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.
This paper presents an detailed study about the development of an integrative DR policy for the optimal home energy management system under stochastic *** this study,home appliances are classified into three categorie...
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ISBN:
(纸本)9781467397155
This paper presents an detailed study about the development of an integrative DR policy for the optimal home energy management system under stochastic *** this study,home appliances are classified into three categories and detailed modeling of all kinds of home appliances is ***,the optimal HEMS problem is formulated as a stochastic programming model considering the uncertainties of PV production and critical loads to minimize a customer's electricity *** Carlo simulation method is used to decompose the problem into a mixed integer linear programming ***,the proposed stochastic programming model is verified through numerical *** simulation results show that the proposed stochastic DR model can reduce the effect of the uncertainties in residential environment on the electricity cost and obtain a better DR policy than the conventional deterministic model.
We consider bounds for the price of a European-style call option under regime switching. stochastic semidefinite programming models are developed that incorporate a lattice generated by a finite-state Markov chain reg...
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We consider bounds for the price of a European-style call option under regime switching. stochastic semidefinite programming models are developed that incorporate a lattice generated by a finite-state Markov chain regime-switching model as a representation of scenarios (uncertainty) to compute bounds. The optimal first-stage bound value is equivalent to a Value at Risk quantity, and the optimal solution can be obtained via simple sorting. The upper (lower) bounds from the stochastic model are bounded below (above) by the corresponding deterministic bounds and are always less conservative than their robust optimization (min-max) counterparts. In addition, penalty parameters in the model allow controllability in the degree to which the regime switching dynamics are incorporated into the bounds. We demonstrate the value of the stochastic solution (bound) and computational experiments using the S&P 500 index are performed that illustrate the advantages of the stochastic programming approach over the deterministic strategy.
The author considers the use of risk measures that allows combining stochastic programming and robust optimization problems within the overall approach. Constructions for the class of polyhedral coherent risk measures...
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The author considers the use of risk measures that allows combining stochastic programming and robust optimization problems within the overall approach. Constructions for the class of polyhedral coherent risk measures are described. It is shown how the use of such measures can reduce problems of linear optimization under uncertainty to deterministic linear programming problems.
This paper focuses on the energy optimal operation problem of microgrids (MGs) under stochastic environment. The deterministic method of MGs operation is often uneconomical because it fails to consider the high random...
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This article presents a model to assist decision makers in the logistics of a flood emergency. The model attempts to optimize inventory levels for emergency supplies as well as vehicles' availability, in order to ...
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This article presents a model to assist decision makers in the logistics of a flood emergency. The model attempts to optimize inventory levels for emergency supplies as well as vehicles' availability, in order to deliver enough supplies to satisfy demands with a given probability. A spatio-temporal stochastic process represents the flood occurrence. The model is approximately solved with sample average approximation. The article presents a method to quantify the impact of the various intervening logistics parameters. An example is provided and a sensitivity analysis is performed. The studied example shows large differences between the impacts of logistics parameters such as number of products, number of periods, inventory capacity and degree of demand fulfillment on the logistics cost and time. This methodology emerges as a valuable tool to help decision makers to allocate resources both before and after a flood occurs, with the aim of minimizing the undesirable effects of such events. (C) 2014 Elsevier Ltd. All rights reserved.
The aim of this paper is to construct a portfolio of eight different stocks from New York Stock Exchange market (AIR, ABM, TSCO, HLX, KO, DIS, AMZN, and VZ) using stochastic programming. The next stage (period) prices...
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Most existing distribution networks are difficult to withstand the impact of meteorological disasters. With the development of active distribution networks(ADNs), more and more upgrading and updating resources are app...
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Most existing distribution networks are difficult to withstand the impact of meteorological disasters. With the development of active distribution networks(ADNs), more and more upgrading and updating resources are applied to enhance the resilience of ADNs. A two-stage stochastic mixed-integer programming(SMIP) model is proposed in this paper to minimize the upgrading and operation cost of ADNs by considering random scenarios referring to different operation scenarios of ADNs caused by disastrous weather events. In the first stage, the planning decision is formulated according to the measures of hardening existing distribution lines, upgrading automatic switches, and deploying energy storage resources. The second stage is to evaluate the operation cost of ADNs by considering the cost of load shedding due to disastrous weather and optimal deployment of energy storage systems(ESSs) under normal weather condition. A novel modeling method is proposed to address the uncertainty of the operation state of distribution lines according to the canonical representation of logical constraints. The progressive hedging algorithm(PHA) is adopted to solve the SMIP model. The IEEE 33-node test system is employed to verify the feasibility and effectiveness of the proposed method. The results show that the proposed model can enhance the resilience of the ADN while ensuring economy.
Two-stage stochastic mixed-integer programs (SMIPs) with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing a sub...
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Two-stage stochastic mixed-integer programs (SMIPs) with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing a subset of the convex hull of feasible integer points of the second-stage subproblem which can be used for solving the SMIP with pure integer recourse. The basic idea is to use the smallest possible subset of the subproblem feasible integer set to generate a valid inequality like Fenchel decomposition cuts with a goal of reducing computation time. An algorithm for obtaining such a subset based on the solution of the subproblem linear programming relaxation is devised and incorporated into a decomposition method for SMIP. To demonstrate the performance of the new integer set reduction methodology, a computational study based on randomly generated knapsack test instances was performed. The results of the study show that integer set reduction aids in speeding up cut generation, leading to better bounds in solving SMIPs with pure integer recourse than using a direct solver.
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