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stochastic Linear programming for Reservoir Operation with Constraints on Reliability and Vulnerability

WATER 2018年第2期10卷 175-175页

作者： Chen, Cheng Kang, Chuanxiong Wang, Jinwen Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Hubei Peoples R China

Reliability and vulnerability (RV) are two very important performance measures but, due to their stage-inseparable nature, they cannot be explicitly incorporated in stochastic dynamic programming (SDP), which is extensively used in reservoir operation. With inflows described as a Markov chain, a stochastic linear programming (SLP) model is formulated in this paper to explicitly incorporate the RV constraints in the reservoir operation, aimed at maximizing the expected power generation by determining the optimal scheduling decisions and their probabilities. Simulation results of the SLP and SDP models indicate the equivalence of the proposed SLP and SDP models without considering the RV constraints, as well as the strength of the SLP in explicitly incorporating the RV constraints. A simulated scheduling solution also reveals a reduction of power generation fluctuation, with the reservoir capacity emptied in advance to meet given reliability and vulnerability.

关键词： stochastic linear programming Markov chain reliability vulnerability reservoir operation stochastic dynamic programming

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Special issue in honor of arie hordijk editorial introduction

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2005年第3期62卷 347-349页

作者： Kallenberg, L Koole, G Spieksma, F Vrije Univ Amsterdam Dept Math NL-1081 HV Amsterdam Netherlands Leiden Univ Leiden Netherlands

The article discusses various reports about mathematician Arie Hordijk published within the issue, including one by Sheldon Ross on the use of antithetic variables.

关键词： Operation Research Markov Decision Process Continuous Time Markov Chain stochastic dynamic programming stochastic Control Problem

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Choice of biodiversity index drives optimal fire management decisions

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ECOLOGICAL APPLICATIONS 2015年第1期25卷 264-277页

作者： Giljohann, K. M. Mccarthy, M. A. Kelly, L. T. Regan, T. J. Univ Melbourne Sch Bot Ctr Excellence Environm Parkville Vic 3010 Australia

Preservation of biodiversity is a central goal of conservation management, yet the conditions that promote persistence may differ for the species in the community. For systems subject to stochastic disturbances such as fire, understanding which management practices promote persistence for all species in a community is complex. Before deciding on the best course of action, an objective must be specified. Yet an overarching goal of species persistence can be specified into a measureable objective many different ways. We investigated four alternative management objectives for maximizing species persistence that use common biodiversity indices: (1) attaining the minimally acceptable mix of successional vegetation states to support species' relative abundances, (2) maximizing the arithmetic mean abundance of species, (3) maximizing the geometric mean abundance of species, and (4) minimizing the average extinction risk of species. We used stochastic dynamic programming to model successional changes in vegetation in the presence of both planned and unplanned fires, and utilize an extensive data set on the occurrence of birds, reptiles, and small mammals in different successional states in semiarid Australia. We investigated the influence the choice of objective function and taxonomic focus has on the optimal fire management recommendations. We also evaluated a recent hazard reduction policy to annually burn a fixed amount of the landscape and compare results to the optimal solution. The optimal management strategy to maximize species persistence over a 100-year period is predominantly to minimize wildfires. This is because the majority of species are more likely to occur in intermediate and late successional vegetation. However the optimal solution showed sensitivity to the objective and the species included in the analysis. These results highlight the need for careful consideration when specifying an objective to represent overarching conservation goals. Using the extinct

关键词： Australia biodiversity index fauna management objectives policy prescribed burning stochastic dynamic programming successional vegetation wildfire

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Physiological adaptations to climate change in pro-ovigenic parasitoids

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JOURNAL OF THEORETICAL BIOLOGY 2012年 309卷 67-77页

作者： Denis, Damien Pierre, Jean-Sebastien van Baaren, Joan van Alphen, Jacques J. M. Univ Rennes 1 UMR ECOBIO 6553 F-35042 Rennes France Univ Amsterdam IBED NL-1090 GE Amsterdam Netherlands Netherlands Ctr Biodivers Nat NL-2300 RA Leiden Netherlands

Temperature increase can affect physiological and behavioural constraints. Here, we use a stochastic dynamic modelling approach to predict changes in physiological adaptations and behaviour in response to temperature increase of pro-ovigenic parasitoids (i.e., parasitoids that mature all of their eggs before emergence). Adults of most species of parasitoids, are not capable of de novo lipogenesis. The allocation of lipids accumulated during the larval stage determines adult lifespan and fecundity. In females, lipids can be allocated either to egg production or to adult lipid reserves leading to a trade-off between fecundity and lifespan. Our results show that selection by an increase in ambient temperature, favours a smaller initial egg load and a larger amount of lipids for maintenance. The cost of habitat exploitation increases with temperature because the rate of lipid consumption increases. Hence, lifetime reproductive success decreases. When the optimal activity rate shifts to match the higher ambient temperature, these effects become less pronounced. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Parasitoids Pro-ovigenic Climate change Egg load stochastic dynamic programming

