arXiv subjects

Pascal Van Hentenryck

Publications and source records attributed to Pascal Van Hentenryck.

At least 181 records · Page 10Linked to original sources

arXiv2019

Assortment and Price Optimization Under the Two-Stage Luce model

This paper studies assortment and pricing optimization problems under the Two-Stage Luce model (2SLM), a discrete choice model introduced by Echenique and Saito (2018) that generalizes the multinomial logit model (MNL). The model employs an utility function as in the the MNL, and a dominance relation between products. When consumers are offered an assortmentS , they first discard all dominated products in S and then select one of the remaining products using the standard MNL. This model may violate the regularity condition, which states that the probability of choosing a product cannot increase if the offer set is enlarged. Therefore, the 2SLM falls outside the large family of discrete choice models based on random utility which contains almost all choice models studied in revenue management. We prove that the assortment problem under the 2SLM is polynomial-time solvable. Moreover, we show that the capacitated assortment optimization problem is NP-hard and but it admits polynomial-time algorithms for the relevant special cases cases where (1) the dominance relation is attractiveness-correlated and (2) its transitive reduction is a forest. The proofs exploit a strong connection between assortments under the 2SLM and independent sets in comparability graphs. Finally, we study the associated joint pricing and assortment problem under this model. First, we show that well known optimal pricing policy for the MNL can be arbitrarily bad. Our main result in this section is the development of an efficient algorithm for this pricing problem. The resulting optimal pricing strategy is simple to describe: it assigns the same price for all products, except for the one with the highest attractiveness and as well as for the one with the lowest attractiveness.

cs.DM↗

arXiv2019

Optimization of Structural Flood Mitigation Strategies

The dynamics of flooding are primarily influenced by the shape, height, and roughness (friction) of the underlying topography. For this reason, mechanisms to mitigate floods frequently employ structural measures that either modify topographic elevation, e.g., through the placement of levees and sandbags, or increase roughness, e.g., through revegetation projects. However, the configuration of these measures is typically decided in an ad hoc manner, limiting their overall effectiveness. The advent of high-performance surface water modeling software and improvements in black-box optimization suggest that a more principled design methodology may be possible. This paper proposes a new computational approach to the problem of designing structural mitigation strategies under physical and budgetary constraints. It presents the development of a problem discretization amenable to simulation-based, derivative-free optimization. However, meta-heuristics alone are found to be insufficient for obtaining quality solutions in a reasonable amount of time. As a result, this paper proposes novel numerical and physics-based procedures to improve convergence to a high-quality mitigation. The efficiency of the approach is demonstrated on hypothetical dam break scenarios of varying complexity under various mitigation budget constraints. In particular, experimental results show that, on average, the final proposed algorithm results in a 65% improvement in solution quality compared to a direct implementation.

math.OC↗

arXiv2019

Modeling Stated Preference for Mobility-on-Demand Transit: A Comparison of Machine Learning and Logit Models

Logit models are usually applied when studying individual travel behavior, i.e., to predict travel mode choice and to gain behavioral insights on traveler preferences. Recently, some studies have applied machine learning to model travel mode choice and reported higher out-of-sample predictive accuracy than traditional logit models (e.g., multinomial logit). However, little research focuses on comparing the interpretability of machine learning with logit models. In other words, how to draw behavioral insights from the high-performance "black-box" machine-learning models remains largely unsolved in the field of travel behavior modeling. This paper aims at providing a comprehensive comparison between the two approaches by examining the key similarities and differences in model development, evaluation, and behavioral interpretation between logit and machine-learning models for travel mode choice modeling. To complement the theoretical discussions, the paper also empirically evaluates the two approaches on the stated-preference survey data for a new type of transit system integrating high-frequency fixed-route services and ridesourcing. The results show that machine learning can produce significantly higher predictive accuracy than logit models. Moreover, machine learning and logit models largely agree on many aspects of behavioral interpretations. In addition, machine learning can automatically capture the nonlinear relationship between the input features and choice outcomes. The paper concludes that there is great potential in merging ideas from machine learning and conventional statistical methods to develop refined models for travel behavior research and suggests some new research directions.

cs.LG↗

arXiv2019

Modeling Heterogeneity in Mode-Switching Behavior Under a Mobility-on-Demand Transit System: An Interpretable Machine Learning Approach

