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Active State Tracking With Sensing Costs: Analysis of Two-States and Methods for n-States

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第11期65卷 2828-2843页

作者： Zois, Daphney-Stavroula Mitra, Urbashi SUNY Albany Elect & Comp Engn Dept Albany NY 12222 USA Univ Southern Calif Ming Hsieh Dept Elect Engn Los Angeles CA 90089 USA

Active state tracking is needed in object classification, target tracking, medical diagnosis, and estimation of sparse signals among other various applications. Herein, active state tracking of a discrete-time, finite-state Markov chain is considered. Noisy Gaussian observations are dynamically collected by exerting appropriate control over their information content, while incurring a related sensing cost. The objective is to devise sensing strategies to optimize the tradeoff between tracking performance and sensing cost. A recently proposed Kalman-like estimator by Zois et al. is employed for state tracking. The associated mean-squared error and a generic sensing cost metric are then used in a partially observable Markov decision process formulation, and the optimal sensing strategy is derived via a dynamic programming recursion. The resulting recursion proves to be nonlinear, challenging control policy design. For two-state systems with scalar measurements, properties of the related cost functions are derived and sufficient conditions are provided regarding the structure of the optimal control policy enabling characterization of when passive state tracking is optimal. To overcome the associated computational burden of the optimal sensing strategy, two lower complexity strategies are proposed, which apply to n-state systems with vector measurements. The performance of the proposed strategies is illustrated in a wireless body sensing application, where cost savings as high as 70% are demonstrated for a 3% detection error with respect to a static equal allocation sensing strategy.

关键词： Active state tracking controlled sensing active classification partially observable Markov decision processes (POMPs) structural results Kalman-like filter stochastic dynamic programming Weiss-Weinstein lower bound discrete state Markov chains body sensing network application

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stochastic Long-Term Hydrothermal Scheduling With Parameter Uncertainty in Autoregressive Streamflow Models

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IEEE TRANSACTIONS ON POWER SYSTEMS 2017年第2期32卷 999-1006页

作者： Bezerra, Bernardo Veiga, Alvaro Barroso, Luiz Augusto Pereira, Mario Pontificia Univ Catolica Rio de Janeiro Dept Elect Engn BR-22453900 Rio de Janeiro Brazil PSR BR-22224006 Rio De Janeiro Brazil PSR Consulting Rio De Janeiro Brazil Comillas Pontifical Univ Inst Res Technol IIT Madrid Spain

The optimal scheduling of hydrothermal systems requires the representation of uncertainties in future streamflows to devise a cost-effective operations policy. stochastic optimization has been widely used as a powerful tool to solve this problem but results will necessarily depend on the stochastic model used to generate future scenarios for streamflows. Periodic autoregressive (PAR) models have been widely used in this task. However, its parameters are typically unknown and must be estimated from historical data, incorporating a natural estimation error. Furthermore, the model is just a linear approximation of the real stochastic process. The consequence is that the operator will be uncertain about the correct linear model that should be used at each period. The objective of this work is to assess the impacts of incorporating the uncertainty of the parameters of the PAR models into a stochastic hydrothermal scheduling model. The proposed methodology is tested with case studies based on data from the Brazilian hydroelectric system. It is shown that when the uncertainty of the parameters is ignored, the policies given by the stochastic optimization tend to be too optimistic.

关键词： Bootstrap hydro scheduling parameter uncertainty stochastic dynamic programming uncertainty assessment

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Approximate solutions and cost error bounds for quantity flexibility replenishment

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2017年 193卷 306-315页

作者： Zhu, Stuart X. Univ Groningen Fac Econ & Business Dept Operat Nettelbosje 2 NL-9747 AE Groningen Netherlands

Under an environment with quantity flexibility replenishment, we explore the approximate solutions to determine ordering quantities when the demand is correlated with dynamic forecast updating. Moreover, we show the optimality of the myopic policy. We further develop the corresponding cost error bounds to evaluate the performance of the approximate solutions. Extensive numerical experiments demonstrate that our approximate solution can achieve a lower cost performance compared with other bounds.

关键词： Approximation Bounds Quantity flexibility stochastic dynamic programming

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Monotone Optimal Threshold Feedback Policy for Sequential Weapon Target Assignment

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JOURNAL OF AEROSPACE INFORMATION SYSTEMS 2017年第1期14卷 68-72页

作者： Kalyanam, Krishnamoorthy Casbeer, David Pachter, Meir Infoscitex Corp Dayton OH 45431 USA US Air Force Res Lab Autonomous Control Branch Wright Patterson AFB OH 45433 USA US Air Force Inst Technol Wright Patterson AFB OH 45433 USA

THE operational scenario is the following. Abomber with identical weapons travels along a designated route/path and sequentially encounters enemy ( ground) targets. Should the bomber decide to engage a target, the target will be destroyed with a probability of p < 1. Upon successful elimination, the bomber receives a positive reward r drawn from a fixed known distribution. We stipulate that, before engagement, the bomber observes the target and is made aware of the reward r. Furthermore, upon releasing a weapon, the bomber is alerted as to whether or not the deployed weapon was successful. In other words, we employ a shoot-look-shoot policy. If the target is destroyed, the bomber moves on to the next target. On the other hand, if the target was not destroyed, the bomber can either reengage the current target or move on to the next target in the sequence. The optimal closed-loop control policy that results in the maximal expected cumulative reward is obtained via stochastic dynamic programming. Not surprisingly, a weapon is dropped on a target if, and only if, the observed reward is no less than a stage- and state-dependent threshold value. We show that the threshold value, as a function, is monotonic decreasing in the number of weapons and monotonic nondecreasing in the number of targets left to be engaged.

