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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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BookDOI
01 Jan 2001
TL;DR: In this article, real-time control of a container crane under state-dependent constraints using nonlinear nonlinear programming (NLP) and sensitivity analysis is used to find the optimal control solution for the nonlinear heat equation.
Abstract: I Optimal Control for Ordinary Differential Equations.- Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods.- Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints.- Real-Time Control of an Industrial Robot under Control and State Constraints.- Real-Time Optimal Control of Shape Memory Alloy Actuators in Smart Structures.- Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy.- Real-Time Optimization of DAE Systems.- Real-Time Solutions of Bang-Bang and Singular Optimal Control Problems.- Conflict Avoidance During Landing Approach Using Parallel Feedback Control.- II Optimal Control for Partial Differential Equations.- Optimal Control Problems with a First Order PDE System - Necessary and Sufficient Optimality Conditions.- Optimal Control Problems for the Nonlinear Heat Equation.- Fast Optimization Methods in the Selective Cooling of Steel.- Real-Time Optimization and Stabilization of Distributed Parameter Systems with Piezoelectric Elements.- Instantaneous Control of Vibrating String Networks.- Modelling, Stabilization, and Control of Flow in Networks of Open Channels.- Optimal Control of Distributed Systems with Break Points.- to Model Based Optimization of Chemical Processes on Moving Horizons.- Multiscale Concepts for Moving Horizon Optimization.- Real-Time Optimization for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column.- Towards Nonlinear Model-Based Predictive Optimal Control of Large-Scale Process Models with Application to Air Separation Plants.- IV Delay Differential Equations in Medical Decision Support Systems.- Differential Equations with State-Dependent Delays.- Biomathematical Models with State-Dependent Delays for Granulocytopoiesis.- Stochastic Optimization for Operating Chemical Processes under Uncertainty.- A Multistage Stochastic Programming Approach in Real-Time Process Control.- Optimal Control of a Continuous Distillation Process under Probabilistic Constraints.- Adaptive Optimal Stochastic Trajectory Planning.- Stochastic Optimization Methods in Robust Adaptive Control of Robots.- Multistage Stochastic Integer Programs: An Introduction.- Decomposition Methods for Two-Stage Stochastic Integer Programs.- Modeling of Uncertainty for the Real-Time Management of Power Systems.- Online Scheduling of Multiproduct Batch Plants under Uncertainty.- VIII Combinatorial Online Planning in Transportation.- Combinatorial Online Optimization in Real Time.- Online Optimization of Complex Transportation Systems.- Stowage and Transport Optimization in Ship Planning.- IX Real-Time Annealing in Image Segmentation.- Basic Principles of Annealing for Large Scale Non-Linear Optimization.- Multiscale Annealing and Robustness: Fast Heuristics for Large Scale Non-linear Optimization.- Author Index.

221 citations

Journal ArticleDOI
TL;DR: In this article, a two-stage stochastic linear programming approach is proposed within a multi-period planning model that takes into account the production and inventory levels, transportation modes, times of shipments, and customer service levels.
Abstract: In this article, we consider the risk management for mid-term planning of a global multi-product chemical supply chain under demand and freight rate uncertainty. A two-stage stochastic linear programming approach is proposed within a multi-period planning model that takes into account the production and inventory levels, transportation modes, times of shipments, and customer service levels. To investigate the potential improvement by using stochastic programming, we describe a simulation framework that relies on a rolling horizon approach. The studies suggest that at least 5% savings in the total real cost can be achieved compared with the deterministic case. In addition, an algorithm based on the multi-cut L-shaped method is proposed to effectively solve the resulting large scale industrial size problems. We also introduce risk management models by incorporating risk measures into the stochastic programming model, and multi-objective optimization schemes are implemented to establish the tradeoffs between cost and risk. To demonstrate the effectiveness of the proposed stochastic models and decomposition algorithms, a case study of a realistic global chemical supply chain problem is presented. 2009 American Institute of Chemical Engineers AIChE J, 55: 931–946, 2009

221 citations

Journal ArticleDOI
TL;DR: The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition and finite convergence of the method is established when Gomory’s fractional cutting plane algorithm or a branch-and-bound algorithm is applied.
Abstract: We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of the method is established when Gomory’s fractional cutting plane algorithm or a branch-and-bound algorithm is applied.

220 citations

Journal ArticleDOI
TL;DR: Numerical simulation results show that DP-derived heuristic rules are developed to coordinate shading blinds and natural ventilation, with simplified optimization strategies for HVAC and lighting systems, and can effectively reduce energy costs and improve human comfort.
Abstract: Buildings account for nearly 40% of global energy consumption. About 40% and 15% of that are consumed, respectively, by HVAC and lighting. These energy uses can be reduced by integrated control of active and passive sources of heating, cooling, lighting, shading and ventilation. However, rigorous studies of such control strategies are lacking since computationally tractable models are not available. In this paper, a novel formulation capturing key interactions of the above building functions is established to minimize the total daily energy cost. To obtain effective integrated strategies in a timely manner, a methodology that combines stochastic dynamic programming (DP) and the rollout technique is developed within the price-based coordination framework. For easy implementation, DP-derived heuristic rules are developed to coordinate shading blinds and natural ventilation, with simplified optimization strategies for HVAC and lighting systems. Numerical simulation results show that these strategies are scalable, and can effectively reduce energy costs and improve human comfort.

219 citations

Journal ArticleDOI
TL;DR: The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations and the concept of r-concave discrete probability distributions is introduced.
Abstract: We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples.

219 citations


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