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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: In this article, the authors consider simultaneous optimization of well locations and dynamic rate allocations under geologic uncertainty using a variant of the simultaneous perturbation and stochastic approximation (SPSA).
Abstract: Development of subsurface energy and environmental resources can be improved by tuning important decision variables such as well locations and operating rates to optimize a desired performance metric. Optimal well locations in a discretized reservoir model are typically identified by solving an integer programming problem while identification of optimal well settings (controls) is formulated as a continuous optimization problem. In general, however, the decision variables in field development optimization can include many design parameters such as the number, type, location, short-term and long-term operational settings (controls), and drilling schedule of the wells. In addition to the large number of decision variables, field optimization problems are further complicated by the existing technical and physical constraints as well as the uncertainty in describing heterogeneous properties of geologic formations. In this paper, we consider simultaneous optimization of well locations and dynamic rate allocations under geologic uncertainty using a variant of the simultaneous perturbation and stochastic approximation (SPSA). In addition, by taking advantage of the robustness of SPSA against errors in calculating the cost function, we develop an efficient field development optimization under geologic uncertainty, where an ensemble of models are used to describe important flow and transport reservoir properties (e.g., permeability and porosity). We use several numerical experiments, including a channel layer of the SPE10 model and the three-dimensional PUNQ-S3 reservoir, to illustrate the performance improvement that can be achieved by solving a combined well placement and control optimization using the SPSA algorithm under known and uncertain reservoir model assumptions.

127 citations

Journal ArticleDOI
01 Jul 1974
TL;DR: In this paper, a review of the recent literature within the power systems field can be found in Section 5.1. The authors point out some specific areas where more work needs to be done.
Abstract: Important power system planning and operation problems have been formulated as mathematical optimization problems. Such problems as the economic dispatch, in many of its facets; var scheduling and allocation; pollution dispatch; maximum interchange; hydrothermal unit commitment and dispatch; generation, transmission, and distribution expansion planning; maintenance scheduling and substation switching, have been formulated and solved. Modern mathematical optimization techniques, such as nonlinear, quadratic, linear, integer and dynamic programming and their many combinations and extensions, have been exploited. Some of the formulations and solutions to these problems as presented in the recent literature within the power systems field are reviewed. The large number of papers available is a measure of the current immense activity in this area. Attempts are made to point out some specific areas where more work needs to be done.

127 citations

Journal ArticleDOI
TL;DR: An overview and classification of stochastic models dealing with price risks in electricity markets is given and shortcomings of existing approaches and open issues that should be addressed by operation research are discussed.

127 citations

Journal ArticleDOI
TL;DR: A multi-stage stochastic programming approach to formulate a flexible energy plan that incorporates multiple future scenarios and provides for mid-course corrections depending upon the actual realizations of future uncertainties can give insights beyond the scope of an analysis based on deterministic scenarios.

127 citations

Journal ArticleDOI
TL;DR: This work shows that convergence towards the extremum of a static map can be guaranteed with a stochastic ES algorithm, and quantifies the behavior of a system with Gaussian-distributed perturbations at the extremu in terms of the ES constants and map parameters.
Abstract: Extremum seeking (ES) using deterministic periodic perturbations has been an effective method for non-model based real time optimization when only limited plant knowledge is available. However, periodicity can naturally lead to predictability which is undesirable in some tracking applications and unrepresentative of biological optimization processes such as bacterial chemotaxis. With this in mind, it is useful to investigate employing stochastic perturbations in the context of a typical ES architecture, and to compare the approach with existing stochastic optimization techniques. In this work, we show that convergence towards the extremum of a static map can be guaranteed with a stochastic ES algorithm, and quantify the behavior of a system with Gaussian-distributed perturbations at the extremum in terms of the ES constants and map parameters. We then examine the closed loop system when actuator dynamics are included, as the separation of time scales between the perturbation signal and plant dynamics recommended in periodic ES schemes cannot be guaranteed with stochastic perturbations. Consequently, we investigate how actuator dynamics influence the allowable range of ES parameters and necessitate changes in the closed loop structure. Finally simulation results are presented to demonstrate convergence and to validate predicted behavior about the extremum. For the sake of analogy with the classical methods of stochastic approximation, stochastic ES in this technical note is pursued in discrete time.

127 citations


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