关键词： Weapon Target Assignment stochastic dynamic programming Closed Loop Control Missile Defense

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stochastic Control for Optimal Execution:Fast Approximation Solution Scheme Under Nested Mean-semi Deviation and Conditional Value at Risk

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Journal of the Operations Research Society of China 2017年第2期5卷 161-176页

作者： Meng-Fei He Duan Li Yuan-Yuan Chen China International Fund Management Ltd Shanghai 200120China Department of Systems Engineering and Engineering Management The Chinese University of Hong KongHong KongChina Risk Management Institute National University of SingaporeSingaporeSingapore

When executing a large order of stocks in a market,one important factor in forming the optimal trading strategy is to consider the price impact of large-volume trading *** a risk measure of the implementation shortfall,i.e.,the difference between the value of a trader’s initial equity position and the sum of cash flow he receives from his trading process,is essentially a stochastic control *** this study,we investigate such a practical problem under a dynamic coherent risk measure in a market in which the stock price dynamics has a feature of momentum *** develop a fast approximation solution scheme,which is critical in highfrequency *** demonstrate some prominent features of our derived solution algorithm in providing useful guidance for real implementation.

关键词： Nested coherent risk measure Momentum effect Approximation solution scheme stochastic dynamic programming

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Capacity reservation and utilization for a manufacturer with uncertain capacity and demand

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OR SPECTRUM 2017年第3期39卷 689-709页

作者： Boulaksil, Y. Fransoo, J. C. Tan, T. United Arab Emirates Univ Coll Business & Econ Al Ain U Arab Emirates Eindhoven Univ Technol Sch Ind Engn Eindhoven Netherlands

We consider an original equipment manufacturer (OEM) who has outsourced the production activities to a contract manufacturer (CM). The CM produces for multiple OEMs on the same capacitated production line. The CM requires that all OEMs reserve capacity slots before ordering and responds to these reservations by acceptance or partial rejection, based on allocation rules that are unknown to the OEM. Therefore, the allocated capacity for the OEM is not known in advance, also because the OEM has no information about the reservations of the other OEMs. Based on a real-life situation, we study this problem from the OEM's perspective who faces stochastic demand and stochastic capacity allocation from the contract manufacturer. We model this problem as a single-item, periodic review inventory system, and we assume linear inventory holding, backorder, and reservation costs. We develop a stochastic dynamic programming model, and we characterize the optimal policy. We conduct a numerical study where we also consider the case that the capacity allocation is dependent on the demand distribution. The results show that the optimal reservation policy is little sensitive to the uncertainty of capacity allocation. In that case, the optimal reservation quantities hardly increase, but the optimal policy suggests increasing the utilization of the allocated capacity. Further, in comparison with a static policy, we show that a dynamic reservation policy is particularly useful when backorder cost and uncertainty are low. Moreover, we show that for the contract manufacturer, to achieve the desired behavior, charging little reservation costs is sufficient.

关键词： Capacity reservation stochastic capacity and demand Outsourcing stochastic dynamic programming

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41 Counterexamples to property (B) of the discrete time bomber problem

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ANNALS OF OPERATIONS RESEARCH 2017年第1-2期248卷 579-588页

作者： Kamihigashi, Takashi Kobe Univ Res Inst Econ & Business Adm RIEB Nada Ku Kobe Hyogo 6578501 Japan

The discrete time "bomber problem" has been one of the longest standing open problems in operations research. In particular, the validity of one of the natural monotonicity conjectures-known as property (B)-has been an unresolved issue since 1968. In this paper we report 41 counterexamples to property (B) of this problem. We have found them by computing the exact solutions for nearly one million pairs of parameter values utilizing the GNU multiple precision arithmetic library. All our counterexamples can readily be verified using a simple Mathematica program included in this paper.