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A primer on partially observable Markov decision processes (POMDPs)

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METHODS IN ECOLOGY AND EVOLUTION 2021年第11期12卷 2058-2072页

作者： Chades, Iadine Pascal, Luz V. Nicol, Sam Fletcher, Cameron S. Ferrer-Mestres, Jonathan CSIRO Dutton Pk Qld Australia ENSTA Palaiseau France CSIRO Atherton Qld Australia

Partially observable Markov decision processes (POMDPs) are a convenient mathematical model to solve sequential decision-making problems under imperfect observations. Most notably for ecologists, POMDPs have helped solve the trade-offs between investing in management or surveillance and, more recently, to optimise adaptive management problems. Despite an increasing number of applications in ecology and natural resources, POMDPs are still poorly understood. The complexity of the mathematics, the inaccessibility of POMDP solvers developed by the Artificial Intelligence (AI) community, and the lack of introductory material are likely reasons for this. We propose to bridge this gap by providing a primer on POMDPs, a typology of case studies drawn from the literature, and a repository of POMDP problems. We explain the steps required to define a POMDP when the state of the system is imperfectly detected (state uncertainty) and when the dynamics of the system are unknown (model uncertainty). We provide input files and solutions to a selected number of problems, reflect on lessons learned applying these models over the last 10 years and discuss future research required on interpretable AI. Partially observable Markov decision processes are powerful decision models that allow users to make decisions under imperfect observations over time. This primer will provide a much-needed entry point to ecologists.

关键词： AI decisions partially observable Markov decision processes stochastic dynamic programming uncertainty

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On aims and methods of collective animal behaviour

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ANIMAL BEHAVIOUR 2024年 210卷 189-197页

作者： Marshall, James A. R. Reina, Andreagiovanni Univ Sheffield Dept Comp Sci Sheffield England Opteran Technol Ltd Sheffield England Univ Libre Bruxelles Inst Interdisciplinary Studies Artificial Intellig Brussels Belgium Univ Konstanz Ctr Adv Study Collect Behav Constance Germany Max Planck Inst Anim Behav Constance Germany

Collective animal behaviour is a subfield of behavioural ecology, making extensive use of its tools of observation, experimental manipulation and model building. However, a fundamental behavioural ecology approach, the application of optimality theory, has been comparatively neglected in collective animal behaviour. This article seeks to address this imbalance, by outlining an evolutionary theory framework for the discipline. The application of optimality theory to collective animal behaviour requires a number of questions to be addressed. First, what is the correct quantity to optimize? This can be achieved via a combination of considering the organisms' life history, alongside tools such as statistical decision theory and stochastic dynamic programming. Second, what mechanism is appropriate for optimal behaviour? This involves ensuring that models are self-consistent rather than assuming parameter values. Third, at what level of selection does optimization act? Selection acts on the individual except in very particular circumstances, yet collective animal behaviour phenomena are group level, thus introducing a risk of confusing at what level adaptive properties emerge. This article presents examples under each of the three questions, as well as discussing mismatches between theory and observation. In doing so, it is hoped that collective animal behaviour fully inherits the tools and philosophy of its parent discipline of behavioural ecology. (c) 2024 The Author(s). Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour. This is an open access article under the CC BY license (http://***/licenses/ by/4.0/).

关键词： behavioural mechanism level of selection optimality theory self-consistency statistical decision theory stochastic dynamic programming

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Robust optimal reinsurance-investment strategy with price jumps and correlated claims

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INSURANCE MATHEMATICS & ECONOMICS 2020年 92卷 27-46页

作者： Chen, Zhiping Yang, Peng Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Xian Int Acad Math & Math Technol Ctr Optimizat Tech & Quantitat Finance Xian 710049 Shaanxi Peoples R China Xijing Univ Sch Sci Xian 710123 Peoples R China

This paper considers the robust optimal reinsurance-investment strategy selection problem with price jumps and correlated claims for an ambiguity-averse insurer (AAI). The correlated claims mean that future claims are correlated with historical claims, which is measured by an extrapolative bias. In our model, the AAI transfers part of the risk due to insurance claims via reinsurance and invests the surplus in a financial market consisting of a risk-free asset and a risky asset whose price is described by a jump-diffusion model. Under the criterion of maximizing the expected utility of terminal wealth, we obtain closed-form solutions for the robust optimal reinsurance-investment strategy and the corresponding value function by using the stochastic dynamic programming approach. In order to examine the influence of investment risk on the insurer's investment behavior, we further study the time-consistent reinsurance-investment strategy under the mean-variance framework and also obtain the explicit solution. Furthermore, we examine the relationship among the optimal reinsurance-investment strategies of the AAI under three typical cases. A series of numerical experiments are carried out to illustrate how the robust optimal reinsurance-investment strategy varies with model parameters, and result analyses reveal some interesting phenomena and provide useful guidances for reinsurance and investment in reality. (c) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Reinsurance-investment strategy Robust optimal Ambiguity Utility maximization Time consistency stochastic dynamic programming

