arXiv subjects

Pascal Van Hentenryck

Publications and source records attributed to Pascal Van Hentenryck.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Linear Programming on GPU Clusters at Extreme Scale

Large linear programs can exceed the memory of a single compute node. Although first-order methods replace sparse factorizations with GPU-suited matrix-vector products, other solver phases can reintroduce a single-node memory limit. We present SHARDLP, a distributed GPU LP solver that keeps the matrix and primal-dual state partitioned from sharded input through solution output. On the Google PDLP benchmark, SHARDLP reaches the published criterion on nine of eleven instances, compared with eight in the published CPU PDLP study. On the largest benchmark, eight H200 GPUs solve a 1.185-billion-variable, 6.338-billion-nonzero LP in 9.9 minutes; the published CPU experiment reports 21.06 hours on different hardware. Beyond this benchmark, separately checked multi-node solves reach up to 13.604 billion variables and 40.807 billion nonzeros, while validated executions span up to 76 GPUs across 29 compute nodes. For column-partitioned solves, support-aware communication skips GPUs that store no coefficients for a row; on an LP with 2.76 billion nonzeros, it cuts modelled communication by 92.97% and improves solver time by 1.27x-1.52x

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arXiv2026

Improving Stability and Economic Operation in Transmission Systems through Volt/VAR Optimization

Transmission system operators often reconcile market-cleared DC dispatches with AC physics through power-flow solves (ACPF), yet the resulting setpoints can still violate voltage (Volt) and reactive-power (VAR) limits. Maintaining secure voltage profiles and adequate VAR support therefore requires fast corrective decisions that are implementable in operation. This paper presents a novel homotopy-based continuation method for discrete-control Volt/VAR Optimization (VVO) that coordinates switchable devices, such as on-load tap-changing transformers (OLTCs) and capacitor banks (CBs). Experiments on IEEE, PEGASE, and RTE systems show that the proposed VVO produces AC-feasible setpoints within practical runtime, while reducing voltage deviation, VAR dispatch, and generation cost. VVO also achieves comparable performance using ACPF-adjusted DC dispatches as inputs relative to AC-feasible dispatches, indicating that it can be integrated naturally into existing transmission dispatch practices to strengthen grid operation.

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arXiv2026

End-to-End Supply Chain Planning in the Paper Industry Via Column Generation and Benders Decomposition

Problem definition: The paper studies an integrated end-to-end planning problem in large-scale paper manufacturing, where production scheduling, trimming decisions, vehicle loading, and multi-period fulfillment of make-to-order and make-to-stock demand must be coordinated over time. In practice, these decisions are often optimized sequentially, leading to material waste, inefficient transportation, and degraded service levels. Solving the fully integrated problem at industrial scale remains computationally challenging due to its combinatorial structure. Methodology/results: A key structural feature of the problem is that downstream fulfillment decisions depend on upstream production and logistics choices only through aggregate supply availability over time. By exploiting this structure, the paper develops an exact mathematical formulation and proposes a two-phase hybrid framework (BDCG-DP) that integrates column generation (CG) using exact dynamic-programming (DP) for supply-side decisions with Benders decomposition (BD) for downstream fulfillment. Computational experiments on proprietary instances from a major North American paper manufacturer show that BDCG-DP lowers total costs by 24.4% compared to a traditional CG-DP on challenging eight-week planning problems. Median runtime for four-week planning problems decreases from over five hours using CG-DP to under one hour using BDCG-DP. Managerial implications: This paper provides the first exact model that integrates production, trimming, load planning, and multi-period fulfillment at an industrial scale. The proposed approach returns integer-feasible plans within 2.3 to 6 hours for the most complex planning problems, enabling planners to access high-quality implementable schedules within hours, a capability that was previously unavailable in practice.

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arXiv2026

PACR: Parameter-Optimized AC Power Flow Restoration for AC Feasible DCOPF Dispatch

The DC optimal power flow is widely used in power system operations because of its computational efficiency and scalability. However, DC dispatches are not guaranteed to satisfy the nonlinear AC power-flow equations or associated operational limits. This paper develops a parameterized, differentiable AC power-flow restoration method for mapping DC dispatches to AC-consistent operating points. The method incorporates distributed slack for active-power balancing and PV/PQ switching for reactive-power regulation, both implemented using smooth differentiable surrogates with tunable parameters, including slack participation factors, voltage setpoints, and regulation steepness. These parameters are trained offline by differentiating through the AC restoration equations using the implicit function theorem. Once trained, the optimized parameters are fixed and used directly during AC power-flow recovery from DC dispatches. The approach is evaluated on IEEE, ACTIVSg, and PEGASE test systems using setpoints computed by standard DC optimal power flow. Results show that the optimized restoration method improves AC feasibility recovery across various systems relative to conventional single-slack AC power-flow recovery. On the 9,241-bus case, the optimized method improves cost difference by 80% relative to the conventional recovery baseline and improves solving time relative to ACOPF by 75%.

