arXiv subjects

Pascal Van Hentenryck

Publications and source records attributed to Pascal Van Hentenryck.

At least 55 records · Page 3Linked to original sources

arXiv2025

Constraint-Informed Active Learning for End-to-End ACOPF Optimization Proxies

This paper studies optimization proxies, machine learning (ML) models trained to efficiently predict optimal solutions for AC Optimal Power Flow (ACOPF) problems. While promising, optimization proxy performance heavily depends on training data quality. To address this limitation, this paper introduces a novel active sampling framework for ACOPF optimization proxies designed to generate realistic and diverse training data. The framework actively explores varied, flexible problem specifications reflecting plausible operational realities. More importantly, the approach uses optimization-specific quantities (active constraint sets) that better capture the salient features of an ACOPF that lead to the optimal solution. Numerical results show superior generalization over existing sampling methods with an equivalent training budget, significantly advancing the state-of-practice for trustworthy ACOPF optimization proxies.

cs.LG↗

arXiv2025

A General and Streamlined Differentiable Optimization Framework

Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface mismatches. This paper presents a general and streamlined framework-an updated DiffOpt.jl-that unifies modeling and differentiation within the Julia optimization stack. The framework computes forward - and reverse-mode solution and objective sensitivities for smooth, potentially nonconvex programs by differentiating the KKT system under standard regularity assumptions. A first-class, JuMP-native parameter-centric API allows users to declare named parameters and obtain derivatives directly with respect to them - even when a parameter appears in multiple constraints and objectives - eliminating brittle bookkeeping from coefficient-level interfaces. We illustrate these capabilities on convex and nonconvex models, including economic dispatch, mean-variance portfolio selection with conic risk constraints, and nonlinear robot inverse kinematics. Two companion studies further demonstrate impact at scale: gradient-based iterative methods for strategic bidding in energy markets and Sobolev-style training of end-to-end optimization proxies using solver-accurate sensitivities. Together, these results demonstrate that differentiable optimization can be deployed as a routine tool for experimentation, learning, calibration, and design-without deviating from standard JuMP modeling practices and while retaining access to a broad ecosystem of solvers.

cs.LG↗

arXiv2025

A community-driven optimization framework for redrawing school attendance boundaries

The vast majority of US public school districts use school attendance boundaries to determine which student addresses are assigned to which schools. Existing work shows how redrawing boundaries can be a powerful policy lever for increasing access and opportunity for historically disadvantaged groups, even while maintaining other priorities like minimizing driving distances and preserving existing social ties between students and families. This study introduces a multi-objective algorithmic school rezoning framework and applies it to a large-scale rezoning effort impacting over 50,000 students through an ongoing researcher-school district partnership. The framework is designed to incorporate feedback from community members and policymakers, both by deciding which goals are optimized and also by placing differential ``importance'' on goals through weights from community surveys. Empirical results reveal the framework's ability to surface school redistricting plans that simultaneously advance a number of objectives often thought to be in competition with one another, including socioeconomic integration, transportation efficiency, and stable feeder patterns (transitions) between elementary, middle, and high schools. The paper also highlights how local education policymakers navigate several practical challenges, like building political will to make change in a polarized policy climate. The framework is built using open-source tools and publicly released to support school districts in exploring and implementing new policies to improve educational access and opportunity in the coming years.

cs.CY↗

arXiv2025

Contextual Stochastic Optimization for Omnichannel Multi-Courier Order Fulfillment Under Delivery Time Uncertainty

The paper studies a large-scale order fulfillment problem for a leading e-commerce company in the United States. The challenge involves selecting fulfillment centers and shipping carriers with observational data only to efficiently process orders from a vast network of physical stores and warehouses. The company's current practice relies on heuristic rules that choose the cheapest fulfillment and shipping options for each unit, without considering opportunities for batching items or the reliability of carriers in meeting expected delivery dates. The paper develops a data-driven Contextual Stochastic Optimization (CSO) framework that integrates distributional forecasts of delivery time deviations with stochastic and robust order fulfillment optimization models. The framework optimizes the selection of fulfillment centers and carriers, accounting for item consolidation and delivery time uncertainty. Validated on a real-world data set containing tens of thousands of products, each with hundreds to thousands of fulfillment options, the proposed CSO framework significantly enhances the accuracy of meeting customer-expected delivery dates compared to current practices. It provides a flexible balance between reducing fulfillment costs and managing delivery time deviation risks, emphasizing the importance of contextual information and distributional forecasts in order fulfillment. This is the first paper that studies the omnichannel multi-courier order fulfillment problem with delivery time uncertainty through the lens of contextual optimization, fusing machine learning and optimization.

