arXiv subjects

Pascal Van Hentenryck

Publications and source records attributed to Pascal Van Hentenryck.

At least 91 records · Page 5Linked to original sources

arXiv2024

Compact Optimality Verification for Optimization Proxies

Recent years have witnessed increasing interest in optimization proxies, i.e., machine learning models that approximate the input-output mapping of parametric optimization problems and return near-optimal feasible solutions. Following recent work by (Nellikkath & Chatzivasileiadis, 2021), this paper reconsiders the optimality verification problem for optimization proxies, i.e., the determination of the worst-case optimality gap over the instance distribution. The paper proposes a compact formulation for optimality verification and a gradient-based primal heuristic that brings substantial computational benefits to the original formulation. The compact formulation is also more general and applies to non-convex optimization problems. The benefits of the compact formulation are demonstrated on large-scale DC Optimal Power Flow and knapsack problems.

math.OC↗

arXiv2024

Dual Lagrangian Learning for Conic Optimization

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible solutions, and therefore valid Lagrangian dual bounds, for linear and nonlinear conic optimization problems. The paper introduces a systematic dual completion procedure, differentiable conic projection layers, and a self-supervised learning framework based on Lagrangian duality. It also provides closed-form dual completion formulae for broad classes of conic problems, which eliminate the need for costly implicit layers. The effectiveness of DLL is demonstrated on linear and nonlinear conic optimization problems. The proposed methodology significantly outperforms a state-of-the-art learning-based method, and achieves 1000x speedups over commercial interior-point solvers with optimality gaps under 0.5\% on average.

math.OC↗

arXiv2024

Scalable Exact Verification of Optimization Proxies for Large-Scale Optimal Power Flow

Optimal Power Flow (OPF) is a valuable tool for power system operators, but it is a difficult problem to solve for large systems. Machine Learning (ML) algorithms, especially Neural Networks-based (NN) optimization proxies, have emerged as a promising new tool for solving OPF, by estimating the OPF solution much faster than traditional methods. However, these ML algorithms act as black boxes, and it is hard to assess their worst-case performance across the entire range of possible inputs than an OPF can have. Previous work has proposed a mixed-integer programming-based methodology to quantify the worst-case violations caused by a NN trained to estimate the OPF solution, throughout the entire input domain. This approach, however, does not scale well to large power systems and more complex NN models. This paper addresses these issues by proposing a scalable algorithm to compute worst-case violations of NN proxies used for approximating large power systems within a reasonable time limit. This will help build trust in ML models to be deployed in large industry-scale power grids.

cs.AI↗

arXiv2024

Optimization-based Learning for Dynamic Load Planning in Trucking Service Networks

The load planning problem is a critical challenge in service network design for parcel carriers: it decides how many trailers to assign for dispatch over time between pairs of terminals. Another key challenge is to determine a flow plan, which specifies how parcel volumes are assigned to planned loads. This paper considers the Outbound Load Planning Problem (OLPP) that considers flow and load planning challenges jointly in order to adjust loads and flows as the demand forecast changes over time before the day of operations in a terminal. The paper aims at developing a decision-support tool to inform planners making these decisions at terminals across the network. The paper formulates the OLPP as a mixed-integer programming model and shows that it admits a large number of symmetries in a network where each commodity can be routed through primary and alternate terminals. As a result, an optimization solver may return fundamentally different solutions to closely related problems, confusing planners and reducing trust in optimization. To remedy this limitation, this paper proposes a lexicographical optimization approach that eliminates those symmetries by generating optimal solutions staying close to a reference plan. Moreover, this paper designs an optimization proxy that addresses the computational challenges of the optimization model. The optimization proxy combines a machine-learning model and a repair procedure to find near-optimal solutions that satisfy real-time constraints imposed by planners in the loop. An extensive computational study on industrial instances shows that the optimization proxy is orders of magnitude faster for generating solutions that are consistent with each other. The proposed approach also demonstrates the benefits of the OLPP for load consolidation and the significant savings obtained from combining machine learning and optimization.

cs.AI↗

arXiv2024

Self-Supervised Learning for Large-Scale Preventive Security Constrained DC Optimal Power Flow

