hard mixed-integer linear or nonlinear programs (MILPs or MINLPs), remains challenging because effective research requires systematically managing competing ideas and long-horizon experimental trajectories. We introduce AutoMIP, a reusable agent skill for organizing long-horizon autoresearch in mixed-integer programming through idea pooling and algorithm tree search. AutoMIP maintains a persistent pool of complementary candidate ideas while organizing executable experiments into an algorithm tree, enabling the agent to preserve unexplored hypotheses, refine promising algorithms, and switch to alternative methodological directions based on historical states. On MILP and MINLP benchmark cohorts, AutoMIP achieves the highest final success rates among the evaluated autoresearch frameworks. On MIPLib, AutoMIP discovers new best solutions for 31 of 60 instances, surpassing existing autoresearch frameworks. On MINLPLib, it achieves new best solutions for 52 of 60 instances. Ablation studies further demonstrate the complementary contributions of idea pooling and algorithm tree search, highlighting the importance of jointly maintaining diverse research ideas and structured experimental trajectories for long-horizon autoresearch.

cs.AI↗

arXiv2026

VLM Fine-Tuning for End-to-End Combinatorial Optimization

Large language models (LLMs) have provided a unified interface for end-to-end combinatorial optimization (CO), but textual serialization alone may obscure spatial and relational structures that are important for generating effective CO solutions. This paper presents a general-purpose vision-language solver that augments textual instance descriptions with input-derived visual representations. A single vision-language model (VLM) is applied across different CO tasks and trained using supervised fine-tuning followed by verifier-guided reinforcement learning. While the visual inputs contain no gold solutions or solution-derived information, our experiments show that the VLM generally improves solution quality over its text-only counterpart, with particularly clear gains on more complex CO problems such as CVRP and JSSP. The advantage of visual information is more pronounced at large problem scales.

cs.CL↗

arXiv2026

LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers

Multi-task neural solvers aim to handle multiple Vehicle Routing Problem (VRP) variants within a unified model, avoiding separate training for each constraint combination. However, VRP variants differ in optimization difficulty, while existing methods lack stage-wise feedback on their training status, making the model biased to some specific variants. Although meta-learning can support adaptive training, it typically requires bi-level optimization and additional gradient updates, increasing computational cost. To address this limitation, we propose LLM-as-Trainer (LaT), a plug-and-play training paradigm that uses a pretrained large language model as an external trainer. LaT periodically analyzes cross-task validation metrics to generate a stage-wise guidance vector. This vector is combined with the current task's constraint vector and injected into each encoder layer, providing the neural solver with additional training information during subsequent policy optimization. Experiments on 16 VRP variants show that LaT improves the solution quality of several state-of-the-art multi-task neural solvers on both trained and unseen variants, supporting the effectiveness and generality of the proposed training paradigm.

cs.AI↗

arXiv2026

Automated Reinforcement Learning: An Overview

Reinforcement Learning and, recently, Deep Reinforcement Learning are popular methods for solving sequential decision-making problems modeled as Markov Decision Processes. RL modeling of a problem and selecting algorithms and hyper-parameters require careful consideration, as different configurations may entail completely different performances. These considerations are mainly the task of RL experts; however, RL is progressively becoming popular in other fields, such as combinatorial optimization, where researchers and system designers are not necessarily RL experts. Besides, many modeling decisions are typically made manually, such as defining state and action space, size of batches, batch update frequency, and time steps. For these reasons, automating different components of RL is of great importance, and it has attracted much attention in recent years. Automated RL provides a framework in which different components of RL, including MDP modeling, algorithm selection, and hyper-parameter optimization, are modeled and defined automatically. In this article, we present the literature on automated RL (AutoRL), including the recent large language model (LLM) based techniques. We also discuss the recent work on techniques that are not presently tailored for automated RL but hold promise for future integration into AutoRL. Furthermore, we discuss the challenges, open questions, and research directions in AutoRL.

