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Mixing stochastic dynamic programming and scenario aggregation

ANNALS OF OPERATIONS RESEARCH 1996年第1期64卷 1-19页

作者： Berland, NJ Haugen, KK NORWEGIAN INST TECHNOL DEPT MANAGEMENT ECON & OPERAT RESN-7034 TRONDHEIMNORWAY

This paper describes a serial and parallel implementation of a hybrid stochastic dynamic programming and progressive hedging algorithm. Numerical experiments show good speedups in the parallel implementation. In spite of this, our hybrid algorithm has difficulties competing with a pure stochastic dynamic programming approach on a given test case from macroeconomic control theory.

关键词： stochastic optimization stochastic dynamic programming progressive hedging parallelization macroeconomic control

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Two-Phase stochastic dynamic programming Model for Optimal Operation of Irrigation Reservoir

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WATER RESOURCES MANAGEMENT 1997年第5期11卷 395-406页

作者： Umamahesh, N. V. Sreenivasulu, P. Reg Engn Coll Water & Environm Div Dept Civil Engn Warrangal India Vasavi Coll Engn Dept Civil Engn Hyderabad Andhra Pradesh India

A two-phase stochastic dynamic programming model is developed for optimal operation of irrigation reservoirs under a multicrop environment. Under a multicrop environment, the crops compete for the available water whenever the water available is less than the irrigation demands. The performance of the reservoir depends on how the deficit is allocated among the competing crops. The proposed model integrates reservoir release decisions with water allocation decisions. The water requirements of crops vary from period to period and are determined from the soil moisture balance equation taking into consideration the contribution of soil moisture and rainfall for the water requirements of the crops. The model is demonstrated over an existing reservoir and the performance of the reservoir under the operating policy derived using the model is evaluated through simulation.

关键词： irrigation reservoirs operation water deficit yield response multicrop environment stochastic dynamic programming soil moisture water allocation simulation

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Persistently Optimal Policies in stochastic dynamic programming with Generalized Discounting

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MATHEMATICS OF OPERATIONS RESEARCH 2013年第1期38卷 108-121页

作者： Jaskiewicz, Anna Matkowski, J. Nowak, A. S. Wroclaw Univ Technol Inst Math & Comp Sci PL-50370 Wroclaw Poland Univ Zielona Gora Fac Math Comp Sci & Econometr PL-65246 Zielona Gora Poland

In this paper we study a Markov decision process with a nonlinear discount function. First, we define a utility on the space of trajectories of the process in the finite and infinite time horizon and then take their expected values. It turns out that the associated optimization problem leads to a nonstationary dynamic programming and an infinite system of Bellman equations, which result in obtaining persistently optimal policies. Our theory is enriched by examples.

关键词： stochastic dynamic programming persistently optimal policies variable discounting Bellman equation resource extraction growth theory

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A Bayesian Inference and stochastic dynamic programming Approach to Determine the Best Binomial Distribution

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2009年第14期38卷 2379-2397页

作者： Nezhad, Mohammad Saber Fallah Niaki, Seyed Taghi Akhavan Sharif Univ Technol Dept Ind Engn Tehran Iran

In this research, we employ Bayesian inference and stochastic dynamic programming approaches to select the binomial population with the largest probability of success from n independent Bernoulli populations based upon the sample information. To do this, we first define a probability measure called belief for the event of selecting the best population. Second, we explain the way to model the selection problem using Bayesian inference. Third, we clarify the model by which we improve the beliefs and prove that it converges to select the best population. In this iterative approach, we update the beliefs by taking new observations on the populations under study. This is performed using Bayesian rule and prior beliefs. Fourth, we model the problem of making the decision in a predetermined number of decision stages using the stochastic dynamic programming approach. Finally, in order to understand and to evaluate the proposed methodology, we provide two numerical examples and a comparison study by simulation. The results of the comparison study show that the proposed method performs better than that of Levin and Robbins (1981) for some values of estimated probability of making a correct selection.