Security-Constrained Optimal Power Flow (SCOPF) plays a crucial role in power grid stability but becomes increasingly complex as systems grow. This paper introduces PDL-SCOPF, a self-supervised end-to-end primal-dual learning framework for producing near-optimal solutions to large-scale SCOPF problems in milliseconds. Indeed, PDL-SCOPF remedies the limitations of supervised counterparts that rely on training instances with their optimal solutions, which becomes impractical for large-scale SCOPF problems. PDL-SCOPF mimics an Augmented Lagrangian Method (ALM) for training primal and dual networks that learn the primal solutions and the Lagrangian multipliers, respectively, to the unconstrained optimizations. In addition, PDL-SCOPF incorporates a repair layer to ensure the feasibility of the power balance in the nominal case, and a binary search layer to compute, using the Automatic Primary Response (APR), the generator dispatches in the contingencies. The resulting differentiable program can then be trained end-to-end using the objective function of the SCOPF and the power balance constraints of the contingencies. Experimental results demonstrate that the PDL-SCOPF delivers accurate feasible solutions with minimal optimality gaps. The framework underlying PDL-SCOPF aims at bridging the gap between traditional optimization methods and machine learning, highlighting the potential of self-supervised end-to-end primal-dual learning for large-scale optimization tasks.

cs.LG↗

arXiv2024

Strong Mixed-Integer Formulations for Transmission Expansion Planning with FACTS Devices

Transmission Network Expansion Planning (TNEP) problems find the most economical way of expanding a given grid given long-term growth in generation capacity and demand patterns. The recent development of Flexible AC Transmission System (FACTS) devices, which can dynamically re-route power flows by adjusting individual branches' impedance, call for their integration into TNEP problems. However, the resulting TNEP+FACTS formulations are significantly harder to solve than traditional TNEP instances, due to the nonlinearity of FACTS behavior. This paper proposes a new mixed-integer formulation for TNEP+FACTS, which directly represents the change in power flow induced by individual FACTS devices. The proposed formulation uses an extended formulation and facet-defining constraints, which are stronger than big-M constraints typically used in the literature. The paper conducts numerical experiments on a synthetic model of the Texas system with high renewable penetration. The results demonstrate the computational superiority of the proposed approach, which achieves a 4x speedup over state-of-the-art formulations, and highlight the potential of FACTS devices to mitigate congestion.

eess.SY↗

arXiv2024

Bound Tightening using Rolling-Horizon Decomposition for Neural Network Verification

Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable their deployment in safety-critical applications. This paper introduces a new approach to neural network verification using a novel mixed-integer programming rolling-horizon decomposition method. The algorithm leverages the layered structure of neural networks, by employing optimization-based bound-tightening on smaller sub-graphs of the original network in a rolling-horizon fashion. This strategy strikes a balance between achieving tighter bounds and ensuring the tractability of the underlying mixed-integer programs. Extensive numerical experiments, conducted on instances from the VNN-COMP benchmark library, demonstrate that the proposed approach yields significantly improved bounds compared to existing effective bound propagation methods. Notably, the parallelizable nature of the proposed method proves effective in solving open verification problems. Our code is built and released as part of the open-source mathematical modeling tool Gravity (https://github.com/coin-or/Gravity), which is extended to support generic neural network models.

math.OC↗

arXiv2024

Dual Conic Proxies for AC Optimal Power Flow

In recent years, there has been significant interest in the development of machine learning-based optimization proxies for AC Optimal Power Flow (AC-OPF). Although significant progress has been achieved in predicting high-quality primal solutions, no existing learning-based approach can provide valid dual bounds for AC-OPF. This paper addresses this gap by training optimization proxies for a convex relaxation of AC-OPF. Namely, the paper considers a second-order cone (SOC) relaxation of AC-OPF, and proposes \revision{a novel architecture} that embeds a fast, differentiable (dual) feasibility recovery, thus providing valid dual bounds. The paper combines this new architecture with a self-supervised learning scheme, which alleviates the need for costly training data generation. Extensive numerical experiments on medium- and large-scale power grids demonstrate the efficiency and scalability of the proposed methodology.

cs.LG↗

arXiv2024

The Impact of Congestion and Dedicated Lanes on On-Demand Multimodal Transit Systems

Traffic congestion can have a detrimental effect on public transit systems, and understanding and mitigating these effects is of critical importance for effective public transportation. Implementing Dedicated Bus Lanes (DBLs) is a well-known intervention to achieve this goal. A DBL is a designated lane for bus transit, which avoids congestion and substantially lowers the travel time. This makes transit more attractive, encouraging more travelers to adopt public transportation. This paper studies the impact of congestion and DBLs on novel On-Demand Multimodal Transit Systems (ODMTS). ODMTS combine traditional rail and bus networks with on-demand shuttles. Previous case studies have shown that ODMTS may simultaneously improve travel time, reduce system cost, and attract new passengers. Those benefits were shown for an ideal world without traffic congestion, and this paper hypothesizes that the advantages of ODMTS can be even more pronounced in the real world. This paper explores this hypothesis by creating realistic congestion scenarios and solving bilevel optimization problems to design ODMTS under these scenarios. The impact of DBLs on ODMTS is evaluated with a comprehensive case study in the Metro Atlanta Area. The results show that DBLs can significantly improve travel times and are effective at increasing adoption of the system.

