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Ben-Tal A.,Technion - Israel Institute of Technology | Brekelmans R.,University of Tilburg | Den Hertog D.,University of Tilburg | Vial J.-P.,Ordecsys
INFORMS Journal on Computing | Year: 2017

Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in their parameters. The classical robust counterpart of a problem requires the solution to be feasible for all uncertain parameter values in a so-called uncertainty set and offers no guarantees for parameter values outside this uncertainty set. The globalized robust counterpart (GRC) extends this idea by allowing controlled constraint violations in a larger uncertainty set. The constraint violations are controlled by the distance of the parameter from the original uncertainty set. We derive tractable GRCs that extend the initial GRCs in the literature: our GRC is applicable to nonlinear constraints instead of only linear or conic constraints, and the GRC is more flexible with respect to both the uncertainty set and distance measure function, which are used to control the constraint violations. In addition, we present a GRC approach that can be used to provide an extended trade-off overview between the objective value and several robustness measures. © 2017 INFORMS.

Holden P.B.,Open University Milton Keynes | Edwards N.R.,Open University Milton Keynes | Garthwaite P.H.,Open University Milton Keynes | Fraedrich K.,Max Planck Institute for Meteorology | And 6 more authors.
Geoscientific Model Development | Year: 2014

Many applications in the evaluation of climate impacts and environmental policy require detailed spatiooral projections of future climate. To capture feedbacks from impacted natural or socio-economic systems requires interactive two-way coupling, but this is generally computationally infeasible with even moderately complex general circulation models (GCMs). Dimension reduction using emulation is one solution to this problem, demonstrated here with the GCM PLASIM-ENTS (Planet Simulator coupled with the efficient numerical terrestrial scheme). Our approach generates temporally evolving spatial patterns of climate variables, considering multiple modes of variability in order to capture non-linear feedbacks. The emulator provides a 188-member ensemble of decadally and spatially resolved (∼ 5° resolution) seasonal climate data in response to an arbitrary future CO2 concentration and non-CO 2 radiative forcing scenario. We present the PLASIM-ENTS coupled model, the construction of its emulator from an ensemble of transient future simulations, an application of the emulator methodology to produce heating and cooling degree-day projections, the validation of the simulator (with respect to empirical data) and the validation of the emulator (with respect to high-complexity models). We also demonstrate the application to estimates of sea-level rise and associated uncertainty. Copyright © 2014 by ASME.

Liao S.,École Centrale Paris | Liao S.,Ecole Polytechnique Federale de Lausanne | Van Delft C.,HEC | Vial J.-P.,Ordecsys
Optimization Methods and Software | Year: 2013

Call centre scheduling aims to determine the workforce so as to meet target service levels. The service level depends on the mean rate of arrival calls, which fluctuates during the day, and from day to day. The staff schedule must adjust the workforce period per period during the day, but the flexibility in doing so is limited by the workforce organization by shifts. The challenge is to balance salary costs and possible failures to meet service levels. In this paper, we consider uncertain arrival rates, that vary according to an intra-day seasonality and a global busyness factor. Both factors (seasonal and global) are estimated from past data and are subject to errors. We propose an approach combining stochastic programming and distributionally robust optimization to minimize the total salary costs under service level constraints. The performance of the robust solution is simulated via Monte-Carlo techniques and compared to the solution based on pure stochastic programming. © 2013 Copyright Taylor and Francis Group, LLC.

Babonneau F.,ORDECSYS | Babonneau F.,Ecole Polytechnique Federale de Lausanne | Haurie A.,ORDECSYS | Loulou R.,KANLO Consultants | Vielle M.,Ecole Polytechnique Federale de Lausanne
Environmental Modeling and Assessment | Year: 2012

In this paper, we explore the impact of several sources of uncertainties on the assessment of energy and climate policies when one uses in a harmonized way stochastic programming in a large-scale bottom-up (BU) model and Monte Carlo simulation in a large-scale top-down (TD) model. The BU model we use is the TIMES Integrated Assessment Model, which is run in a stochastic programming version to provide a hedging emission policy to cope with the uncertainty characterizing climate sensitivity. The TD model we use is the computable general equilibrium model GEMINI-E3. Through Monte Carlo simulations of randomly generated uncertain parameter values, one provides a stochastic micro- and macro-economic analysis. Through statistical analysis of the simulation results, we analyse the impact of the uncertainties on the policy assessment. © 2011 Springer Science+Business Media B.V.

Babonneau F.,ORDECSYS | Babonneau F.,Ecole Polytechnique Federale de Lausanne | Haurie A.,ORDECSYS | Vielle M.,Ecole Polytechnique Federale de Lausanne
Computational Management Science | Year: 2013

This paper deals with an application of the robust equilibrium concept in game theory to the assessment of the possible international agreement on climate that could be achieved in the conference of the parties negotiations organized by the UNFCCC. It is shown in particular that an acceptable, self-enforcing agreement could be obtained to maintain the temperature rise below 2°C at the end of twenty-first century, with a balanced welfare loss among 11 groups of countries representing the parties limited to 1.8 % of their total discounted household consumption. To design this possible agreement we use a reduced order meta game where the players are the 11 groups of countries considered as the parties in negotiation, the strategies are the supply of emission quotas on an international emissions trading system and the payoffs are the net gains obtained from the emissions, trading and changes in the terms of trade minus the damage cost associated with the cumulative emissions during the 2010-2050 period. To identify the abatement costs that serve in the calculation of the payoffs and the gains due changes of terms of trade we use a statistical emulation of the GEMINI-E3 macroeconomic model. To obtain surrogate damage cost functions we introduce a coupled constraint in the game, imposing a limit to the cumulative emissions of all parties, which we call the global safety emissions budget. The multipliers intervening in the equilibrium necessary conditions are then interpreted as marginal damage costs. Games with coupled constraints admit a manifold of normalized equilibria and we show that they correspond to equilibria in games where each player is constrained by a given share of the safety emissions budget. Among all the normalized equilibria we look for the one which minimizes the maximum welfare loss, expressed in percentage of household consumption, among the 11 groups of countries. To take into account the uncertainty created by the statistical emulation approach and the approximate description of the emissions trading system we introduce robustness in the equilibrium computation. © 2013 Springer-Verlag Berlin Heidelberg.

Babonneau F.,ORDECSYS | Babonneau F.,Ecole Polytechnique Federale de Lausanne | Nesterov Y.,Catholic University of Louvain | Vial J.-P.,ORDECSYS
Operations Research | Year: 2012

Problems dealing with the design and operations of gas transmission networks are challenging. The standard approaches lead to a difficult nonlinear nonconvex optimization problem. To get around this difficulty, we use a minimum energy principle to define stationary flows in the network. This solution minimizes the total energy dissipated in the system. We extend the minimization process to the choice of suitable diameters on the reinforcing arcs and add a constraint that limits the monetary cost of investment and of purchase and delivery of gas. Under a suitable and acceptable approximation of the structure of the investment cost function, the new problem turns out to be convex and tractable even for very large networks. © 2012 INFORMS.

Ben-Tal A.,Technion - Israel Institute of Technology | Ben-Tal A.,University of Tilburg | den Hertog D.,University of Tilburg | Vial J.-P.,Ordecsys
Mathematical Programming | Year: 2014

In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Conveniently, these two computations are completely independent. This approach has several advantages. First, it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. We also study some cases where the inequality is nonconcave in the uncertain parameters. © 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

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