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Minimizing Energy Costs in Federated Datacenters Under Uncertain Green Energy Availability

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Minimizing Energy Costs in Federated Datacenters Under Uncer...

International Conference on Transparent Optical Networks

作者： M. Ruiz A. Asensio L. Velasco Optical Communications Group (GCO) Universitat Politecnica de Catalunya (UPC) Barcelona Spain

ISBN: (纸本)9781479956029

The cost of energy represents, by far, the largest fraction of total operational expenditures that datacenter operators ought to face. For this very reason, several studies have focused on evaluating how such energy costs can be reduced and on quantifying that reduction;using green energy sources (e.g. solar) that can be generated by installing infrastructures nearby datacenters is clearly an interesting option. Assuming that green energy is available, workloads consolidation in those datacenters with the highest amount of self-generated energy allows reducing remarkably the consumption of brown energy. Workload management is of paramount importance to increase green energy consumption in the context of distributed datacenters. In that scenario, a centralized and orchestrated operation leads to large energy cost savings. To this end, we firstly present a model to estimate the amount of green energy produced in each location as a function of the specific time period and the expected weather conditions. Next, the problem of minimizing energy costs by properly placing workloads in federated datacenters under uncertainty in the availability of green energy in each location is faced using stochastic programming techniques. Illustrative numerical results validate the usefulness of the proposed stochastic approach.

关键词： federated datacenters green energy energy minimization statistical models stochastic programming

An improved benders decomposition algorithm for steady-state dispatch problem in an integrated electricity-gas system

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arXiv 2020年

作者： Gao, Han Li, Zhengshuo School of Electrical Engineering Shandong University Jinan China

Optimally operating an integrated electricity-gas system (IEGS) is significant for the energy sector. However, the IEGS operation model’s nonconvexity makes it challenging to solve the optimal dispatch problem in the IEGS. This letter proposes an improved Benders decomposition (IBD) algorithm catering to a commonly used steady-state dispatch model of the IEGS. This IBD algorithm leverages a refined decomposition structure where the subproblems become linear and ready to be solved in parallel. We analytically compare our IBD algorithm with an existing Benders decomposition algorithm and a typical piecewise linearization method. Case studies have substantiated the higher computational efficiency of our IBD algorithm. © 2020, CC BY.

关键词： stochastic programming

Conic Reformulations for Kullback-Leibler Divergence Constrained Distributionally Robust Optimization and Applications

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arXiv 2020年

作者： Kocuk, Burak Industrial Engineering Program Faculty of Engineering and Natural Sciences Sabancı University Istanbul Turkey

In this paper, we consider a distributionally robust optimization (DRO) model in which the ambiguity set is defined as the set of distributions whose Kullback-Leibler (KL) divergence to an empirical distribution is bounded. Utilizing the fact that KL divergence is an exponential cone representable function, we obtain the robust counterpart of the KL divergence constrained DRO problem as a dual exponential cone constrained program under mild assumptions on the underlying optimization problem. The resulting conic reformulation of the original optimization problem can be directly solved by a commercial conic programming solver. We specialize our generic formulation to two classical optimization problems, namely, the Newsvendor Problem and the Uncapacitated Facility Location Problem. Our computational study in an out-of-sample analysis shows that the solutions obtained via the DRO approach yield significantly better performance in terms of the dispersion of the cost realizations while the central tendency deteriorates only slightly compared to the solutions obtained by stochastic programming. Copyright © 2020, The Authors. All rights reserved.

关键词： stochastic programming

A stochastic Model for Budget Distribution over Time in Search Advertisements

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A Stochastic Model for Budget Distribution over Time in Sear...

2014 IEEE International Conference on Service Operations and Logistics,and Informatics

作者： Rui Qin Yong Yuan Juanjuan Li Yanwu Yang The State Key Laboratory of Management and Control for Complex Systems Institute of AutomationChinese Academy of Sciences Qingdao Academy of Intelligent Industries Beijing Engineering Research Center of Intelligent Systems and Technology Institute of AutomationChinese Academy of Sciences School of Management Huazhong University of Science and Technology

In search advertisements,advertisers have to seek for an effective allocation strategy to distribute the limited budget over a series of sequential temporal slots(e.g.,days).However,advertisers usually have no sufficient knowledge to determine the optimal budget for each temporal slot,because there exist much uncertainty in search advertising *** this paper,we present a stochastic model for budget distribution over a series of sequential temporal slots under a finite time horizon,assuming that the best budget is a random *** study some properties and feasible solutions for our model,taking the best budget being characterized by either normal distribution or uniform distribution,***,we also make some experiments to evaluate our model and identify strategies with the real-world data collected from practical advertising *** results show that a)our strategies outperform the baseline strategy that is commonly used in practice;b)the optimal budget is more likely to be normally distributed than uniformly distributed.

