Due to the interaction between the planning and operation of micro energy network, considering the operation optimization can better play the role of micro energy network. But due to the influence of various uncertain...
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Due to the interaction between the planning and operation of micro energy network, considering the operation optimization can better play the role of micro energy network. But due to the influence of various uncertainties, the deterministic programming solution may be sub-optimal. In this context, the two-stage stochastic programming of micro energy network is of great significance. In this paper, from the perspective of electric energy, the closely related P2G, storage system and fuel cell are modeled as a whole, so that the model is simplified to a certain extent. stochastic scenarios that considers multiple uncertain factors are constructed considering the correlation between electricity demand, wind speed and solar radiation intensity. And a two-stage stochastic programming model of micro energy network is established. Through the case study, the influence of P2GSS on micro energy network planning under uncertainty environment as well as the difference between stochastic programming and deterministic programming of micro energy network is analyzed. The simulation results show that P2GSS can reduce the economic cost and CO2 emission of micro energy network planning solution. Through the comparison of different planning schemes, it can provides a reference for the planning and construction of the micro-energy network.
The literature of portfolio optimization is extensive and covers several important aspects of the asset allocation problem. However, previous works consider simplified linear borrowing cost functions that leads to sub...
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The literature of portfolio optimization is extensive and covers several important aspects of the asset allocation problem. However, previous works consider simplified linear borrowing cost functions that leads to suboptimal allocations. This paper aims at efficiently solving the leveraged portfolio selection problem with a thorough borrowing cost representation comprising a number lenders with different rates and credit limits. We propose a two-stage stochastic programming model for asset and debt allocation considering a CVaR-based risk constraint and a convex piecewise-linear borrowing cost function. We compare our model to its counterpart with the fixed borrowing rate approximation used in literature. Numerical results show our model significantly improves performance in terms of risk-return trade-off.
This paper presents the development of an enhanced L-Shaped method applied to an inventory management problem that considers a replenishment control system based on the periodic review (R, S) policy. We consider singl...
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This paper presents the development of an enhanced L-Shaped method applied to an inventory management problem that considers a replenishment control system based on the periodic review (R, S) policy. We consider single-item one-echelon problems with uncertain demands and partial backorder that are modeled using two-stage stochastic programming. To enable the consideration of large-scale problems, the classical single-cut L-Shaped method and its extended multi-cut form were initially applied. Preliminary computational results indicated that the classical L-Shaped method outperformed its multi-cut counterpart, even though the former required more iterations to converge to the optimal solution. This observation inspired the development of the techniques presented for enhancing the L-Shape method, which consist of the combination of a novel acceleration technique with an efficient formulation and valid inequalities for the proposed model. Numerical experiments suggest that the proposed approach significantly reduced the computational time required to solve large-scale problems. (C) 2018 Elsevier B.V. All rights reserved.
The aim of this paper is to show that in some cases risk averse multistage stochastic programming problems can be reformulated in a form of risk neutral setting. This is achieved by a change of the reference probabili...
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The aim of this paper is to show that in some cases risk averse multistage stochastic programming problems can be reformulated in a form of risk neutral setting. This is achieved by a change of the reference probability measure making "bad" (extreme) scenarios more frequent. As a numerical example we demonstrate advantages of such change-of-measure approach applied to the Brazilian Interconnected Power System operation planning problem. (C) 2020 Elsevier B.V. All rights reserved.
In this paper, a new model for generation and transmission expansion is presented. This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capac...
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In this paper, a new model for generation and transmission expansion is presented. This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capacity factor of the transmission lines. In order to incorporate these random events into an optimization model, stochastic programming and probabilistic constraints are used. A risk factor is introduced in the objective function by means of the mean-variance Markowitz theory. The solved optimization problem is a mixed integer nonlinear program. The expected value of perfect information is obtained in order to show the cost of ignoring uncertainty. The proposed model is illustrated by a six- and a 21-node network using a dc approximation.
We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program w...