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arXiv2026

Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application

Sequential contextual stochastic programs model real-time decision systems in which each time epoch commits to an action under uncertainty whose consequences propagate into future decisions. In many practical contexts, these programs require obtaining solutions rapidly as new information becomes available. These problems can be represented through scenario approximations to be solved by off-the-shelf optimization solvers, which achieve high decision quality offline but typically run in seconds to minutes per instance, falling short of the sub-second responses that peak periods of planning require. This paper develops a learning-based optimization proxy: a scenario-embedded neural network trained offline on solver-generated labels, paired online with a decoder that enforces feasibility, replacing the per-epoch solve with a single forward pass. The framework is specialized to omnichannel order fulfillment, where each arriving order requires a sub-second assignment of products to distribution centers and carrier services under stochastic delivery times and future demand. A two-stage contextual stochastic program is introduced to formulate this problem, and its contextual sample average approximation (C-SAA) supplies the offline labels, while a composite training loss combines label imitation, a constraint-violation penalty, and self-supervised cost alignment. In a calibrated simulator built from JD.com transactional records, a detailed computational study is provided. The proxy reduces decision latency by roughly 2800x relative to the online finite-sample C-SAA reference and improves over it by 3.3% in realized fulfillment cost. Relative to established fulfillment policies, the proxy lowers total realized cost by at least 10.7% and roughly halves the late-delivery rate.

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arXiv2026

Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs

Large-scale optimization problems are often solved repeatedly under similar structural conditions, leading to substantial computational overhead. This occurs in applications such as power systems, transportation, and supply chain networks, where the underlying structure is fixed while parameters frequently vary under perturbations. This paper proposes a Learning to Optimize (LTO) framework that accelerates the solution of large-scale general mixed-integer problems by leveraging the concept of a backdoor, i.e., a subset of variables that drive most of the computational complexity. The proposed BIPC framework consists of three phases. Phase I is an identification procedure that discovers a backdoor for a set of instances in the distribution. Phase II uses supervised learning to develop machine learning models that, given an instance, predict values for bounded-domain backdoor variables and intervals for wide-domain backdoor variables. These predictions define a reduced optimization problem where the predictions constrain the backdoor variables, while the other variables remain free. Phase III optimizes this reduced problem and, if necessary, applies a correction step to restore feasibility or the optimality guarantees. Experiments on real-world, large-scale problems show substantial reductions in solution time with only a limited loss in solution quality. The framework enables organizations to solve large-scale optimization problems efficiently in the presence of frequent perturbations, such as unexpected events, demand fluctuations, or operational changes. Because these changes affect parameters rather than the problem structure, BIPC can quickly provide high-quality, feasible solutions, offering a practical approach to integrating machine learning into existing optimization pipelines.

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arXiv2026

The Proxy Benders Decomposition

Benders decomposition is a fundamental framework for solving large-scale mixed-integer optimization problems with complicating variables that, when fixed, yield significantly easier subproblems. However, classical Benders decomposition repeatedly solves highly similar subproblems and often exhibits zigzagging behavior across iterations, leading to slow convergence in large-scale settings. Motivated by the repetitive structure and parametric nature of Benders subproblems, this paper introduces the proxy Benders decomposition (Proxy-BD), a new decomposition framework in which subproblem optimization is replaced by certified optimization proxies rather than repeated exact solves. The proposed proxy follows a self-supervised predict-project-and-complete mechanism that produces dual-feasible solutions for generating provably valid Benders cuts. The framework preserves the theoretical validity of the decomposition independently of prediction quality through a projection-and-completion certification layer. A formal characterization of proxy-induced cuts is established, and the framework naturally extends to modern decomposition schemes, including branch-and-Benders-cut algorithms. Computational experiments on large-scale facility location and network design problems demonstrate that Proxy-BD substantially reduces the computational effort of subproblems while maintaining near-optimal solution quality. On large-scale uncapacitated facility location instances up to 2000x2000, Proxy-BD achieves median optimality gaps below 0.5%, yields up to 161x median speedups, and reduces the number of generated cuts by more than 240x on the largest instances. The computational gains consistently increase with recourse complexity, indicating that proxy-based inference scales substantially more favorably than repeated exact subproblem optimization in large-scale decomposition settings.