关键词： search advertisement budget distribution optimal budget stochastic programming budget constraint

Data-Driven Sample Average Approximation with Covariate Information

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arXiv 2022年

作者： Kannan, Rohit Bayraksan, Güzin Luedtke, James R. Los Alamos National Laboratory Los AlamosNM United States Department of Integrated Systems Engineering The Ohio State University ColumbusOH United States Department of Industrial & Systems Engineering Wisconsin Institute for Discovery University of Wisconsin-Madison MadisonWI United States

We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate three data-driven frameworks that integrate a machine learning prediction model within a stochastic programming sample average approximation (SAA) for approximating the solution to this problem. Two of the SAA frameworks are new and use out-of-sample residuals of leave-one-out prediction models for scenario generation. The frameworks we investigate are flexible and accommodate parametric, nonparametric, and semiparametric regression techniques. We derive conditions on the data generation process, the prediction model, and the stochastic program under which solutions of these data-driven SAAs are consistent and asymptotically optimal, and also derive convergence rates and finite sample guarantees. Computational experiments validate our theoretical results, demonstrate the potential advantages of our data-driven formulations over existing approaches (even when the prediction model is misspecified), and illustrate the benefits of our new data-driven formulations in the limited data *** Codes 90C15 Copyright © 2022, The Authors. All rights reserved.

关键词： stochastic programming

Strong Convexity for Risk-Averse Two-Stage Models with Fixed Complete Linear Recourse

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arXiv 2018年

作者： Claus, Matthias Spürkel, Kai University Duisburg-Essen Thea Leymann-Straße 9 EssenD-45127 Germany

This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of the expected excess functional with respect to the decision variable and the threshold parameter. These results allow to derive sufficient conditions for strong convexity of models building on the conditional value-at-risk due to its variational representation. Via Kusuoka representation these carry over to comonotonic and distortion risk measures, where we obtain verifiable conditions in terms of the distortion function. For stochastic optimisation models, we point out implications for quantitative stability with respect to perturbations of the underlying probability measure. Recent work in [3] and [29] also gives testimony to the importance of strong convexity for the convergence rates of modern stochastic subgradient descent algorithms and in the setting of machine *** Codes 90C15, 90C31 Copyright © 2018, The Authors. All rights reserved.

关键词： stochastic programming

Reducing congestion-induced renewable curtailment with corrective network reconfiguration in day-ahead scheduling

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arXiv 2020年

作者： Ramesh, Arun Venkatesh Li, Xingpeng Department of Electrical and Computer Engineering University of Houston Houston TX United States

Renewable energy sources (RES) has gained a lot of interest recently. The limited transmission capacity serving RES often leads to network congestion since they are located in remote favorable locations. As a result, when poorly scheduled, the intermittent nature of RES may result in high curtailments of the free resource. Currently, grid operators utilize a static network when performing day-ahead scheduling and ignore transmission flexibility. This paper explores the possibility of utilizing network reconfiguration as a corrective action to reduce the transmission congestion and thereby the reduction of RES curtailments in day-ahead scheduling. To facilitate the RES integration in the grid, a stochastic N-1 security-constrained unit-commitment with corrective network reconfiguration (SSCUC-CNR) is modelled. SSCUC-CNR model is studied on a modified IEEE 24-bus system with RES. The simulation results demonstrates that CNR not only leads to a lower cost solution by reducing network congestion but also facilitates RES integration by reducing congestion-induced curtailments in high penetration cases. Emission studies demonstrate that more green generators are committed resulting in reduced carbon emissions when CNR is implemented. Copyright © 2020, The Authors. All rights reserved.

关键词： stochastic programming

A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs

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arXiv 2018年

作者： Ogbe, Emmanuel Li, Xiang Department of Chemical Engineering Queen's University KingstonONK7L 3N6 Canada

This paper proposes a joint decomposition method that combines Lagrangian decomposition and generalized Benders decomposition, to eficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global optimality, without the need for explicit branch and bound search. In this approach, we view the variables coupling the scenario dependent variables and those causing nonconvexity as complicating variables. We systematically solve the Lagrangian decomposition subproblems and the generalized Benders decomposition subproblems in a unified framework. The method requires the solution of a di_cult relaxed master problem, but the problem is only solved when necessary. Enhancements to the method are made to reduce the number of the relaxed master problems to be solved and ease the solution of each relaxed master problem. We consider two scenario-based, two-stage stochastic nonconvex MINLP problems that arise from integrated design and operation of process networks in the case study, and we show that the proposed method can solve the two problems significantly faster than stateof-the-art global optimization solvers. Copyright © 2018, The Authors. All rights reserved.

关键词： stochastic programming

Index-based policy for risk-averse multi-armed bandit

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arXiv 2018年

作者： Xu, Jianyu Haskell, William B. Ye, Zhisheng Department of Industrial Systems Engineering and Management National University of Singapore 1 Engineering Drive 2 Singapore

The multi-armed bandit (MAB) is a classical online optimization model for the trade-off between exploration and exploitation. The traditional MAB is concerned with finding the arm that minimizes the mean cost. However, minimizing the mean does not take the risk of the problem into account. We now want to accommodate risk-averse decision makers. In this work, we introduce a coherent risk measure as the criterion to form a risk-averse MAB. In particular, we derive an index-based online sampling framework for the risk-averse MAB. We develop this framework in detail for three specific risk measures, i.e. the conditional value-at-risk, the mean-deviation and the shortfall risk measures. Under each risk measure, the convergence rate for the upper bound on the pseudo regret, defined as the difference between the expectation of the empirical risk based on the observation sequence and the true risk of the optimal arm, is established. Copyright © 2018, The Authors. All rights reserved.

关键词： stochastic programming