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Managing and learning with multiple models: Objectives and optimization algorithms

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BIOLOGICAL CONSERVATION 2011年第4期144卷 1237-1245页

作者： Probert, William J. M. Hauser, Cindy E. McDonald-Madden, Eve Runge, Michael C. Baxter, Peter W. J. Possingham, Hugh P. Univ Queensland Ctr Appl Environm Decis Anal Sch Biol Sci St Lucia Qld 4069 Australia Univ Queensland Dept Math St Lucia Qld 4069 Australia Univ Melbourne Australian Ctr Excellence Risk Anal Parkville Vic 3010 Australia Univ Melbourne Ctr Appl Environm Decis Anal Sch Bot Parkville Vic 3010 Australia CSIRO Sustainable Ecosyst St Lucia Qld 4069 Australia US Geol Survey Patuxent Wildlife Res Ctr Laurel MD 20708 USA

The quality of environmental decisions should be gauged according to managers' objectives. Management objectives generally seek to maximize quantifiable measures of system benefit, for instance population growth rate. Reaching these goals often requires a certain degree of learning about the system. Learning can occur by using management action in combination with a monitoring system. Furthermore, actions can be chosen strategically to obtain specific kinds of information. Formal decision making tools can choose actions to favor such learning in two ways: implicitly via the optimization algorithm that is used when there is a management objective (for instance, when using adaptive management), or explicitly by quantifying knowledge and using it as the fundamental project objective, an approach new to conservation. This paper outlines three conservation project objectives - a pure management objective, a pure learning objective, and an objective that is a weighted mixture of these two. We use eight optimization algorithms to choose actions that meet project objectives and illustrate them in a simulated conservation project. The algorithms provide a taxonomy of decision making tools in conservation management when there is uncertainty surrounding competing models of system function. The algorithms build upon each other such that their differences are highlighted and practitioners may see where their decision making tools can be improved. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Adaptive management Conservation biology Decision theory Uncertainty Optimization stochastic dynamic programming

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ON THE ADAPTIVE VALUE OF PHYSIOLOGICAL INTEGRATION IN CLONAL PLANTS

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ECOLOGY 1991年第1期72卷 81-93页

作者： CARACO, T KELLY, CK UNIV OXFORD EDWARD GREY INST OXFORD OX1 3PS ENGLAND

In clonal plants, genetically identical ramets arise from a common stolon or rhizome. Anatomical connection often allows physiological integration, the translocation of resources from a larger "mother" ramet to a developing "daughter" ramet. Translocation of a limiting resource can reduce the mother's growth while increasing the daughter's growth. Our models predict patterns in resource translocation;the models assume that fitness increases with the expected biomass a genet attains over a season of vegetative growth in a stochastic environment. In each model a ramet's growth depends nonlinearly on its level of a limiting resource. If resource availability varies both spatially and temporally, and a ramet's growth does not depend on its size, an analytical approximation for total genet growth leads to several new predictions. If a ramet's growth increases as a concave function (i.e., a function with decreasing positive slope) of resource level, physiological integration should increase when spatial variance increases and spatial convariance is negative. If a ramet's growth increases as a convex function (increasing positive slope) of resource level (the less likely case), spatial variance-convariance in resource availability has the opposite effect on translocation. Independently of the concavity or convexity of the growth function, increasing temporal variance in the mother ramet's resource availability reduces translocation, and increasing temporal variance in the daughter ramet's resource availability increases translocation. When a ramet's growth increases with both its resource level and its size, translocation and growth in one time interval influence the value of future physiological integration. For this case a stochastic dynamic programming model demonstrates how translocation can depend on time and the sizes of the mother and daughter ramets, as well as on spatiotemporal resource variability. The predictions qualitatively match those deduced from the model

关键词： CLONAL PLANTS GENET PHYSIOLOGICAL INTEGRATION RAMET RESOURCE TRANSLOCATION stochastic dynamic programming

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Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks

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INSURANCE MATHEMATICS & ECONOMICS 2014年第1期55卷 105-115页

作者： Guan, Guohui Liang, Zongxia Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

In this paper, we investigate an optimal reinsurance and investment problem for an insurer whose surplus process is approximated by a drifted Brownian motion. Proportional reinsurance is to hedge the risk of insurance. Interest rate risk and inflation risk are considered. We suppose that the instantaneous nominal interest rate follows an Ornstein-Uhlenbeck process, and the inflation index is given by a generalized Fisher equation. To make the market complete, zero-coupon bonds and Treasury Inflation Protected Securities (TIPS) are included in the market. The financial market consists of cash, zero-coupon bond, TIPS and stock. We employ the stochastic dynamic programming to derive the closed-forms of the optimal reinsurance and investment strategies as well as the optimal utility function under the constant relative risk aversion (CRRA) utility maximization. Sensitivity analysis is given to show the economic behavior of the optimal strategies and optimal utility. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Optimal proportional reinsurance strategy Optimal investment strategy CRRA utility stochastic dynamic programming stochastic inflation index stochastic interest rate

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