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arXiv2026

Decision-Focused On-Policy Learning for Contextual Linear Optimization with Partial Feedback

Decision-focused learning (DFL) trains predictive models by optimizing downstream decision quality rather than standalone prediction accuracy. For contextual linear optimization, most existing DFL methods assume offline data and full observations of the objective cost vector. We develop an on-policy learning method for sequential contextual linear optimization under partial feedback, generalizing the standard bandit feedback setting. Our method learns a stochastic predict-then-optimize policy that samples a cost-vector prediction from a conditional distribution and solves the resulting downstream linear optimization problem. To update this distributional model, we introduce a two-component hybrid gradient estimator. The first component is a score function estimator, which provides an unbiased but potentially high-variance policy gradient estimate. The second is a decision-focused plug-in component that uses an auxiliary nuisance estimate of the latent cost vector to exploit the downstream optimization structure, becoming more informative as the estimate improves. We prove an $\mathcal{O}(T^{-1/2})$ bound on the average squared policy-gradient norm, matching the standard non-convex SGD rate. Experiments on top-$k$ selection, shortest path, combinatorial pricing, and a real-data energy-scheduling benchmark show that the hybrid gradient approach achieves lower cumulative regret than contextual-bandit-style baselines across all benchmarks, using both Gaussian and richer conditional generative models. Code is available at https://github.com/Joeyetinghan/on-policy-bandit-dfl.

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arXiv2026

Democratizing Large-Scale Re-Optimization with LLM-Guided Model Patches

Optimization models developed by operations research (OR) experts are often deployed as decision-support systems in industrial settings. However, real-world environments are dynamic, with evolving business rules and unforeseen perturbations. In such contexts, end users should ideally re-optimize models to recover feasible and implementable solutions, often without access to the original model developers. This paper introduces an agentic re-optimization framework in which a large language model (LLM) acts as an OR expert, dynamically supporting end users through natural-language interaction. The LLM translates user prompts into structured updates of the underlying optimization model, selects suitable re-optimization techniques from an optimization toolbox, and solves the resulting instance to return implementable solutions. The toolbox leverages primal information, including historical solutions, valid inequalities, solver configurations, and metaheuristics, to accelerate re-optimization while preserving solution quality. The proposed framework enables interactive and continuous adaptation of deployed optimization models, reducing dependence on OR experts, and improving the sustainability of decision-support systems. Extensive experiments on two complementary large-scale real-world case studies demonstrate the effectiveness and scalability of the proposed framework. The first considers online supply chain re-optimization, where solutions must be generated rapidly while remaining close to the deployed plan, whereas the second focuses on offline university exam scheduling, where solution quality is prioritized over runtime. Results show that the toolbox-driven architecture significantly improves computational efficiency through primal-based and solver-aware re-optimization techniques, while the structured patch-based updates improve interpretability and traceability of model modifications.

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arXiv2026

Scheduling and Routing in the Flexible Job Shop with Heterogeneous Transbots and Zoning: A Constraint Programming Approach

Coordinating production and material transfers is increasingly important in modern manufacturing systems equipped with mobile transfer robots, known as transbots. This study considers a flexible job shop environment in which heterogeneous transbots transport parts between machines. The shop floor is partitioned into zones, with each transbot assigned to a specific zone, and inter-zone movements are facilitated through designated handoff points. These zoning constraints, transbot heterogeneity, and inter-zone handoffs give rise to a challenging variant of the flexible job shop problem with embedded transbot-routing features, resulting in substantial computational complexity. Motivated by a real manufacturing setting, two constraint programming formulations that integrate production scheduling with transbot routing are proposed: an arc-based formulation that explicitly models machine-to-machine transfers, and an operation-embedded formulation that embeds transfer decisions directly within the operation scheduling structure, leading to tighter synchronization between production and transportation decisions. Both formulations capture machine flexibility, zoning restrictions, handoff coordination, and collision-free path planning. To efficiently solve the resulting problem, a book-and-release strategy is proposed. It coordinates transbot movements without enforcing rigid routing patterns. Computational experiments on case study-adapted benchmark-based demonstrate that the proposed formulations generate high-quality solutions with strong computational performance. The generation of instances is described in detail to support future work in this emerging area.

