arXiv subjects

Pascal Van Hentenryck

Publications and source records attributed to Pascal Van Hentenryck.

At least 163 records · Page 9Linked to original sources

arXiv2020

Lagrangian Duality for Constrained Deep Learning

This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems which must be solved repeatedly and include hard physical and operational constraints. The paper also considers applications where the learning task must enforce constraints on the predictor itself, either because they are natural properties of the function to learn or because it is desirable from a societal standpoint to impose them. This paper demonstrates experimentally that Lagrangian duality brings significant benefits for these applications. In energy domains, the combination of Lagrangian duality and deep learning can be used to obtain state-of-the-art results to predict optimal power flows, in energy systems, and optimal compressor settings, in gas networks. In transprecision computing, Lagrangian duality can complement deep learning to impose monotonicity constraints on the predictor without sacrificing accuracy. Finally, Lagrangian duality can be used to enforce fairness constraints on a predictor and obtain state-of-the-art results when minimizing disparate treatments.

cs.LG↗

arXiv2020

Real-Time Dispatching of Large-Scale Ride-Sharing Systems: Integrating Optimization, Machine Learning, and Model Predictive Control

This paper considers the dispatching of large-scale real-time ride-sharing systems to address congestion issues faced by many cities. The goal is to serve all customers (service guarantees) with a small number of vehicles while minimizing waiting times under constraints on ride duration. This paper proposes an end-to-end approach that tightly integrates a state-of-the-art dispatching algorithm, a machine-learning model to predict zone-to-zone demand over time, and a model predictive control optimization to relocate idle vehicles. Experiments using historic taxi trips in New York City indicate that this integration decreases average waiting times by about 30% over all test cases and reaches close to 55% on the largest instances for high-demand zones.

math.OC↗

arXiv2020

Large-Scale Zone-Based Evacuation Planning: Models, Algorithms, and Evaluation

In zone-based evacuation planning, the region to evacuate is divided into zones and each zone must be assigned a path to safety and departure times along the path. Zone-based evacuations are highly desirable in practice because they allow emergency services to communicate evacuation orders and to control the evacuation more accurately. Zone-based evacuations may also be combined with contraflows (to maximize the network capacities) and may impose additional constraints on the evacuation path (e,g,. path convergence) and the departure times (e.g., non-preemption). This paper presents a systematic study large-scale zone-based evacuation planning, both from an effectiveness and a computational standpoint. It reviews existing optimization algorithms, and presents new ones, and evaluates them, on a real, large-scale case study, both from a macroscopic standpoint and through microscopic simulations under a variety of assumptions. The results provide some unique perspectives on the strengths and weaknesses of each approach and the implications of evacuation functionalities. The paper also suggests new directions for future research in zone-based evacuation and beyond in order to address the fundamental challenges by emergency services around the world.

math.OC↗

arXiv2020

Differentially Private Distributed Optimal Power Flow

Distributed algorithms enable private Optimal Power Flow (OPF) computations by avoiding the need in sharing sensitive information localized in algorithms sub-problems. However, adversaries can still infer this information from the coordination signals exchanged across iterations. This paper seeks formal privacy guarantees for distributed OPF computations and provides differentially private algorithms for OPF computations based on the consensus Alternating Direction Method of Multipliers (ADMM). The proposed algorithms attain differential privacy by introducing static and dynamic random perturbations of OPF sub-problem solutions at each iteration. These perturbations are Laplacian and designed to prevent the inference of sensitive information, as well as to provide theoretical privacy guarantees for ADMM sub-problems. Using a standard IEEE 118-node test case, the paper explores the fundamental trade-offs among privacy, algorithmic convergence, and optimality losses.

math.OC↗

arXiv2020

Differential Privacy for Stackelberg Games

This paper introduces a differentially private (DP) mechanism to protect the information exchanged during the coordination of sequential and interdependent markets. This coordination represents a classic Stackelberg game and relies on the exchange of sensitive information between the system agents. The paper is motivated by the observation that the perturbation introduced by traditional DP mechanisms fundamentally changes the underlying optimization problem and even leads to unsatisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg Mechanism (PPSM), a framework that enforces the notions of feasibility and fidelity of the privacy-preserving information to the original problem objective. PPSM complies with the notion of differential privacy and ensures that the outcomes of the privacy-preserving coordination mechanism are close-to-optimality for each agent. Experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the approach.