math.OC↗

arXiv2025

Conformal Predictive Distributions for Order Fulfillment Time Forecasting

Accurate estimation of order fulfillment time is critical for e-commerce logistics, yet traditional rule-based approaches often fail to capture the inherent uncertainties in delivery operations. This paper introduces a novel framework for distributional forecasting of order fulfillment time, leveraging Conformal Predictive Systems and Cross Venn-Abers Predictors -- model-agnostic techniques that provide rigorous coverage or validity guarantees. The proposed machine learning methods integrate granular spatiotemporal features, capturing fulfillment location and carrier performance dynamics to enhance predictive accuracy. Additionally, a cost-sensitive decision rule is developed to convert probabilistic forecasts into reliable point predictions. Experimental evaluation on a large-scale industrial dataset demonstrates that the proposed methods generate competitive distributional forecasts, while machine learning-based point predictions significantly outperform the existing rule-based system -- achieving up to 14% higher prediction accuracy and up to 75% improvement in identifying late deliveries.

cs.LG↗

arXiv2025

Practice-Based Optimization for the Strategic Locomotive Assignment Problem

This study addresses the challenge of efficiently assigning locomotives in large freight rail networks, where operational complexity and power imbalances make cost-effective planning difficult. It presents a strategic optimization framework for the Locomotive Assignment Problem (LAP), developed in collaboration with a major North American Class I Freight Railroad. The problem is formulated as a network-based integer program over a cyclic space-time network, producing a repeatable weekly locomotive assignment plan. The model captures a comprehensive set of real-world operational constraints and jointly optimizes the placement of pick-up and set-out locomotive work events, improving the effectiveness of downstream planning. To solve large-scale instances exactly for the first time, novel reduction rules are introduced to dramatically reduce the number of light travel arcs in the space-time network. Extensive computational experiments demonstrate the performance and trade-offs on real instances under a variety of practical constraints. Beyond delivering scalable, high-quality solutions, the proposed framework serves as a practical decision-support tool grounded in the operational realities of modern freight railroads.

math.OC↗

arXiv2025

Route Optimization Over Scheduled Services For Large-Scale Package Delivery Networks

This paper introduces the Trailer Path Optimization with Schedule Services Problem (TPOSSP) and proposes a column-generation heuristic (CG-heuristic) to find high-quality solutions to large-scale instances. The TPOSSP aims at determining trailer routes over a time-dependent network using existing scheduled services, while considering tractor capacity constraints and time windows for trailer pickups and deliveries. The objective is to minimize both the number of schedules used and the total miles traveled. To address the large scale of industrial instances, the paper proposes a network reduction technique that identifies the set of feasible schedule-legs for each requests. Moreover, to address the resulting MIP models, that still contains hundred of millions variables, the paper proposes a stabilized column-generation, whose pricing problem is a time-dependent shortest path. The approach is evaluated on industrial instances both for tactical planning where requests for the entire network are re-optimized and for real-time operations where new requests are inserted. In the tactical planning setting, the column-generation heuristic returns solutions with a 3.7%-5.7% optimality gap (based on a MIP relaxation) in under 1.7-10.3 hours, and improves the current practice by 2.3-3.2%, with translates into savings of tens of millions of dollars a year. In the real-time setting, the column-generation heuristic returns solution within 3% of optimality in under 1 minute, which makes it adequate for real-time deployment. The results also show that the network reduction decreases run times by 85% for the column-generation heuristic.

math.OC↗

arXiv2025

Parallel Batch Scheduling With Incompatible Job Families Via Constraint Programming