math.OC↗

arXiv2024

Path-Based Formulations for the Design of On-demand Multimodal Transit Systems with Adoption Awareness

This paper reconsiders the ODMTS Design with Adoptions problem (ODMTS-DA) to capture the latent demand in on-demand multimodal transit systems. The ODMTS-DA is a bilevel optimization problem, for which Basciftci and Van Hentenryck (2022) proposed an exact combinatorial Benders decomposition. Unfortunately, their proposed algorithm only finds high-quality solutions for medium-sized cities and is not practical for large metropolitan areas. The main contribution of this paper is to propose a new path-based optimization model, called P-Path, to address these computational difficulties. The key idea underlying P-Path is to enumerate two specific sets of paths which capture the essence of the choice model associated with the adoption behavior of riders. With the help of these path sets, the ODMTS-DA can be formulated as a single-level mixed-integer programming model. In addition, the paper presents preprocessing techniques that can reduce the size of the model significantly. P-Path is evaluated on two comprehensive case studies: the mid-size transit system of the Ann Arbor Ypsilanti region in Michigan (which was studied by Basciftci and Van Hentenryck (2022)) and the large-scale transit system for the city of Atlanta. The experimental results show that P-Path solves the Michigan ODMTS-DA instances in a few minutes, bringing more than two orders of magnitude improvements compared to the existing approach. For Atlanta, the results show that P-Path can solve large-scale ODMTS-DA instances (about 17 millions of variables and 37 millions of constraints) optimally in a few hours or in a few days. These results show the tremendous computational benefits of P-Path which provides a scalable approach to the design of on-demand multimodal transit systems with latent demand.

math.OC↗

arXiv2023

Multi-resolution spatio-temporal prediction with application to wind power generation

Wind energy is becoming an increasingly crucial component of a sustainable grid, but its inherent variability and limited predictability present challenges for grid operators. The energy sector needs novel forecasting techniques that can precisely predict the generation of renewable power and offer precise quantification of prediction uncertainty. This will facilitate well-informed decision-making by operators who wish to integrate renewable energy into the power grid. This paper presents a novel approach to wind speed prediction with uncertainty quantification using a multi-resolution spatio-temporal Gaussian process. By leveraging information from multiple sources of predictions with varying accuracies and uncertainties, the joint framework provides a more accurate and robust prediction of wind speed while measuring the uncertainty in these predictions. We assess the effectiveness of our proposed framework using real-world wind data obtained from the Midwest region of the United States. Our results demonstrate that the framework enables predictors with varying data resolutions to learn from each other, leading to an enhancement in overall predictive performance. The proposed framework shows a superior performance compared to other state-of-the-art methods. The goal of this research is to improve grid operation and management by aiding system operators and policymakers in making better-informed decisions related to energy demand management, energy storage system deployment, and energy supply scheduling. This results in potentially further integration of renewable energy sources into the existing power systems.

stat.AP↗

arXiv2023

Predict-Then-Optimize by Proxy: Learning Joint Models of Prediction and Optimization

Many real-world decision processes are modeled by optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. Recent works show that decision quality can be improved in this setting by solving and differentiating the optimization problem in the training loop, enabling end-to-end training with loss functions defined directly on the resulting decisions. However, this approach can be inefficient and requires handcrafted, problem-specific rules for backpropagation through the optimization step. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by predictive models. The approach is generic, and based on an adaptation of the Learning-to-Optimize paradigm, from which a rich variety of existing techniques can be employed. Experimental evaluations show the ability of several Learning-to-Optimize methods to provide efficient, accurate, and flexible solutions to an array of challenging Predict-Then-Optimize problems.

cs.LG↗

arXiv2023

Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks

The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they involve intricate, non-convex considerations related to Alternating Current (AC) power flow, which are essential for the safety and practicality of electrical grids. However, solving the OPF problem for varying conditions within stringent time frames poses practical challenges. To address this, operators resort to model simplifications of varying accuracy. Unfortunately, better approximations (tight convex relaxations) are often computationally intractable. This research explores machine learning (ML) to learn convex approximate solutions for faster analysis in the online setting while still allowing for coupling into other convex dependent decision problems. By trading off a small amount of accuracy for substantial gains in speed, they enable the efficient exploration of vast solution spaces in these complex problems.