math.OC↗

arXiv2019

Bilevel Optimization for On-Demand Multimodal Transit Systems

This study explores the design of an On-Demand Multimodal Transit System (ODMTS) that includes segmented mode switching models that decide whether potential riders adopt the new ODMTS or stay with their personal vehicles. It is motivated by the desire of transit agencies to design their network by taking into account both existing and latent demand, as quality of service improves. The paper presents a bilevel optimization where the leader problem designs the network and each rider has a follower problem to decide her best route through the ODMTS. The bilevel model is solved by a decomposition algorithm that combines traditional Benders cuts with combinatorial cuts to ensure the consistency of mode choices by the leader and follower problems. The approach is evaluated on a case study using historical data from Ann Arbor, Michigan, and a user choice model based on the income levels of the potential transit riders.

math.OC↗

arXiv2019

Transfer-Expanded Graphs for On-Demand Multimodal Transit Systems

This paper considers a generalization of the network design problem for On-Demand Multimodal Transit Systems (ODMTS). An ODMTS consists of a selection of hubs served by high frequency buses, and passengers are connected to the hubs by on-demand shuttles which serve the first and last miles. This paper generalizes prior work by including three additional elements that are critical in practice. First, different frequencies are allowed throughout the network. Second, additional modes of transit (e.g., rail) are included. Third, a limit on the number of transfers per passenger is introduced. Adding a constraint to limit the number of transfers has a significant negative impact on existing Benders decomposition approaches as it introduces non-convexity in the subproblem. Instead, this paper enforces the limit through transfer-expanded graphs, i.e., layered graphs in which each layer corresponds to a certain number of transfers. A real-world case study is presented for which the generalized ODMTS design problem is solved for the city of Atlanta. The results demonstrate that exploiting the problem structure through transfer-expanded graphs results in significant computational improvements.

math.OC↗

arXiv2019

Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often needed to be solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the prior states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of widely adopted OPF linear DC approximation by at least two orders of magnitude.

eess.SP↗

arXiv2019

PPSM: A Privacy-Preserving Stackelberg Mechanism: Privacy Guarantees for the Coordination of Sequential Electricity and Gas Markets

This paper introduces a differentially private mechanism to protect the information exchanged during the coordination of the sequential market-clearing of electricity and natural gas systems. The coordination between these sequential and interdependent markets represents a classic Stackelberg game and relies on the exchange of sensitive information between the system agents, including the supply and demand bids in each market or the characteristics of the systems. The paper is motivated by the observation that traditional differential privacy mechanisms are unsuitable for the problem of interest: The perturbation introduced by these mechanisms fundamentally changes the underlying optimization problem and even leads to unsatisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg Mechanism (PPSM), a framework that enforces the notions of consistency and fidelity of the privacy-preserving information to the original problem objective. The PPSM has strong properties: It complies with the notion of differential privacy and ensures that the outcomes of the privacy-preserving coordination mechanisms are close-to-optimality for each agent. The fidelity property is analyzed by providing theoretical guarantees on the cost of privacy of PPSM and experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the approach.

eess.SY↗

arXiv2019

Optimization Models for Estimating Transit Network Origin-Destination Flows with AVL/APC Data