Recent years have witnessed an increased focus on interpretability and the use of machine learning to inform policy analysis and decision making. This paper applies machine learning to examine travel behavior and, in particular, on modeling changes in travel modes when individuals are presented with a novel (on-demand) mobility option. It addresses the following question: Can machine learning be applied to model individual taste heterogeneity (preference heterogeneity for travel modes and response heterogeneity to travel attributes) in travel mode choice? This paper first develops a high-accuracy classifier to predict mode-switching behavior under a hypothetical Mobility-on-Demand Transit system (i.e., stated-preference data), which represents the case study underlying this research. We show that this classifier naturally captures individual heterogeneity available in the data. Moreover, the paper derives insights on heterogeneous switching behaviors through the generation of marginal effects and elasticities by current travel mode, partial dependence plots, and individual conditional expectation plots. The paper also proposes two new model-agnostic interpretation tools for machine learning, i.e., conditional partial dependence plots and conditional individual partial dependence plots, specifically designed to examine response heterogeneity. The results on the case study show that the machine-learning classifier, together with model-agnostic interpretation tools, provides valuable insights on travel mode switching behavior for different individuals and population segments. For example, the existing drivers are more sensitive to additional pickups than people using other travel modes, and current transit users are generally willing to share rides but reluctant to take any additional transfers.

cs.LG↗

arXiv2019

Unit Commitment With Gas Network Awareness

Recent changes in the fuel mix for electricity generation and, in particular, the increase in Gas-Fueled Power Plants (GFPP), have created significant interdependencies between the electrical power and natural gas transmission systems. However, despite their physical and economic couplings, these networks are still operated independently, with asynchronous market mechanisms. This mode of operation may lead to significant economic and reliability risks in congested environments as revealed by the 2014 polar vortex event experienced by the northeastern United States. To mitigate these risks, while preserving the current structure of the markets, this paper explores the idea of introducing gas network awareness into the standard unit commitment model. Under the assumption that the power system operator has some (or full) knowledge of gas demand forecast and the gas network, the paper proposes a tri-level mathematical program where natural gas zonal prices are given by the dual solutions of natural-gas flux conservation constraints and commitment decisions are subject to bid-validity constraints that ensure the economic viability of the committed GFPPs. This tri-level program can be reformulated as a single-level Mixed-Integer Second-Order Cone program which can then be solved using a dedicated Benders decomposition. The approach is validated on a case study for the Northeastern United States [1] that can reproduce the gas and electricity price spikes experienced during the early winter of 2014. The results on the case study demonstrate that gas awareness in unit commitment is instrumental in avoiding the peaks in electricity prices while keeping the gas prices to reasonable levels.

math.OC↗

arXiv2019

Mobility-on-demand versus fixed-route transit systems: an evaluation of traveler preferences in low-income communities

Emerging transportation technologies, such as ride-hailing and autonomous vehicles, are disrupting the transportation sector and transforming public transit. Some transit observers envision future public transit to be integrated transit systems with fixed-route services running along major corridors and on-demand ridesharing services covering lower-density areas. A switch from a conventional fixed-route service model to this kind of integrated mobility-on-demand transit system, however, may elicit varied responses from local residents. This paper evaluates traveler preferences for a proposed integrated mobility-on-demand transit system versus the existing fixed-route system, with a particular focus on disadvantaged travelers. We conducted a survey in two low-resource communities in the United States, namely, Detroit and Ypsilanti, Michigan. A majority of survey respondents preferred a mobility-on-demand transit system over a fixed-route one. Based on ordered logit model outputs, we found a stronger preference for mobility-on-demand transit among males, college graduates, individuals who have never heard of or used ride-hailing before, and individuals who currently receive inferior transit services. By contrast, preferences varied little by age, income, race, or disability status. The most important benefit of a mobility-on-demand transit system perceived by the survey respondents is enhanced transit accessibility to different destinations, whereas their major concerns include the need to actively request rides, possible transit-fare increases, and potential technological failures. Addressing the concerns of female riders and accommodating the needs of less technology-proficient individuals should be major priorities for transit agencies that are considering mobility-on-demand initiatives.

