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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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TL;DR: A spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren, a critically endangered Australian bird, is built and the capacity of population viability analysis (PVA) is extended to manage threatened species.
Abstract: A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus mala- churus intermedius), a critically endangered Australian bird Using discrete-time Markov chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combi- nation of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step However, it is generally limited by computational constraints to rather small networks of patches The model shows that optimal metapopulation management decisions depend great- ly on the current state of the metapopulation, and there is no strategy that is universally the best The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of man- agement actions for a metapopulation This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species

105 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a two-stage stochastic programming approach to incorporate the various possible scenarios for renewable energy generation and cost in the planning of microgrids to tackle uncertainty.

104 citations

Journal ArticleDOI
TL;DR: Two approaches for moment design sensitivities are presented,one involving response function expansions over both design and uncertain variables and one involving response derivative expansions over only the uncertain variables.
Abstract: Non-intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification (UQ) due to their strong mathematical basis and ability to produce functional representations of stochastic variability. PCE estimates coefficients for known orthogonal polynomial basis functions based on a set of response function evaluations, using sampling, linear regression, tensor-product quadrature, or Smolyak sparse grid approaches. SC, on the other hand, forms interpolation functions for known coefficients, and requires the use of structured collocation point sets derived from tensor product or sparse grids. When tailoring the basis functions or interpolation grids to match the forms of the input uncertainties, exponential convergence rates can be achieved with both techniques for general probabilistic analysis problems. Once PCE or SC representations have been obtained for a response metric of interest, analytic expressions can be derived for the moments of the expansion and for the design derivatives of these moments, allowing for efficient design under uncertainty formulations involving moment control (e.g., robust design). This paper presents two approaches for moment design sensitivities, one involving response function expansions over both design and uncertain variables and one involving response derivative expansions over only the uncertain variables. These approaches present a trade-off between increased dimensionality in the expansions (and therefore increased simulation runs required to construct them) with global expansion validity versus increased data requirements per simulation with local expansion validity. Given this capability for analytic moments and their sensitivities, we explore bilevel, sequential, and multifidelity formulations for OUU. Initial experiences with these approaches is presented for a number of benchmark test problems.

104 citations

Journal ArticleDOI
TL;DR: To solve the proposed model, a Lagrangian relaxation-based algorithm formulated by a new adaptive strategy is employed, which considers both upper and lower bounds of the problem to reach a performance solution.

104 citations

Journal ArticleDOI
TL;DR: This comment points out several mathematical errors in the proof of Therorem 3, and gives the correct expression of B3.
Abstract: This paper considers a stochastic optimization approach for job scheduling and server management in large-scale, geographically distributed data centers. Randomly arriving jobs are routed to a choice of servers. The number of active servers depends on server activation decisions that are updated at a slow time scale, and the service rates of the servers are controlled by power scaling decisions that are made at a faster time scale. We develop a two-time-scale decision strategy that offers provable power cost and delay guarantees. The performance and robustness of the approach is illustrated through simulations.

104 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532