With the increasing adoption of Automatic Vehicle Location (AVL) and Automatic Passenger Count (APC) technologies by transit agencies, a massive amount of time-stamped and location-based passenger boarding and alighting count data can be collected on a continuous basis. The availability of such large-scale transit data offers new opportunities to produce estimates for Origin-Destination (O-D) flows, helping inform transportation planning and transit management. However, the state-of-the-art methodologies for AVL/APC data analysis mostly tackle the O-D flow estimation problem within routes and barely infer the transfer activities across the entire transit network. This paper proposes three optimization models to identify transfers and approximate network-level O-D flows by minimizing the deviations between estimated and observed proportions or counts of transferring passengers: A Quadratic Integer Program (QIP), a feasible rounding procedure for the Quadratic Convex Programming (QCP) relaxation of the QIP, and an Integer Program (IP). The inputs of the models are readily available by applying the various route-level flow estimation algorithms to the automatically collected AVL/APC data and the output of the models is a network O-D estimation at varying geographical resolutions. The optimization models were evaluated on a case study for Ann Arbor-Ypsilanti area in Michigan. The IP model outperforms the QCP approach in terms of accuracy and remains tractable from an efficiency standpoint, contrary to the QIP. Its estimated O-D matrix achieves an R-Squared metric of 95.57% at the Traffic Analysis Zone level and 92.39% at the stop level, compared to the ground-truth estimates inferred from the state-of-practice trip-chaining methods.

math.OC↗

arXiv2019

Distilling Black-Box Travel Mode Choice Model for Behavioral Interpretation

Machine learning has proved to be very successful for making predictions in travel behavior modeling. However, most machine-learning models have complex model structures and offer little or no explanation as to how they arrive at these predictions. Interpretations about travel behavior models are essential for decision makers to understand travelers' preferences and plan policy interventions accordingly. Therefore, this paper proposes to apply and extend the model distillation approach, a model-agnostic machine-learning interpretation method, to explain how a black-box travel mode choice model makes predictions for the entire population and subpopulations of interest. Model distillation aims at compressing knowledge from a complex model (teacher) into an understandable and interpretable model (student). In particular, the paper integrates model distillation with market segmentation to generate more insights by accounting for heterogeneity. Furthermore, the paper provides a comprehensive comparison of student models with the benchmark model (decision tree) and the teacher model (gradient boosting trees) to quantify the fidelity and accuracy of the students' interpretations.

stat.ML↗

arXiv2019

A Bid-Validity Mechanism for Sequential Heat and Electricity Market Clearing

Coordinating the operation of units at the interface between heat and electricity systems, such as combined heat and power plants and heat pumps, is essential to reduce inefficiencies in each system and help achieve a cost-effective and efficient operation of the overall energy system. These energy systems are currently operated by sequential markets, which interface the technical and economic aspects of the systems. In that context, this study introduces an electricity-aware heat unit commitment model, which seeks to optimize the operation of the heat system while accounting for the techno-economic interdependencies between heat and electricity markets. These interdependencies are represented by bid-validity constraints, which model the linkage between the heat and electricity outputs and costs of combined heat and power plants and heat pumps. This approach also constitutes a novel market mechanism for the coordination of heat and electricity systems, which defines heat bids conditionally on electricity prices. Additionally, a tractable reformulation of the resulting trilevel optimization problem as a mixed integer linear program is proposed. Finally, it is shown on a case study that the proposed model yields a 23% reduction in total operating cost and a 6% reduction in wind curtailment compared to a traditional decoupled unit commitment model.

eess.SY↗

arXiv2019

Shared E-scooters: Business, Pleasure, or Transit?

Shared e-scooters have become a familiar sight in many cities around the world. Yet the role they play in the mobility space is still poorly understood. This paper presents a study of the use of Bird e-scooters in the city of Atlanta. Starting with raw data which contains the location of available Birds over time, the study identifies trips and leverages the Google Places API to associate each trip origin and destination with a Point of Interest (POI). The resulting trip data is then used to understand the role of e-scooters in mobility by clustering trips using 10 collections of POIs, including business, food and recreation, parking, transit, health, and residential. The trips between these POI clusters reveal some surprising, albeit sensible, findings about the role of e-scooters in mobility, as well as the time of the day where they are most popular.

cs.CY↗

arXiv2019

An Exact and Scalable Problem Decomposition for Security-Constrained Optimal Power Flow