关键词： The discrete time bomber problem Error-free methods GNU multiple precision (GMP) arithmetic library stochastic dynamic programming

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PHASE TRANSITION IN A SEQUENTIAL ASSIGNMENT PROBLEM ON GRAPHS

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ANNALS OF APPLIED PROBABILITY 2017年第4期27卷 2098-2129页

作者： Jarai, Antal A. Univ Bath Dept Math Sci Bath BA1 7AY Avon England

We study the following game on a finite graph G = (V,E). Each edge e is an element of E starts with an integer value n(e) >= 0, and we write n = Sigma eE n(e). At time t, 1 infinity, the expected reward under the ... 详细信息

We study the following game on a finite graph G = (V,E). Each edge e is an element of E starts with an integer value n(e) >= 0, and we write n = Sigma eE n(e). At time t, 1 <= t <= n, a uniformly random vertex v is an element of V is generated, and one of the edges f incident with v must be selected. The value of f is then decreased by 1. There is a unit final reward if the configuration (0,...,0) is reached. Our main result is that there is a phase transition: as n -> infinity, the expected reward under the optimal policy approaches a constant c(G) > 0 when (n(e)/n : e is an element of E) converges to a point in the interior of a certain convex set R-G, and goes to 0 exponentially when (n(e)/n : e is an element of E) is bounded away from R-G. We also obtain estimates in the near-critical region, that is when (ne/n : e. E) lies close to partial derivative RG. We supply quantitative error bounds in our arguments.

关键词： Phase transition critical phenomenon stochastic sequential assignment Markov decision process stochastic dynamic programming discrete stochastic optimal control

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State-dependent behavioural theory for assessing the fitness consequences of anthropogenic disturbance on capital and income breeders

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METHODS IN ECOLOGY AND EVOLUTION 2017年第5期8卷 552-560页

作者： McHuron, Elizabeth A. Costa, Daniel P. Schwarz, Lisa Mangel, Marc Univ Calif Santa Cruz Dept Ecol & Evolutionary Biol Santa Cruz CA 95064 USA Univ Calif Santa Cruz Inst Marine Sci Santa Cruz CA 95064 USA Univ Calif Santa Cruz Dept Appl Math & Stat Santa Cruz CA 95064 USA Univ Bergen Dept Biol N-9020 Bergen Norway

Anthropogenic disturbance is of increasing concern for wildlife populations, necessitating the development of models that link behavioural changes at the individual level with biologically meaningful changes at the population level. We developed a general framework for estimating the fitness consequences of disturbance that affects foraging behaviour using state-dependent behavioural theory implemented by stochastic dynamic programming (SDP). We illustrate this framework using generalized examples of pinnipeds, a group of marine carnivores that include both capital- and income-breeding species. We examined how disturbance affected pup recruitment separately for each reproductive strategy, and the impact of foraging decisions and parameter values on model results. The effect of disturbance on pup recruitment was greater for income than capital breeders for all disturbance scenarios. Disturbance had negligible effects on pup recruitment when it occurred within less frequented foraging patches, but moderate to large effects when it occurred within an important foraging patch. Model results were sensitive to values of patch productivity (the energy gained from successful foraging), the probability of disturbance and individual behavioural choices in the face of disturbance. State-dependent behavioural theory implemented by SDP is a powerful tool for investigating when behavioural changes in response to disturbance may be meaningful at the population level. This approach allows us to incorporate many factors that are known to influence the behavioural and physiological responses of animals to anthropogenic disturbance, and places disturbance within the context of a temporally and spatially variable environment. The general framework we have developed can be used to estimate the consequences of anthropogenic disturbance across a broad range of species.

关键词： mammal pinniped Population Consequences of Disturbance stochastic dynamic programming

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The value of flexibility in conservation financing

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CONSERVATION BIOLOGY 2017年第3期31卷 666-674页

作者： Lennox, Gareth D. Fargione, Joseph Spector, Sacha Williams, Gwyn Armsworth, Paul R. Univ Lancaster Lancaster Environm Ctr Lancaster LA1 4YQ England Nature Conservancy 1101 West River PkwySuite 200 Minneapolis MN 55415 USA Scen Hudson One Civ Ctr PlazaSuite 200 Poughkeepsie NY 12601 USA Royal Soc Protect Birds Potton Rd Sandy SG19 2DL Beds England Univ Tennessee Dept Ecol & Evolutionary Biol Knoxville TN 37996 USA

Land-acquisition strategies employed by conservation organizations vary in their flexibility. Conservation-planning theory largely fails to reflect this by presenting models that are either extremely inflexibleparcel acquisitions are irreversible and budgets are fixedor extremely flexiblepreviously acquired parcels can readily be sold. This latter approach, the selling of protected areas, is infeasible or problematic in many situations. We considered the value to conservation organizations of increasing the flexibility of their land-acquisition strategies through their approach to financing deals. Specifically, we modeled 2 acquisition-financing methods commonly used by conservation organizations: borrowing and budget carry-over. Using simulated data, we compared results from these models with those from an inflexible fixed-budget model and an extremely flexible selling model in which previous acquisitions could be sold to fund new acquisitions. We then examined 3 case studies of how conservation organizations use borrowing and budget carry-over in practice. Model comparisons showed that borrowing and budget carry-over always returned considerably higher rewards than the fixed-budget model. How they performed relative to the selling model depended on the relative conservation value of past acquisitions. Both the models and case studies showed that incorporating flexibility through borrowing or budget carry-over gives conservation organizations the ability to purchase parcels of higher conservation value than when budgets are fixed without the problems associated with the selling of protected areas.

关键词： conservation finance conservation planning land conservation option value protected areas stochastic dynamic programming

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