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arXiv2026

A Hybrid Decomposition Approach for Stochastic Unit Commitment with Combined-Cycle Generators

The U.S. power grid is undergoing a paradigm shift as energy demand grows in scale and volatility. In response to this growing need, the U.S. has increased adoption of combined-cycle generators (CCs). CCs are fast-ramping generators that utilize variable configurations of combustion turbines (CTs) and steam turbines (STs) to achieve higher efficiency than traditional CTs. For schedule optimization, modeling these CCs requires the addition of a large number of binary constraints and variables to Unit Commitment (UC) problem formulations. This paper presents a novel hybrid Benders' (BD) and Dantzig-Wolfe (DW) decomposition algorithm, called CRG, for stochastic UC problems with CCs. CRG exploits the separability of the linear constraints in UC through BD and the integer CC constraints through DW. A novel set of valid inequalities are proposed for significantly tightening the lower bound produced by CRG. CRG is tested on the 935-generator FERC test data set, modified to include CC mode data. Results demonstrate better primal solutions than BD on cases with at least 20 load scenarios. CRG scales computationally better than Gurobi's branch-and-bound solver, which exceeds 64GB RAM allocations at 45 scenarios. Results show that the proposed algorithm is a scalable approach for solving large-scale stochastic UC with CCs.

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arXiv2026

Uncertainty-Aware Delivery Delay Duration Prediction via Multi-Task Deep Learning

Accurate delivery delay prediction is critical for maintaining operational efficiency and customer satisfaction across modern supply chains. Yet the increasing complexity of logistics networks, spanning multimodal transportation, cross-country routing, and pronounced regional variability, makes this prediction task inherently challenging. This paper introduces a multi-task deep learning model for delivery delay duration prediction in the presence of significant imbalanced data, where delayed shipments are rare but operationally consequential. The model embeds high-dimensional shipment features with dedicated embedding layers for tabular data, and then uses a classification-then-regression strategy to predict the delivery delay duration for on-time and delayed shipments. Unlike sequential pipelines, this approach enables end-to-end training, improves the detection of delayed cases, and supports probabilistic forecasting for uncertainty-aware decision making. The proposed approach is evaluated on a large-scale real-world dataset from an industrial partner, comprising more than 10 million historical shipment records across four major source locations with distinct regional characteristics. The proposed model is compared with traditional machine learning methods. Experimental results show that the proposed method achieves a mean absolute error of 0.67-0.91 days for delayed-shipment predictions, outperforming single-step tree-based regression baselines by 41-64% and two-step classify-then-regress tree-based models by 15-35%. These gains demonstrate the effectiveness of the proposed model in operational delivery delay forecasting under highly imbalanced and heterogeneous conditions.

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arXiv2026

Deep Neural Network-Enhanced Frequency-Constrained Optimal Power Flow with Multi-Governor Dynamics

To ensure frequency security in power systems, both the rate of change of frequency (RoCoF) and the frequency nadir (FN) must be explicitly accounted for in real-time frequency-constrained optimal power flow (FCOPF). However, accurately modeling sys-tem frequency dynamics through analytical formulations is chal-lenging due to their inherent nonlinearity and complexity. To address this issue, deep neural networks (DNNs) are utilized to capture the nonlinear mapping between system operating condi-tions and key frequency performance metrics. In this paper, a DNN-based frequency prediction model is developed and trained using the high-fidelity time-domain simulation data generated in PSCAD/EMTDC. The trained DNN is subsequently transformed into an equivalent mixed-integer linear programming (MILP) form and embedded into the FCOPF problem as additional con-straints to explicitly enforce frequency security, leading to the proposed DNN-FCOPF formulation. For benchmarking, two alternative models are considered: a conventional optimal power flow without frequency constraints and a linearized FCOPF in-corporating system-level RoCoF and FN constraints. The effec-tiveness of the proposed method is demonstrated by comparing the solutions of these three models through extensive PSCAD/EMTDC time-domain simulations under various loading scenarios.

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arXiv2026

Copula-Based Aggregation and Context-Aware Conformal Prediction for Reliable Renewable Energy Forecasting

The rapid growth of renewable energy penetration has intensified the need for reliable probabilistic forecasts to support grid operations at aggregated (fleet or system) levels. In practice, however, system operators often lack access to fleet-level probabilistic models and instead rely on site-level forecasts produced by heterogeneous third-party providers. Constructing coherent and calibrated fleet-level probabilistic forecasts from such inputs remains challenging due to complex cross-site dependencies and aggregation-induced miscalibration. This paper proposes a calibrated probabilistic aggregation framework that directly converts site-level probabilistic forecasts into reliable fleet-level forecasts in settings where system-level models cannot be trained or maintained. The framework integrates copula-based dependence modeling to capture cross-site correlations with Context-Aware Conformal Prediction (CACP) to correct miscalibration at the aggregated level. This combination enables dependence-aware aggregation while providing valid coverage and maintaining sharp prediction intervals. Experiments on large-scale solar generation datasets from MISO, ERCOT, and SPP demonstrate that the proposed Copula+CACP approach consistently achieves near-nominal coverage with significantly sharper intervals than uncalibrated aggregation baselines.