stat.AP↗

arXiv2018

OptStream: Releasing Time Series Privately

Many applications of machine learning and optimization operate on data streams. While these datasets are fundamental to fuel decision-making algorithms, often they contain sensitive information about individuals and their usage poses significant privacy risks. Motivated by an application in energy systems, this paper presents OPTSTREAM, a novel algorithm for releasing differentially private data streams under the w-event model of privacy. OPTSTREAM is a 4-step procedure consisting of sampling, perturbation, reconstruction, and post-processing modules. First, the sampling module selects a small set of points to access in each period of interest. Then, the perturbation module adds noise to the sampled data points to guarantee privacy. Next, the reconstruction module reassembles non-sampled data points from the perturbed sample points. Finally, the post-processing module uses convex optimization over the private output of the previous modules, as well as the private answers of additional queries on the data stream, to improve accuracy by redistributing the added noise. OPTSTREAM is evaluated on a test case involving the release of a real data stream from the largest European transmission operator. Experimental results show that OPTSTREAM may not only improve the accuracy of state-of-the-art methods by at least one order of magnitude but also supports accurate load forecasting on the private data.

cs.CR↗

arXiv2018

Phase Transitions for Optimality Gaps in Optimal Power Flows A Study on the French Transmission Network

This paper investigates phase transitions on the optimality gaps in Optimal Power Flow (OPF) problem on real-world power transmission systems operated in France. The experimental results study optimal power flow solutions for more than 6000 scenarios on the networks with various load profiles, voltage feasibility regions, and generation capabilities. The results show that bifurcations between primal solutions and the QC, SOCP, and SDP relaxation techniques frequently occur when approaching congestion points. Moreover, the results demonstrate the existence of multiple bifurcations for certain scenarios when load demands are increased uniformly. Preliminary analysis on these bifurcations were performed.

math.OC↗

arXiv2018

DistFlow Extensions for AC Transmission Systems

Convex relaxations of the power flow equations and, in particular, the Semi-Definite Programming (SDP), Second-Order Cone (SOC), and Convex DistFlow (CDF) relaxations, have attracted significant interest in recent years. Thus far, studies of the CDF model and its connection to the other relaxations have been limited to power distribution systems, which omit several parameters necessary for modeling transmission systems. To increase the applicability of the CDF relaxation, this paper develops an extended CDF model that is suitable for transmission systems by incorporating bus shunts, line charging, and transformers. Additionally, a theoretical result shows that the established equivalence of the SOC and CDF models for distribution systems also holds in this transmission system extension.

math.OC↗

arXiv2018

Communication-Constrained Expansion Planning for Resilient Distribution Systems

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes impor- tant to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustains their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communi- cation Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connec- tivity of the smart grid components, and a set of scenarios which specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC which features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster inten- sities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach.

math.OC↗

arXiv2017

Constraint and Mathematical Programming Models for Integrated Port Container Terminal Operations

This paper considers the integrated problem of quay crane assignment, quay crane scheduling, yard location assignment, and vehicle dispatching operations at a container terminal. The main objective is to minimize vessel turnover times and maximize the terminal throughput, which are key economic drivers in terminal operations. Due to their computational complexities, these problems are not optimized jointly in existing work. This paper revisits this limitation and proposes Mixed Integer Programming (MIP) and Constraint Programming (CP) models for the integrated problem, under some realistic assumptions. Experimental results show that the MIP formulation can only solve small instances, while the CP model finds optimal solutions in reasonable times for realistic instances derived from actual container terminal operations.

cs.AI↗

arXiv2017

Popularity Signals in Trial-Offer Markets with Social Influence and Position Bias

This paper considers trial-offer markets where consumer preferences are modeled by a multinomial logit with social influence and position bias. The social signal for a product is given by its current market share raised to power r (or equivalently the number of purchases raised to the power of r). The paper shows that, when r is strictly between 0 and 1, and a static position assignment (e.g., a quality ranking) is used, the market converges to a unique equilibrium where the market shares depend only on product quality, not their initial appeals or the early dynamics. When r is greater than 1, the market becomes unpredictable. In many cases, the market goes to a monopoly for some product: Which product becomes a monopoly depends on the initial conditions of the market. These theoretical results are complemented by an agent-based simulation which indicates that convergence is fast when r is between 0 and 1, and that the quality ranking dominates the well-known popularity ranking in terms of market efficiency. These results shed a new light on the role of social influence which is often blamed for unpredictability, inequalities, and inefficiencies in markets. In contrast, this paper shows that, with a proper social signal and position assignment for the products, the market becomes predictable, and inequalities and inefficiencies can be controlled appropriately.