cs.LG↗

arXiv2023

Real-Time Risk Analysis with Optimization Proxies

The increasing penetration of renewable generation and distributed energy resources requires new operating practices for power systems, wherein risk is explicitly quantified and managed. However, traditional risk-assessment frameworks are not fast enough for real-time operations, because they require numerous simulations, each of which requires solving multiple economic dispatch problems sequentially. The paper addresses this computational challenge by proposing proxy-based risk assessment, wherein optimization proxies are trained to learn the input-to-output mapping of an economic dispatch optimization solver. Once trained, the proxies make predictions in milliseconds, thereby enabling real-time risk assessment. The paper leverages self-supervised learning and end-to-end-feasible architecture to achieve high-quality sequential predictions. Numerical experiments on large systems demonstrate the scalability and accuracy of the proposed approach.

math.OC↗

arXiv2023

Asset Bundling for Wind Power Forecasting

The growing penetration of intermittent, renewable generation in US power grids, especially wind and solar generation, results in increased operational uncertainty. In that context, accurate forecasts are critical, especially for wind generation, which exhibits large variability and is historically harder to predict. To overcome this challenge, this work proposes a novel Bundle-Predict-Reconcile (BPR) framework that integrates asset bundling, machine learning, and forecast reconciliation techniques. The BPR framework first learns an intermediate hierarchy level (the bundles), then predicts wind power at the asset, bundle, and fleet level, and finally reconciles all forecasts to ensure consistency. This approach effectively introduces an auxiliary learning task (predicting the bundle-level time series) to help the main learning tasks. The paper also introduces new asset-bundling criteria that capture the spatio-temporal dynamics of wind power time series. Extensive numerical experiments are conducted on an industry-size dataset of 283 wind farms in the MISO footprint. The experiments consider short-term and day-ahead forecasts, and evaluates a large variety of forecasting models that include weather predictions as covariates. The results demonstrate the benefits of BPR, which consistently and significantly improves forecast accuracy over baselines, especially at the fleet level.

stat.ME↗

arXiv2023

MARTA Reach: Piloting an On-Demand Multimodal Transit System in Atlanta

This paper reports on the results of the six-month pilot MARTA Reach, which aimed to demonstrate the potential value of On-Demand Multimodal Transit Systems (ODMTS) in the city of Atlanta, Georgia. ODMTS take a transit-centric view by integrating on-demand services and traditional fixed routes in order to address the first/last mile problem. ODMTS combine fixed routes and on-demand shuttle services by design (not as an after-thought) into a transit system that offers a door-to-door multimodal service with fully integrated operations and fare structure. The paper fills a knowledge gap, i.e., the understanding of the impact, benefits, and challenges of deploying ODMTS in a city as complex as Atlanta, Georgia. The pilot was deployed in four different zones with limited transit options, and used on-demand shuttles integrated with the overall transit system to address the first/last mile problem. The paper describes the design and operations of the pilot, and presents the results in terms of ridership, quality of service, trip purposes, alternative modes of transportation, multimodal nature of trips, challenges encountered, and cost estimates. The main findings of the pilot are that Reach offered a highly valued service that performed a large number of trips that would have otherwise been served by ride-hailing companies, taxis, or personal cars. Moreover, the wide majority of Reach trips were multimodal, with connections to rail being most prominent.

cs.CY↗

arXiv2023

Constraint Programming to Improve Hub Utilization in Autonomous Transfer Hub Networks

The Autonomous Transfer Hub Network (ATHN) is one of the most promising ways to adapt self-driving trucks for the freight industry. These networks use autonomous trucks for the middle mile, while human drivers perform the first and last miles. This paper extends previous work on optimizing ATHN operations by including transfer hub capacities, which are crucial for labor planning and policy design. It presents a Constraint Programming (CP) model that shifts an initial schedule produced by a Mixed Integer Program to minimize the hub capacities. The scalability of the CP model is demonstrated on a case study at the scale of the United States, based on data provided by Ryder System, Inc. The CP model efficiently finds optimal solutions and lowers the necessary total hub capacity by 42%, saving $15.2M in annual labor costs. The results also show that the reduced capacity is close to a theoretical (optimistic) lower bound.

math.OC↗

arXiv2023

Modern Constraint Programming Education: Lessons for the Future

This paper details an outlook on modern constraint programming (CP) education through the lens of a CP instructor. A general overview of current CP courses and instructional methods is presented, with a focus on online and virtually-delivered courses. This is followed by a discussion of the novel approach taken to introductory CP education for engineering students at large scale at the Georgia Institute of Technology (Georgia Tech) in Atlanta, GA, USA. The paper summarizes important takeaways from the Georgia Tech CP course and ends with a discussion on the future of CP education. Some ideas for instructional methods, promotional methods, and organizational changes are proposed to aid in the long-term growth of CP education.

cs.CY↗