关键词： Bayesian inference Best binomial distribution Beta distribution Optimum stopping problem stochastic dynamic programming

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On parallelization of a stochastic dynamic programming algorithm for solving large-scale mixed 0-1 problems under uncertainty

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TOP 2015年第3期23卷 703-742页

作者： Aldasoro, Unai Escudero, Laureano F. Merino, Maria Monge, Juan F. Perez, Gloria Univ Basque Country Dept Matemat Aplicada Leioa 48940 Bizkaia Spain Univ Rey Juan Carlos Dept Estadist & Invest Operat Madrid Spain Univ Basque Country Dept Matemat Aplicada Estadist & Invest Operat Barrio Sarriena S-N Leioa 48940 Bizkaia Spain Univ Miguel Hernandez Ctr Invest Operat Elche Spain

A parallel computing implementation of a Serial stochastic dynamic programming approach referred to as the S-SDP algorithm is introduced to solve large-scale multiperiod mixed 0-1 optimization problems under uncertainty. The paper presents Inner and Outer Parallelization versions of the S-SDP algorithm, referred to as Inner P-SDP and Outer P-SDP, respectively, so that the problem solving elapsed time and gap reduction is analyzed. The basic idea of Inner P-SDP consists of parallelizing the optimization of variations of the MIP subproblems attached to the sets of scenario clusters created by the modeler-defined stages to decompose the original problem. The Outer P-SDP performs simultaneous interconnected executions of the serial algorithm, so that a wider feasibility area is explored using iterative communication to redefine search directions. Strategies are presented to analyze the performance of parallel computation based on Message-Passing Interface threads to solve stage-related subproblems versus the serial version of SDP methodology. The results of using the parallelization are remarkable, as not only faster but also better solutions than the serial version are obtained. In particular, we report up to 10 times speedup for 12 threads on the Inner P-SDP algorithm. The new approach allows problems to be solved using less computing time than a state-of-the-art MIP solver. It can thus solve very large-scale problems that could not otherwise be achieved by plain use of the solver or by the S-SDP algorithm in acceptable elapsed time, if any.

关键词： stochastic dynamic programming Inner and outer parallelization Multistage stochastic mixed 0-1 optimization Parallel computing Message-passing interface

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A stochastic dynamic programming model with fuzzy storage states for reservoir operations

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ADVANCES IN WATER RESOURCES 2004年第11期27卷 1105-1110页

作者： Mousavi, SJ Mahdizadeh, K Afshar, A Univ Sci & Technol Dept Civil Engn Hydrostruct Res Ctr Tehran 16844 Iran Amirkabir Univ Technol Dept Civil Engn Tehran Iran

Application of stochastic dynamic programming (SDP) models to reservoir optimization calls for state variables discretization. Reservoir storage volume is an important variable whose discretization has a pronounced effect on the computational efforts. The error caused by storage volume discretization is examined by considering it as a fuzzy state variable. In this approach, the point-to-point transitions between storage volumes at the beginning and end of each period are replaced by transitions between storage intervals. This is achieved by using fuzzy arithmetic operations with fuzzy numbers. In this approach, instead of aggregating single-valued crisp numbers, the membership functions of fuzzy numbers are combined. Running a simulation model with optimal release policies derived from fuzzy and non-fuzzy SDP models shows that a fuzzy SDP with a coarse discretization scheme performs as well as a classical SDP having much finer discretized space. It is believed that this advantage in the fuzzy SDP model is due to the smooth transitions between storage intervals which benefit from soft boundaries. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： fuzzy set theory reservoir operations smooth transition stochastic dynamic programming

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stochastic dynamic programming and stochastic Fluid-Flow Models in the Design and Analysis of Web-Server Farms

Stochastic Dynamic Programming and Stochastic Fluid-Flow Mod...

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作者： Goel, Piyush Texas A&M University

A Web-server farm is a specialized facility designed specifically for housing Web servers catering to one or more Internet facing Web sites. In this dissertation, stochastic dynamic programming technique is used to obtain the optimal admission control policy with different classes of customers, and stochastic uid- ow models are used to compute the performance measures in the network. The two types of network traffic considered in this research are streaming (guaranteed bandwidth per connection) and elastic (shares available bandwidth equally among connections). We first obtain the optimal admission control policy using stochastic dynamic programming, in which, based on the number of requests of each type being served, a decision is made whether to allow or deny service to an incoming request. In this subproblem, we consider a xed bandwidth capacity server, which allocates the requested bandwidth to the streaming requests and divides all of the remaining bandwidth equally among all of the elastic requests. The performance metric of interest in this case will be the blocking probability of streaming traffic, which will be computed in order to be able to provide Quality of Service (QoS) guarantees. Next, we obtain bounds on the expected waiting time in the system for elastic requests that enter the system. This will be done at the server level in such a way that the total available bandwidth for the requests is constant. Trace data will be converted to an ON-OFF source and fluid- flow models will be used for this analysis. The results are compared with both the mean waiting time obtained by simulating real data, and the expected waiting time obtained using traditional queueing models. Finally, we consider the network of servers and routers within the Web farm where data from servers flows and merges before getting transmitted to the requesting users via the Internet. We compute the waiting time of the elastic requests at intermediate and edge nodes by obtaining the