cs.SI↗

arXiv2017

Expecting to be HIP: Hawkes Intensity Processes for Social Media Popularity

Modeling and predicting the popularity of online content is a significant problem for the practice of information dissemination, advertising, and consumption. Recent work analyzing massive datasets advances our understanding of popularity, but one major gap remains: To precisely quantify the relationship between the popularity of an online item and the external promotions it receives. This work supplies the missing link between exogenous inputs from public social media platforms, such as Twitter, and endogenous responses within the content platform, such as YouTube. We develop a novel mathematical model, the Hawkes intensity process, which can explain the complex popularity history of each video according to its type of content, network of diffusion, and sensitivity to promotion. Our model supplies a prototypical description of videos, called an endo-exo map. This map explains popularity as the result of an extrinsic factor - the amount of promotions from the outside world that the video receives, acting upon two intrinsic factors - sensitivity to promotion, and inherent virality. We use this model to forecast future popularity given promotions on a large 5-months feed of the most-tweeted videos, and found it to lower the average error by 28.6% from approaches based on popularity history. Finally, we can identify videos that have a high potential to become viral, as well as those for which promotions will have hardly any effect.

cs.SI↗

arXiv2017

Resilient Transmission Grid Design: AC Relaxation vs. DC approximation

As illustrated in recent years (Superstorm Sandy, the Northeast Ice Storm of 1998, etc.), extreme weather events pose an enormous threat to the electric power transmission systems and the associated socio-economic systems that depend on reliable delivery of electric power. Besides inevitable malfunction of power grid components, deliberate malicious attacks can cause high risks to the service. These threats motivate the need for approaches and methods that improve the resilience of power systems. In this paper, we develop a model and tractable methods for optimizing the upgrade of transmission systems through a combination of hardening existing components, adding redundant lines, switches, generators, and FACTS and phase-shifting devices. While many of these controllable components are included in traditional design (expansion planning) problems, we uniquely assess their benefits from a resiliency point of view. More importantly, perhaps, we evaluate the suitability of using state-of-the-art AC power flow relaxations versus the common DC approximation in resilience improvement studies. The resiliency model and algorithms are tested on a modified version of the RTS-96 (single area) system.

math.OC↗

arXiv2017

Graphical Models and Belief Propagation-hierarchy for Optimal Physics-Constrained Network Flows

In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network flow type with additional constraints related to the physics of the flow. We illustrate the general concepts on a number of enabling examples from power system and natural gas transmission (continental scale) and distribution (district scale) systems.

eess.SY↗

arXiv2016

Trial-Offer Markets with Continuation

Trial-offer markets, where customers can sample a product before deciding whether to buy it, are ubiquitous in the online experience. Their static and dynamic properties are often studied by assuming that consumers follow a multinomial logit model and try exactly one product. In this paper, we study how to generalize existing results to a more realistic setting where consumers can try multiple products. We show that a multinomial logit model with continuation can be reduced to a standard multinomial logit model with different appeal and product qualities. We examine the consequences of this reduction on the performance and predictability of the market, the role of social influence, and the ranking policies.

cs.GT↗

arXiv2016

Graphical Models for Optimal Power Flow

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for "smart grid" applications like control of distributed energy resources. We evaluate our technique numerically on several benchmark networks and show that practical OPF problems can be solved effectively using this approach.

eess.SY↗

arXiv2016

Interdependent Scheduling Games

We propose a model of interdependent scheduling games in which each player controls a set of services that they schedule independently. A player is free to schedule his own services at any time; however, each of these services only begins to accrue reward for the player when all predecessor services, which may or may not be controlled by the same player, have been activated. This model, where players have interdependent services, is motivated by the problems faced in planning and coordinating large-scale infrastructures, e.g., restoring electricity and gas to residents after a natural disaster or providing medical care in a crisis when different agencies are responsible for the delivery of staff, equipment, and medicine. We undertake a game-theoretic analysis of this setting and in particular consider the issues of welfare maximization, computing best responses, Nash dynamics, and existence and computation of Nash equilibria.

cs.GT↗