This paper addresses the incompatible case of parallel batch scheduling, where compatible jobs belong to the same family, and jobs from different families cannot be processed together in the same batch. The state-of-the-art constraint programming (CP) model for this problem relies on specific functions and global constraints only available in a well established commercial CP solver. This paper expands the literature around this problem by proposing four new CP models that can be implemented in commercial and open-source solvers: a new model that relies on automaton constraints, and three alternative models that integrate assignment and scheduling decisions with different strategies and global constraints. Extensive computational experiments on standard test cases under multiple objectives and multiple solvers demonstrate the implementation flexibility and competitive performance of the proposed models.

eess.SY↗

arXiv2025

Electricity-Aware Bid Format for Coordinated Heat and Electricity Market Clearing

Coordination between heat and electricity markets is essential to achieve a cost-effective and efficient operation of the energy system. In the current sequential market practice, the heat market is cleared before the electricity market and has no insight into the impacts of heat dispatch on the electricity market. While preserving this sequential practice, this paper introduces an electricity-aware bid format for the coordination of heat and electricity systems. This novel market mechanism defines heat bids conditionally on the day-ahead electricity prices. Prior to clearing heat and electricity markets, the proposed bid selection mechanism selects the valid bids which minimize the heat system operating cost while anticipating heat and electricity market clearing. This mechanism is modeled as a trilevel optimization problem, which we recast as a mixed-integer linear program using a lexicographic function. We use a realistic case study based on the Danish electricity and heat system and show that the proposed bid selection mechanism yields a 4.5% reduction in the total operating cost of heat and electricity systems compared to the existing market-clearing procedure while reducing the financial losses of combined heat and power plants and heat pumps due to invalid bids by up to 20.3 million euros.

eess.SY↗

arXiv2025

Constraint Programming Models For Serial Batch Scheduling With Minimum Batch Size

In serial batch (s-batch) scheduling, jobs are grouped in batches and processed sequentially within their batch. This paper considers multiple parallel machines, nonidentical job weights and release times, and sequence-dependent setup times between batches of different families. Although s-batch has been widely studied in the literature, very few papers have taken into account a minimum batch size, typical in practical settings such as semiconductor manufacturing and the metal industry. The problem with this minimum batch size requirement has been mostly tackled with dynamic programming and meta-heuristics, and no article has ever used constraint programming (CP) to do so. This paper fills this gap by proposing, three CP models for s-batching with minimum batch size: (i) an \textit{Interval Assignment} model that computes and bounds the size of the batches using the presence literals of interval variables of the jobs. (ii) A \textit{Global} model that exclusively uses global constraints that track the size of the batches over time. (iii) And a \textit{Hybrid} model that combines the benefits of the extra global constraints with the efficiency of the sum-of-presences constraints to ensure the minimum batch sizes. The computational experiments on standard cases compare the three CP models with two existing mixed-integer programming (MIP) models from the literature. The results demonstrate the versatility of the proposed CP models to handle multiple variations of s-batching; and their ability to produce, in large instances, better solutions than the MIP models faster.

cs.DC↗

arXiv2025

Optimizing Multiple-Control Toffoli Quantum Circuit Design with Constraint Programming

As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the necessary background in quantum computing to comprehend the problem. While this is a well-studied problem, optimization models that minimize the true objective have only been explored recently. This paper introduces a new optimization model and symmetry-breaking constraints that improve solving time by up to two orders of magnitude compared to earlier work when a Constraint Programming solver is used. Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits, obtained by any method, for well-known benchmarks. Several in-depth analyses are presented to validate the effectiveness of the symmetry-breaking constraints from multiple perspectives. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.

math.OC↗

arXiv2025

Boosting Column Generation with Graph Neural Networks for Joint Rider Trip Planning and Crew Shift Scheduling

Optimizing service schedules is pivotal to the reliable, efficient, and inclusive on-demand mobility. This pressing challenge is further exacerbated by the increasing needs of an aging population, the oversubscription of existing services, and the lack of effective solution methods. This study addresses the intricacies of service scheduling, by jointly optimizing rider trip planning and crew scheduling for a complex dynamic mobility service. The resulting optimization problems are extremely challenging computationally for state-of-the-art methods. To address this fundamental gap, this paper introduces the Joint Rider Trip Planning and Crew Shift Scheduling Problem (JRTPCSSP) and a novel solution method, called Attention and Gated GNN-Informed Column Generation (AGGNNI-CG), that hybridizes column generation and machine learning to obtain near-optimal solutions to the JRTPCSSP with real-life constraints of the application. The key idea of the machine-learning component is to dramatically reduce the number of paths to explore in the pricing problem, accelerating the most time-consuming component of the column generation. The machine learning component is a graph neural network with an attention mechanism and a gated architecture, which is particularly suited to cater for the different input sizes coming from daily operations. AGGNNI-CG has been applied to a challenging, real-world dataset from the Paratransit system of Chatham County in Georgia. It produces substantial improvements compared to the baseline column generation approach, which typically cannot produce high-quality feasible solutions in reasonable time on large-scale complex instances. AGGNNI-CG also produces significant improvements in service quality compared to the existing system.