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arXiv2026

Volt/VAR Optimization in Transmission Networks with Discrete-Control Devices

Voltage (Volt) and reactive-power (VAR) control in transmission networks is critical for reliability and increasingly needs fast, implementable decisions. This paper presents a transmission Volt/VAR Optimization (VVO) framework that co-optimizes discrete control of on-load tap-changing transformers (OLTCs) and capacitor banks (CBs) with AC power flow (ACPF) physics to improve voltage stability and minimize VAR generation. The framework follows a relax-round-resolve pipeline: a continuous relaxation proposes targets, a rounding step selects feasible discrete settings, and a final solve enforces AC power flow physics. Extensive experiments on IEEE, PEGASE, and RTE systems show consistent improvements in voltage and VAR quality metrics with modest generator redispatch while preserving economic operation and achieving compatible runtimes with real-time transmission operations.

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arXiv2026

The Impact of Shared Autonomous Vehicles in Microtransit Systems: A Case Study in Atlanta

Microtransit systems represent an enhancement to solve the first- and last-mile problem, integrating traditional rail and bus networks with on-demand shuttles into a flexible, integrated system. This type of demand responsive transport provides greater accessibility and higher quality levels of service compared to conventional fixed-route transit services. Advances in technology offer further opportunities to enhance microtransit performance. In particular, shared autonomous vehicles (SAVs) have the potential to transform the mobility landscape by enabling more sustainable operations, enhanced user convenience, and greater system reliability. This paper investigates the integration of SAVs in microtransit systems, advancing the technological capabilities of on-demand shuttles. A shuttle dispatching optimization model is enhanced to accommodate for driver behavior and SAV functionalities. A model predictive control approach is proposed that dynamically rebalances on-demand shuttles towards areas of higher demand without relying on vast historical data. Scenario-driven experiments are conducted using data from the MARTA Reach microtransit pilot. The results demonstrate that SAVs can elevate both service quality and user experience compared to traditional on-demand shuttles in microtransit systems.

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arXiv2026

Transit Network Design with Two-Level Demand Uncertainties: A Machine Learning and Contextual Stochastic Optimization Framework

Transit Network Design is a well-studied problem in the field of transportation, typically addressed by solving optimization models under fixed demand assumptions. Considering the limitations of these assumptions, this paper proposes a new framework, namely the Two-Level Rider Choice Transit Network Design (2LRC-TND), that leverages machine learning and contextual stochastic optimization (CSO) through constraint programming (CP) to incorporate two layers of demand uncertainties into the network design process. The first level identifies travelers who rely on public transit (core demand), while the second level captures the conditional adoption behavior of those who do not (latent demand), based on the availability and quality of transit services. To capture these two types of uncertainties, 2LRC-TND relies on two travel mode choice models, that use multiple machine learning models. To design a network, 2LRC-TND integrates the resulting choice models into a CSO that is solved using a CP-SAT solver. 2LRC-TND is evaluated through a case study involving over 6,600 travel arcs and more than 38,000 trips in the Atlanta metropolitan area. The computational results demonstrate the effectiveness of the 2LRC-TND in designing transit networks that account for demand uncertainties and contextual information, offering a more realistic alternative to fixed-demand models.

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arXiv2026

A Rolling-Space Branch-and-Price Algorithm for the Multi-Compartment Vehicle Routing Problem with Multiple Time Windows

This paper investigates the multi-compartment vehicle routing problem with multiple time windows (MCVRPMTW), an extension of the classical vehicle routing problem with time windows that considers vehicles equipped with multiple compartments and customers requiring service across several delivery time windows. The problem incorporates three key compartment-related features: (i) compartment flexibility in the number of compartments, (ii) item-to-compartment compatibility, and (iii) item-to-item compatibility. The problem also accommodates practical operational requirements such as driver breaks. To solve the MCVRPMTW, we develop an exact branch-and-price (B&P) algorithm in which the pricing problem is solved using a labeling algorithm. Several acceleration strategies are introduced to limit symmetry during label extensions, improve the stability of dual solutions in column generation, and enhance the branching process. To handle large-scale instances, we propose a rolling-space B&P algorithm that integrates clustering techniques into the solution framework. Extensive computational experiments on instances inspired by a real-world industrial application demonstrate the effectiveness of the proposed approach and provide useful managerial insights for practical implementation.

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