关键词： stochastic Fluid-Flow stochastic dynamic programming Web-server farm On-Off flow Multiplexing data Admission Control policy Performance Analysis Book Thesis

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Combining metamodelling and stochastic dynamic programming for the design of reservoir release policies

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ENVIRONMENTAL MODELLING & SOFTWARE 2010年第2期25卷 209-222页

作者： Galelli, S. Soncini-Sessa, R. Politecn Milan Dipartimento Elettron & Informaz I-20133 Milan Italy

Increasing worldwide water withdrawal for irrigation purposes requires a more efficient management of water resources and an accurate description of irrigation water demand. This paper, with the aim of thinking 'in blue and green water terms', proposes a new approach for the design of release policies in reservoir systems serving irrigation districts. It is based on the solution of an optimal control problem, where the dynamics of the irrigation demand is modelled through a metamodel, i.e. a simple model identified on the basis of the data produced by a distributed-parameter, conceptual model. The metamodel inherits the physical description of the distributed-parameter model and, at same time, is sufficiently simple to allow the solution of the optimal control problem with stochastic dynamic programming. The proposed approach is tested on a real-world case study, the management of the Lake Como system, for which it provides satisfactory results. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Integrated water resources management Metamodelling Distributed-parameter models stochastic dynamic programming Water reservoirs management Irrigation canals control

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A Multi-Stage Two-Machines Replacement Strategy Using Mixture Models, Bayesian Inference, and stochastic dynamic programming

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2011年第4期40卷 702-725页

作者： Nezhad, Mohammad Saber Fallah Niaki, Seyed Taghi Akhavan Yazd Univ Dept Ind Engn Yazd Iran Sharif Univ Technol Dept Ind Engn Tehran Iran

If at least one out of two serial machines that produce a specific product in manufacturing environments malfunctions, there will be non conforming items produced. Determining the optimal time of the machines' maintenance is the one of major concerns. While a convenient common practice for this kind of problem is to fit a single probability distribution to the combined defect data, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defects as arising from a mixture population: one due to the first machine failures and the other due to the second one. In this article, a mixture model along with both Bayesian inference and stochastic dynamic programming approaches are used to find the multi-stage optimal replacement strategy. Using the posterior probability of the machines to be in state (1), (2) (the failure rates of defective items produced by machine 1 and 2, respectively), we first formulate the problem as a stochastic dynamic programming model. Then, we derive some properties for the optimal value of the objective function and propose a solution algorithm. At the end, the application of the proposed methodology is demonstrated by a numerical example and an error analysis is performed to evaluate the performances of the proposed procedure. The results of this analysis show that the proposed method performs satisfactorily when a different number of observations on the times between productions of defective products is available.

关键词： Bayesian inference Gamma distribution Mixture models Production processes Replacement strategy stochastic dynamic programming Primary 90B25 Secondary 62F15

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Converging marriage in honey-bees optimization and application to stochastic dynamic programming

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JOURNAL OF GLOBAL OPTIMIZATION 2006年第3期35卷 423-441页

作者： Chang, Hyeong Soo Sogang Univ Dept Comp Sci & Engn Seoul 121742 South Korea Sogang Univ Program Integrated Biotechnol Seoul South Korea

In this paper, we first refine a recently proposed metaheuristic called "Marriage in Honey-Bees Optimization" (MBO) for solving combinatorial optimization problems with some modifications to formally show that MBO converges to the global optimum value. We then adapt MBO into an algorithm called "Honey-Bees Policy Iteration" (HBPI) for solving infinite horizon-discounted cost stochastic dynamic programming problems and show that HBPI also converges to the optimal value.

关键词： honey-bees optimization Markov decision process policy iteration stochastic dynamic programming swarm intelligence

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