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We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the probability of future capacity requirements to be violated are simultaneously minimized. Assuming the existence of a finite number of possible future states of the world, an algorithm for the problem is elaborated. The algorithm determines all non-dominated solutions to the problem by a reduced feasible region method, solving a sequence of restricted subproblems by a cutting plane procedure. Computational results are reported for three different problem instances, one of which is a real-life problem faced by SONOFON, a Danish communications network operator.
stochastic programming models are large-scale optimization problems that are used to facilitate decision making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs o...
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stochastic programming models are large-scale optimization problems that are used to facilitate decision making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand is an optimization problem. In turn, the recourse function has to be estimated using techniques such as scenario trees or Monte Carlo methods, both of which require numerous functional evaluations to produce accurate results for large-scale problems with multiple periods and high-dimensional uncertainty. In this work, we introduce an importance sampling framework for stochastic programming that can produce accurate estimates of the recourse function using a small number of samples. Our framework combines Markov chain Monte Carlo methods with kernel density estimation algorithms to build a nonparametric importance sampling distribution, which can then be used to produce a lower-variance estimate of the recourse function. We demonstrate the increased accuracy and efficiency of our approach using variants of well-known multistage stochastic programming problems. Our numerical results show that our framework produces more accurate estimates of the optimal value of stochastic programming models, especially for problems with moderate variance, multimodal, or rare-event distributions.
Several approaches for the Bayesian design of experiments have been proposed in the literature (e.g., D-optimal, E-optimal, A-optimal designs). Most of these approaches assume that the available prior knowledge is rep...
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Several approaches for the Bayesian design of experiments have been proposed in the literature (e.g., D-optimal, E-optimal, A-optimal designs). Most of these approaches assume that the available prior knowledge is represented by a normal probability distribution. In addition, most nonlinear design approaches involve assuming normality of the posterior distribution and approximate its variance using the expected Fisher information matrix. In order to be able to relax these assumptions, we address and generalize the problem by using a stochastic programming formulation. Specifically, the optimal Bayesian experimental design is mathematically posed as a three-stage stochastic program, which is then discretized using a scenario based approach. Given the prior probability distribution, a Smolyak rule (sparse-grids) is used for the selection of scenarios. Two retrospective case studies related to population pharmacokinetics are presented. The benefits and limitations of the proposed approach are demonstrated by comparing the numerical results to those obtained by implementing a more exhaustive experimentation and the D-optimal design. (C) 2014 Elsevier Ltd. All rights reserved.
stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review basic ideas of cutting plane methods, augmented Lagrangian and splitting methods,...
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stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review basic ideas of cutting plane methods, augmented Lagrangian and splitting methods, and stochastic decomposition methods for convex polyhedral multi-stage stochastic programming problems. (C) 1997 The Mathematical programming Society, Inc. Published by Elsevier Science B.V.
The paper focuses on the optimal management of distributed energy resources aggregated within a coalition. The problem is analyzed from the viewpoint of an aggregator, seen as an entity called to optimize the availabl...
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The paper focuses on the optimal management of distributed energy resources aggregated within a coalition. The problem is analyzed from the viewpoint of an aggregator, seen as an entity called to optimize the available resources so to satisfy the aggregated demand by eventually trading in the Day-Ahead Electricity Market. Both a full and a residual perspective in the management of the integrated resources is investigated and compared. The inherent uncertainty affecting the optimal decision problem, mainly related to the demand profile, electricity prices and production from renewable sources, is dealt by adopting the two-stage stochastic programming paradigm. The proposed models (different for the full and residual case) present a bi-objective function, integrating the expected profit and a risk measure, the Conditional Value at Risk, to control undesirable effects caused by the random variations of the uncertain parameters. A broad numerical study has been carried out on real case study. The analysis of the results clearly shows the benefits deriving from the stochastic optimization approach and the effect of considering different levels of risk aversion. (C) 2017 Elsevier Ltd. All rights reserved.
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