cs.LG↗

arXiv2026

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

Mixed-integer linear programming (MILP) is a foundational framework for combinatorial optimization across science and engineering, but remains hard to solve at scale due to NP-hardness. Recent learning-based methods typically model MILP instances as variable-constraint bipartite graphs and use Graph Neural Networks (GNNs) for representation learning, yet their locality limits representation power. We propose an attention-driven neural backbone that adopts an element-centric view of variables and constraints, with dual attention performing parallel intra-type self-attention and inter-type cross-attention. Across three representative tasks at the instance, element, and solving-state levels, our model consistently outperforms conventional GNN-based architectures, highlighting attention-based, element-centric modeling as a powerful foundation for learning-enhanced combinatorial optimization.

cs.AI↗

arXiv2026

Vision-Assisted Foundation Model for Solving Multi-Task Vehicle Routing Problems

Multi-task vehicle routing problems play a critical role in enhancing efficiency across various industries and service sectors. These problems consist of multiple variants that optimize routing costs while meeting diverse customer constraints. Existing multi-task VRP solvers solely utilize a graph-based modality, limiting their ability to address variants with multiple constraints. As a format to represent complex semantics, vision modality shows great potential for encoding diverse VRP constraints. This motivates us to learn patch-level semantics from the vision images, and then integrate them into a graph-based model to solve various VRP variants simultaneously. However, directly applying this approach to multi-task VRPs presents three challenges: 1) existing VRP images lack constraint representations, which are essential for multi-task VRPs, 2) the fixed receptive field of individual patches cannot effectively accommodate varying requirements across tasks, and 3) imbalanced pixel distribution among constraints may cause the model to overlook constraints with fewer pixels. In this paper, we propose a vision-assisted foundation model (VaFM) to address these challenges. In the vision modality, input images tailored to all constraints are encoded by a convolutional neural network. The obtained patch embeddings are fused with graph-based nodes to generate solutions, with an auxiliary task designed to address the pixel-imbalanced issue. The performance of VaFM is evaluated across 16 different VRP variants. The experimental results demonstrate the superiority of VaFM over state-of-the-art methods, especially for variants with complex constraints.

cs.CV↗

arXiv2026

Newton Method for Soft Quadratic Surface Support Vector Machine with 0-1 Loss Function

A nonlinear kernel-free soft quadratic surface support vector machine model with 0-1 loss function ($L_{0/1}$-SQSSVM) is proposed for binary classification problems, which is non-convex discontinuous. We are devoted to establishing the first and the second-order optimality conditions for the $L_{0/1}$-SQSSVM. We establish a stationary equation using the properties of proximal operator of 0-1 loss function. We design a Newton method based on the stationary equation to solve $L_{0/1}$-SQSSVM model and prove that the Newton method has local quadratic convergence under the second-order sufficient condition. Numerical experience on artificial datasets and benchmark datasets demonstrate that the Newton method for $L_{0/1}$-SQSSVM achieves higher classification accuracy with less CPU time cost than other state-of-the-art methods.

math.OC↗

arXiv2026

Generalizable Heuristic Generation Through LLMs with Meta-Optimization

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC) heuristic-optimizers and single-task training schemes, which may constrain the exploration of diverse heuristic algorithms and hinder the generalization of the resulting heuristics. To address these issues, we propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the optimizer level, discovering effective heuristic-optimizers through the principle of meta-learning. Specifically, MoH leverages LLMs to iteratively refine a meta-optimizer that autonomously constructs diverse heuristic-optimizers through (self-)invocation, thereby eliminating the reliance on a predefined EC heuristic-optimizer. These constructed heuristic-optimizers subsequently evolve heuristics for downstream tasks, enabling broader heuristic exploration. Moreover, MoH employs a multi-task training scheme to promote its generalization capability. Experiments on classic COPs demonstrate that MoH constructs an effective and interpretable meta-optimizer, achieving state-of-the-art performance across various downstream tasks, particularly in cross-size settings. Our code is available at: https://github.com/yiding-s/MoH.

cs.LG↗

arXiv2026

RESCHED: Rethinking Flexible Job Shop Scheduling from a Transformer-based Architecture with Simplified States

