Probably Approximately Correct Nash Equilibrium Learning

We consider a multi-agent noncooperative game with agents' objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We treat the Nash equilibrium computation problem within the realm of probably approximately correct (PAC) learning. Building upon recent developments in scenario-based optimization, we accompany the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected (in probabilistic terms) when a new uncertainty realization is encountered. For a wide class of games, we also show that the computation of the so called compression set - a key concept in scenario-based optimization - can be directly obtained as a byproduct of the proposed solution methodology. Finally, we illustrate how to overcome differentiability issues, arising due to the introduction of scenarios, and compute a Nash equilibrium solution in a decentralized manner. We demonstrate the efficacy of the proposed approach on an electric vehicle charging control problem.Comment: Preprint submitted to IEEE Transactions on Automatic Contro

Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services

This study develops an online predictive optimization framework for dynamically operating a transit service in an area of crowd movements. The proposed framework integrates demand prediction and supply optimization to periodically redesign the service routes based on recently observed demand. To predict demand for the service, we use Quantile Regression to estimate the marginal distribution of movement counts between each pair of serviced locations. The framework then combines these marginals into a joint demand distribution by constructing a Gaussian copula, which captures the structure of correlation between the marginals. For supply optimization, we devise a linear programming model, which simultaneously determines the route structure and the service frequency according to the predicted demand. Importantly, our framework both preserves the uncertainty structure of future demand and leverages this for robust route optimization, while keeping both components decoupled. We evaluate our framework using a real-world case study of autonomous mobility in a university campus in Denmark. The results show that our framework often obtains the ground truth optimal solution, and can outperform conventional methods for route optimization, which do not leverage full predictive distributions.Comment: 34 pages, 12 figures, 5 table

Dynamic vehicle routing problems: Three decades and counting

Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are (1) type of problem, (2) logistical context, (3) transportation mode, (4) objective function, (5) fleet size, (6) time constraints, (7) vehicle capacity constraints, (8) the ability to reject customers, (9) the nature of the dynamic element, (10) the nature of the stochasticity (if any), and (11) the solution method. We comment on technological vis-à-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics.© 2015 Wiley Periodicals, Inc

An event-driven optimization framework for dynamic vehicle routing

International audienceThe real-time operation of a fleet of vehicles introduces challenging optimization problems. In this work, we propose an event-driven framework which anticipates unknown changes arising in the context of dynamic vehicle routing. The framework is intrinsically parallelized to take advantage of modern multi-core and multi-threaded computing architectures. It is also designed to be easily embeddable in decision support systems that cope with a wide range of contexts and side constraints. We illustrate the flexibility of the framework by showing how it can be adapted to tackle the dynamic vehicle routing problem with stochastic demands

Overweight Vehicle Permitting Alternatives

Overweight vehicles exceed the federal and/or state statutory limits for either the gross vehicle weight (GVW) or the weight of individual axles or axle groups. National and state limits on vehicle weights were established to preserve the highway infrastructure. Past research has shown that overweight operations, while causing significant damage to roads and bridges, can enhance the trucking industry productivity, and thus yield economic benefits both regionally and nationally. In the United States, individual states administer oversize and overweight vehicle permit programs to regulate and collect revenues from overweight operations. Differences in the truck size and weight limits and overweight permit programs across the states inhibit seamless and efficient truck travel across the country. Agencies responsible for maintaining the highway infrastructure realize that the cost of consumption of the infrastructure far exceeds the collected revenues. The current study examines four options to improve overweight vehicle permitting systems: multiobjective optimization of traditional mechanisms, incentives for infrastructure-friendly vehicles, application of an auction-based quota for overweight vehicle operations, and opportunities for harmonizing the regulations covering overweight vehicle operations that differ across the states. The first three options are qualitatively and quantitatively applied to a case study involving Indiana\u27s newly-established overweight commodity permits for vehicles carrying metal (up to 120,000 lbs), and agricultural (up to 97,000 lbs) goods. An incremental approach to harmonization of truck size and weight regulations and overweight vehicle permitting systems is qualitatively described, including available tools and data needs to promote harmonization. The four options are not mutually exclusive; collectively, they provide opportunities for transportation decision makers to improve overweight vehicle permitting. Each option contributes to the ongoing discussion about how to address the issue of uncompensated consumption of highway infrastructure assets attributable to overweight vehicles. The multiobjective optimization formulated herein better reflects actual decisions made by both the agency and carriers than limited previous quantitative research. The quantification of willingness to pay for investment informs state agencies about the extent to which incentives for infrastructure-friendly vehicles can be adopted. The quota framework contained herein is an extension of strategies used previously to mitigate demand into a tool for controlling the amount of allowable infrastructure damage while collecting necessary revenues to protect infrastructure from undue damage. Finally, the harmonization of overweight vehicle permitting programs can streamline interstate overweight operations for both state agencies and carriers. The combination of several options can result in greater improvements to both the trucking industry\u27s productivity and the preservation of highway infrastructure than any option alone

On the potential contribution of rooftop PV to a sustainable electricity mix: the case of Spain

This work evaluates the potential contribution of rooftop PV to the future electricity mix. Several sustainable scenarios are considered, each comprising different shares of centralized renewables, rooftop PV and storage. For each generation scenario, the storage capacity that balances the net hourly demand is determined, and the portfolio combination that minimizes the cost of supplying electricity is obtained. The analysis is applied to mainland Spain, using public information and detailed granular models, both in time (hourly resolution) and space (municipal level). For the Spanish case, when the flexibility of hydro and biomass generation is taken into account, the least-cost portfolio involves rather modest storage capacities, in the order of daily rather than seasonal values. This shows that a sustainable, almost emissions-free electricity system for Spain is possible, at a cost that can be even lower than current wholesale market prices.Comment: 7 tables & 11 figures in the main body (24 pages), and 13 pages for the supplementary material, wit

Technical, economic and energetic competitiveness of rail-road combined transport: evaluation of the effects of possible ITS applications on intermodal terminal.

L'abstract è presente nell'allegato / the abstract is in the attachmen

Cooperation or Coordination of Underwater Glider Networks? An Assessment from Observing System Simulation Experiments in the Ligurian Sea

Abstract The coordinated and cooperative-unaware networking of glider fleets have been proposed to obtain a performance gain in ocean sampling over naïve collective behavior. Whether one of these implementations results in a more efficient sampling of the ocean variability remains an open question. This article aims at a performance evaluation of cooperative-unaware and coordinated networks of gliders to reduce the uncertainty in operational temperature model predictions. The evaluation is based on an observing system simulation experiment (OSSE) implemented in the northern Ligurian Sea (western Mediterranean) from 21 August to 1 September 2010. The OSSE confronts the forecast skills obtained by the Regional Ocean Modeling System (ROMS) when assimilating data gathered from a cooperative and unaware network of three gliders with the prediction skill obtained when data comes from a coordinated configuration. An asynchronous formulation of the ensemble Kalman filter with a 48-h window is used to assimilate simulated temperature observations. Optimum sampling strategies of the glider networks, based on a pattern search optimization algorithm, are computed for each 48-h forecasting period using a covariance integrated in time and in the vertical direction to reduce the dimensionality of the problem and to enable a rapid resolution. Perturbations of the depth-averaged current field in glider motions are neglected. Results indicate a better performance of the coordinated network configuration due to an enhanced capacity to capture an eddy structure that is responsible for the largest forecast error in the experimental domain