In this paper, we present decomposition techniques for solving large-scale instances of the security-constrained optimal power flow (SCOPF) problem with primary response. Specifically, under each contingency state, we require that the nodal demands are met and that the synchronized units generating below their limits follow a linear model for primary response. The resulting formulation is a mixed-integer linear program since the primary response model introduces disjunctions to the SCOPF problem. Unfortunately, exact methods relying on traditional Benders' decomposition do not scale well. As an alternative, we propose a decomposition scheme based on the column-and-constraint-generation algorithm where we iteratively add disjunctions and cuts. We provide procedures for preprocessing dedicated cuts and for numerically determining the post-contingency responses based on the master problem solutions. We also discuss heuristics to generate high-quality primal solutions and upper bounds for the method. Finally, we demonstrate the efficiency of the proposed method on large-scale systems.

math.OC↗

arXiv2019

Privacy-Preserving Obfuscation for Distributed Power Systems

This paper considers the problem of releasing privacy-preserving load data of a decentralized operated power system. The paper focuses on data used to solve Optimal Power Flow (OPF) problems and proposes a distributed algorithm that complies with the notion of Differential Privacy, a strong privacy framework used to bound the risk of re-identification. The problem is challenging since the application of traditional differential privacy mechanisms to the load data fundamentally changes the nature of the underlying optimization problem and often leads to severe feasibility issues. The proposed differentially private distributed algorithm is based on the Alternating Direction Method of Multipliers (ADMM) and guarantees that the released privacy-preserving data retains high fidelity and satisfies the AC power flow constraints. Experimental results on a variety of OPF benchmarks demonstrate the effectiveness of the approach.

math.OC↗

arXiv2019

The Commute Trip Sharing Problem

Parking pressure has been steadily increasing in cities as well as in university and corporate campuses. To relieve this pressure, this paper studies a car-pooling platform that would match riders and drivers, while guaranteeing a ride back and exploiting spatial and temporal locality. In particular, the paper formalizes the Commute Trip Sharing Problem (CTSP) to find a routing plan that maximizes ride sharing for a set of commute trips. The CTSP is a generalization of the vehicle routing problem with routes that satisfy time window, capacity, pairing, precedence, ride duration, and driver constraints. The paper introduces two exact algorithms for the CTPS: A route-enumeration algorithm and a branch-and-price algorithm. Experimental results show that, on a high-fidelity, real-world dataset of commute trips from a mid-size city, both algorithms optimally solve small and medium-sized problems and produce high-quality solutions for larger problem instances. The results show that car pooling, if widely adopted, has the potential to reduce vehicle usage by up to 57% and decrease vehicle miles traveled by up to 46% while only incurring a 22% increase in average ride time per commuter for the trips considered.

math.OC↗

arXiv2019

Privacy-Preserving Obfuscation of Critical Infrastructure Networks

The paper studies how to release data about a critical infrastructure network (e.g., the power network or a transportation network) without disclosing sensitive information that can be exploited by malevolent agents, while preserving the realism of the network. It proposes a novel obfuscation mechanism that combines several privacy-preserving building blocks with a bi-level optimization model to significantly improve accuracy. The obfuscation is evaluated for both realism and privacy properties on real energy and transportation networks. Experimental results show the obfuscation mechanism substantially reduces the potential damage of an attack exploiting the released data to harm the real network.

cs.CR↗

arXiv2019

Differential Privacy for Power Grid Obfuscation

The availability of high-fidelity energy networks brings significant value to academic and commercial research. However, such releases also raise fundamental concerns related to privacy and security as they can reveal sensitive commercial information and expose system vulnerabilities. This paper investigates how to release power networks where the parameters of transmission lines and transformers are obfuscated. It does so by using the framework of Differential Privacy (DP), that provides strong privacy guarantees and has attracted significant attention in recent years. Unfortunately, simple DP mechanisms often result in AC-infeasible networks. To address these concerns, this paper presents a novel differential privacy mechanism that guarantees AC-feasibility and largely preserves the fidelity of the obfuscated network. Experimental results also show that the obfuscation significantly reduces the potential damage of an attacker exploiting the release of the dataset.

cs.AI↗