Neural approaches to the Flexible Job Shop Scheduling Problem (FJSP), particularly those based on deep reinforcement learning (DRL), have gained growing attention in recent years. However, existing methods rely on complex feature-engineered state representations (i.e., often requiring more than 20 handcrafted features) and graph-biased neural architectures. To reduce modeling complexity and advance a more generalizable framework for FJSP, we introduce \textsc{ReSched}, a minimalist DRL framework that rethinks both the scheduling formulation and model design. First, by revisiting the Markov Decision Process (MDP) formulation of FJSP, we condense the state space to just four essential features, eliminating historical dependencies through a subproblem-based perspective. Second, we employ Transformer blocks with dot-product attention, augmented by three lightweight but effective architectural modifications tailored to scheduling tasks. Extensive experiments show that \textsc{ReSched} outperforms classical dispatching rules and state-of-the-art DRL methods on FJSP. Moreover, \textsc{ReSched} also generalizes well to the Job Shop Scheduling Problem (JSSP) and the Flexible Flow Shop Scheduling Problem (FFSP), achieving competitive performance against neural baselines specifically designed for these variants.

cs.LG↗

arXiv2026

Towards Efficient Constraint Handling in Neural Solvers for Routing Problems

Neural solvers have achieved impressive progress in addressing simple routing problems, particularly excelling in computational efficiency. However, their advantages under complex constraints remain nascent, for which current constraint-handling schemes via feasibility masking or implicit feasibility awareness can be inefficient or inapplicable for hard constraints. In this paper, we present Construct-and-Refine (CaR), the first general and efficient constraint-handling framework for neural routing solvers based on explicit learning-based feasibility refinement. Unlike prior construction-search hybrids that target reducing optimality gaps through heavy improvements yet still struggle with hard constraints, CaR achieves efficient constraint handling by designing a joint training framework that guides the construction module to generate diverse and high-quality solutions well-suited for a lightweight improvement process, e.g., 10 steps versus 5k steps in prior work. Moreover, CaR presents the first use of construction-improvement-shared representation, enabling potential knowledge sharing across paradigms by unifying the encoder, especially in more complex constrained scenarios. We evaluate CaR on typical hard routing constraints to showcase its broader applicability. Results demonstrate that CaR achieves superior feasibility, solution quality, and efficiency compared to both classical and neural state-of-the-art solvers.

cs.AI↗

arXiv2025

Tilt stability of Ky-Fan $κ$-norm composite optimization

This paper concerns the tilt stability for the minimization of the sum of a twice continuously differentiable matrix-valued function and the Ky-Fan $κ$-norm. To achieve this goal, we first provide a sufficient and necessary condition for a local minimizer of the composite $f=φ+g$ to be tilt-stable with the second subderivative of $g$, where $g$ is a closed proper convex function, and $φ$ is a twice continuously differentiable function that is locally convex at the local minimizer. Then, we apply the sufficient and necessary condition to the concerned Ky-Fan $κ$-norm composite problem, and employ the expression of second subderivative of the Ky-Fan $κ$-norm to derive a verifiable criterion to identify the tilt stability of a local minimum for this class of nonconvex and nonsmooth problems. As a byproduct, a practical criterion is obtained for identifying the tilt stablity of solutions to the nuclear-norm and spectral norm regularized minimization problems.

math.OC↗

arXiv2025

Twice Epi-Differentiability of Orthogonally Invariant Matrix Functions and Application

In this paper, our focus lies on the study of the second-order variational analysis of orthogonally invariant matrix functions. It is well-known that an orthogonally invariant matrix function is an extended-real-value function defined on ${\mathbb M}_{m,n}\,(n \leqslant m)$ of the form $f \circ σ$ for an absolutely symmetric function $f \colon \R^n \rightarrow [-\infty,+\infty]$ and the singular values $σ\colon {\mathbb M}_{m,n} \rightarrow \R^{n}$. We establish several second-order properties of orthogonally invariant matrix functions, such as parabolic epi-differentiability, parabolic regularity, and twice epi-differentiability when their associated absolutely symmetric functions enjoy some properties. Specifically, we show that the nuclear norm of a real $m \times n$ matrix is twice epi-differentiable and we derive an explicit expression of its second-order epi-derivative. Moreover, for a convex orthogonally invariant matrix function, we calculate its second subderivative and present sufficient conditions for twice epi-differentiability. This enables us to establish second-order optimality conditions for a class of matrix optimization problems.