math.OC↗

arXiv2025

PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flow

Machine Learning (ML) techniques for Optimal Power Flow (OPF) problems have recently garnered significant attention, reflecting a broader trend of leveraging ML to approximate and/or accelerate the resolution of complex optimization problems. These developments are necessitated by the increased volatility and scale in energy production for modern and future grids. However, progress in ML for OPF is hindered by the lack of standardized datasets and evaluation metrics, from generating and solving OPF instances, to training and benchmarking machine learning models. To address this challenge, this paper introduces PGLearn, a comprehensive suite of standardized datasets and evaluation tools for ML and OPF. PGLearn provides datasets that are representative of real-life operating conditions, by explicitly capturing both global and local variability in the data generation, and by, for the first time, including time series data for several large-scale systems. In addition, it supports multiple OPF formulations, including AC, DC, and second-order cone formulations. Standardized datasets are made publicly available to democratize access to this field, reduce the burden of data generation, and enable the fair comparison of various methodologies. PGLearn also includes a robust toolkit for training, evaluating, and benchmarking machine learning models for OPF, with the goal of standardizing performance evaluation across the field. By promoting open, standardized datasets and evaluation metrics, PGLearn aims at democratizing and accelerating research and innovation in machine learning applications for optimal power flow problems. Datasets are available for download at https://www.huggingface.co/PGLearn.

cs.LG↗

arXiv2025

DualSchool: How Reliable are LLMs for Optimization Education?

Consider the following task taught in introductory optimization courses which addresses challenges articulated by the community at the intersection of (generative) AI and OR: generate the dual of a linear program. LLMs, being trained at web-scale, have the conversion process and many instances of Primal to Dual Conversion (P2DC) at their disposal. Students may thus reasonably expect that LLMs would perform well on the P2DC task. To assess this expectation, this paper introduces DualSchool, a comprehensive framework for generating and verifying P2DC instances. The verification procedure of DualSchool uses the Canonical Graph Edit Distance, going well beyond existing evaluation methods for optimization models, which exhibit many false positives and negatives when applied to P2DC. Experiments performed by DualSchool reveal interesting findings. Although LLMs can recite the conversion procedure accurately, state-of-the-art open LLMs fail to consistently produce correct duals. This finding holds even for the smallest two-variable instances and for derivative tasks, such as correctness, verification, and error classification. The paper also discusses the implications for educators, students, and the development of large reasoning systems.

cs.LG↗

arXiv2025

Sobolev Training of End-to-End Optimization Proxies

Optimization proxies - machine learning models trained to approximate the solution mapping of parametric optimization problems in a single forward pass - offer dramatic reductions in inference time compared to traditional iterative solvers. This work investigates the integration of solver sensitivities into such end to end proxies via a Sobolev training paradigm and does so in two distinct settings: (i) fully supervised proxies, where exact solver outputs and sensitivities are available, and (ii) self supervised proxies that rely only on the objective and constraint structure of the underlying optimization problem. By augmenting the standard training loss with directional derivative information extracted from the solver, the proxy aligns both its predicted solutions and local derivatives with those of the optimizer. Under Lipschitz continuity assumptions on the true solution mapping, matching first order sensitivities is shown to yield uniform approximation error proportional to the training set covering radius. Empirically, different impacts are observed in each studied setting. On three large Alternating Current Optimal Power Flow benchmarks, supervised Sobolev training cuts mean squared error by up to 56 percent and the median worst case constraint violation by up to 400 percent while keeping the optimality gap below 0.22 percent. For a mean variance portfolio task trained without labeled solutions, self supervised Sobolev training halves the average optimality gap in the medium risk region (standard deviation above 10 percent of budget) and matches the baseline elsewhere. Together, these results highlight Sobolev training whether supervised or self supervised as a path to fast reliable surrogates for safety critical large scale optimization workloads.