math.OC↗

arXiv2024

Learning to Handle Complex Constraints for Vehicle Routing Problems

Vehicle Routing Problems (VRPs) can model many real-world scenarios and often involve complex constraints. While recent neural methods excel in constructing solutions based on feasibility masking, they struggle with handling complex constraints, especially when obtaining the masking itself is NP-hard. In this paper, we propose a novel Proactive Infeasibility Prevention (PIP) framework to advance the capabilities of neural methods towards more complex VRPs. Our PIP integrates the Lagrangian multiplier as a basis to enhance constraint awareness and introduces preventative infeasibility masking to proactively steer the solution construction process. Moreover, we present PIP-D, which employs an auxiliary decoder and two adaptive strategies to learn and predict these tailored masks, potentially enhancing performance while significantly reducing computational costs during training. To verify our PIP designs, we conduct extensive experiments on the highly challenging Traveling Salesman Problem with Time Window (TSPTW), and TSP with Draft Limit (TSPDL) variants under different constraint hardness levels. Notably, our PIP is generic to boost many neural methods, and exhibits both a significant reduction in infeasible rate and a substantial improvement in solution quality.

cs.AI↗

arXiv2024

Collaboration! Towards Robust Neural Methods for Routing Problems

Despite enjoying desirable efficiency and reduced reliance on domain expertise, existing neural methods for vehicle routing problems (VRPs) suffer from severe robustness issues -- their performance significantly deteriorates on clean instances with crafted perturbations. To enhance robustness, we propose an ensemble-based Collaborative Neural Framework (CNF) w.r.t. the defense of neural VRP methods, which is crucial yet underexplored in the literature. Given a neural VRP method, we adversarially train multiple models in a collaborative manner to synergistically promote robustness against attacks, while boosting standard generalization on clean instances. A neural router is designed to adeptly distribute training instances among models, enhancing overall load balancing and collaborative efficacy. Extensive experiments verify the effectiveness and versatility of CNF in defending against various attacks across different neural VRP methods. Notably, our approach also achieves impressive out-of-distribution generalization on benchmark instances.

cs.AI↗

arXiv2024

Cross-Problem Learning for Solving Vehicle Routing Problems

Existing neural heuristics often train a deep architecture from scratch for each specific vehicle routing problem (VRP), ignoring the transferable knowledge across different VRP variants. This paper proposes the cross-problem learning to assist heuristics training for different downstream VRP variants. Particularly, we modularize neural architectures for complex VRPs into 1) the backbone Transformer for tackling the travelling salesman problem (TSP), and 2) the additional lightweight modules for processing problem-specific features in complex VRPs. Accordingly, we propose to pre-train the backbone Transformer for TSP, and then apply it in the process of fine-tuning the Transformer models for each target VRP variant. On the one hand, we fully fine-tune the trained backbone Transformer and problem-specific modules simultaneously. On the other hand, we only fine-tune small adapter networks along with the modules, keeping the backbone Transformer still. Extensive experiments on typical VRPs substantiate that 1) the full fine-tuning achieves significantly better performance than the one trained from scratch, and 2) the adapter-based fine-tuning also delivers comparable performance while being notably parameter-efficient. Furthermore, we empirically demonstrate the favorable effect of our method in terms of cross-distribution application and versatility.

cs.AI↗

arXiv2024

Learning Topological Representations with Bidirectional Graph Attention Network for Solving Job Shop Scheduling Problem

Existing learning-based methods for solving job shop scheduling problems (JSSP) usually use off-the-shelf GNN models tailored to undirected graphs and neglect the rich and meaningful topological structures of disjunctive graphs (DGs). This paper proposes the topology-aware bidirectional graph attention network (TBGAT), a novel GNN architecture based on the attention mechanism, to embed the DG for solving JSSP in a local search framework. Specifically, TBGAT embeds the DG from a forward and a backward view, respectively, where the messages are propagated by following the different topologies of the views and aggregated via graph attention. Then, we propose a novel operator based on the message-passing mechanism to calculate the forward and backward topological sorts of the DG, which are the features for characterizing the topological structures and exploited by our model. In addition, we theoretically and experimentally show that TBGAT has linear computational complexity to the number of jobs and machines, respectively, strengthening our method's practical value. Besides, extensive experiments on five synthetic datasets and seven classic benchmarks show that TBGAT achieves new SOTA results by outperforming a wide range of neural methods by a large margin. All the code and data are publicly available online at https://github.com/zcaicaros/TBGAT.

cs.LG↗