cs.LG↗

arXiv2025

Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow

The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e., machine learning models that predict high-quality, close-to-optimal solutions. More recently, dual conic proxy architectures have been proposed, which combine machine learning and convex relaxations of AC-OPF, to provide valid certificates of optimality using learning-based methods. Building on this methodology, this paper proposes, for the first time, a dual conic proxy architecture for the semidefinite (SDP) relaxation of AC-OPF problems. Although the SDP relaxation is stronger than the second-order cone relaxation considered in previous work, its practical use has been hindered by its computational cost. The proposed method combines a neural network with a differentiable dual completion strategy that leverages the structure of the dual SDP problem. This approach guarantees dual feasibility, and therefore valid dual bounds, while providing orders of magnitude of speedups compared to interior-point algorithms. The paper also leverages self-supervised learning, which alleviates the need for time-consuming data generation and allows to train the proposed models efficiently. Numerical experiments are presented on several power grid benchmarks with up to 500 buses. The results demonstrate that the proposed SDP-based proxies can outperform weaker conic relaxations, while providing several orders of magnitude speedups compared to a state-of-the-art interior-point SDP solver.

math.OC↗

arXiv2025

Integrating Column Generation and Large Neighborhood Search for Bus Driver Scheduling with Complex Break Constraints

The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimization problem with the goal to design shifts to cover prearranged bus tours. The objective takes into account the operational cost as well as the satisfaction of drivers. This problem is heavily constrained due to strict legal rules and collective agreements. The objective of this article is to provide state-of-the-art exact and hybrid solution methods that can provide high-quality solutions for instances of different sizes. This work presents a comprehensive study of both an exact method, Branch and Price (B&P), as well as a Large Neighborhood Search (LNS) framework which uses B&P or Column Generation (CG) for the repair phase to solve the BDSP. It further proposes and evaluates a novel deeper integration of B&P and LNS, storing the generated columns from the LNS subproblems and reusing them for other subproblems, or to find better global solutions. The article presents a detailed analysis of several components of the solution methods and their impact, including general improvements for the B&P subproblem, which is a high-dimensional Resource Constrained Shortest Path Problem (RCSPP), and the components of the LNS. The evaluation shows that our approach provides new state-of-the-art results for instances of all sizes, including exact solutions for small instances, and low gaps to a known lower bound for mid-sized instances. Conclusions: We observe that B&P provides the best results for small instances, while the tight integration of LNS and CG can provide high-quality solutions for larger instances, further improving over LNS which just uses CG as a black box. The proposed methods are general and can also be applied to other rule sets and related optimization problems

math.OC↗

arXiv2025

SPOT: Spatio-Temporal Pattern Mining and Optimization for Load Consolidation in Freight Transportation Networks

Freight consolidation has significant potential to reduce transportation costs and mitigate congestion and pollution. An effective load consolidation plan relies on carefully chosen consolidation points to ensure alignment with existing transportation management processes, such as driver scheduling, personnel planning, and terminal operations. This complexity represents a significant challenge when searching for optimal consolidation strategies. Traditional optimization-based methods provide exact solutions, but their computational complexity makes them impractical for large-scale instances and they fail to leverage historical data. Machine learning-based approaches address these issues but often ignore operational constraints, leading to infeasible consolidation plans. This work proposes SPOT, an end-to-end approach that integrates the benefits of machine learning (ML) and optimization for load consolidation. The ML component plays a key role in the planning phase by identifying the consolidation points through spatio-temporal clustering and constrained frequent itemset mining, while the optimization selects the most cost-effective feasible consolidation routes for a given operational day. Extensive experiments conducted on industrial load data demonstrate that SPOT significantly reduces travel distance and transportation costs (by about 50% on large terminals) compared to the existing industry-standard load planning strategy and a neighborhood-based heuristic. Moreover, the ML component provides valuable tactical-level insights by identifying frequently recurring consolidation opportunities that guide proactive planning. In addition, SPOT is computationally efficient and can be easily scaled to accommodate large transportation networks.

cs.LG↗