Topic
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: The approximate method, proposed, minimize the cost functions of the resulting nonlinear programming problems include complex averaging operations, and is considered as an extension to the Ritz method, for which fixed basis functions are used.
Abstract: Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as an extension to the Ritz method, for which fixed basis functions are used). Then, the functional optimization problem can be approximated by nonlinear programming problems. Linear combinations of basis functions are called approximating networks when they benefit from suitable density properties. We term such networks nonlinear (linear) approximating networks if their basis functions contain (do not contain) free parameters. For certain classes of d-variable functions to be approximated, nonlinear approximating networks may require a number of parameters increasing moderately with d, whereas linear approximating networks may be ruled out by the curse of dimensionality. Since the cost functions of the resulting nonlinear programming problems include complex averaging operations, we minimize such functions by stochastic approximation algorithms. As important special cases, we consider stochastic optimal control and estimation problems. Numerical examples show the effectiveness of the method in solving optimization problems stated in high-dimensional setting, involving for instance several tens of state variables.
138 citations
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TL;DR: In this article, the optimal operation of a VPP considering the risk factors affecting its daily operation profits is modelled in both day ahead and balancing markets as a two-stage stochastic mixed integer linear programming in order to maximize a GenCo (generation companies) expected profit.
138 citations
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TL;DR: Based on Lyapunov-like function method and It's formula, comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established and the stability properties of stochastically impulsive Systems are derived by the corresponding stability Properties of a deterministic impulsive system.
Abstract: This note studies stability problem of solutions for stochastic impulsive systems. By employing Lyapunov-like function method and It's formula, comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established. Based on these comparison principles, the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system. As the application, the stability results are used to design impulsive control for the stabilization of unstable stochastic systems. Finally, one example is given to illustrate the obtained results.
138 citations
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TL;DR: In this paper, a reinforcement learning approach, called fitted Q-iteration, is presented: it combines the principle of continuous approximation of the value functions with a process of learning off-line from experience to design daily, cyclostationary operating policies.
Abstract: [1] Although being one of the most popular and extensively studied approaches to design water reservoir operations, Stochastic Dynamic Programming is plagued by a dual curse that makes it unsuitable to cope with large water systems: the computational requirement grows exponentially with the number of state variables considered (curse of dimensionality) and an explicit model must be available to describe every system transition and the associated rewards/costs (curse of modeling). A variety of simplifications and approximations have been devised in the past, which, in many cases, make the resulting operating policies inefficient and of scarce relevance in practical contexts. In this paper, a reinforcement-learning approach, called fitted Q-iteration, is presented: it combines the principle of continuous approximation of the value functions with a process of learning off-line from experience to design daily, cyclostationary operating policies. The continuous approximation, performed via tree-based regression, makes it possible to mitigate the curse of dimensionality by adopting a very coarse discretization grid with respect to the dense grid required to design an equally performing policy via Stochastic Dynamic Programming. The learning experience, in the form of a data set generated combining historical observations and model simulations, allows us to overcome the curse of modeling. Lake Como water system (Italy) is used as study site to infer general guidelines on the appropriate setting for the algorithm parameters and to demonstrate the advantages of the approach in terms of accuracy and computational effectiveness compared to traditional Stochastic Dynamic Programming.
138 citations
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TL;DR: A stochastic method for the hourly scheduling of optimal reserves when the hourly forecast errors of wind energy and load are considered and the Monte Carlo method is applied.
Abstract: This paper presents a stochastic method for the hourly scheduling of optimal reserves when the hourly forecast errors of wind energy and load are considered. The approach utilizes the stochastic security-constrained unit commitment (SCUC) model and a two-stage stochastic programming for the day-ahead scheduling of wind energy and conventional units with N-1 contingencies. The effect of aggregated hourly demand (DR) response is considered as a means of mitigating transmission violations when uncertainties are considered. The proposed mixed-integer programming (MIP) model applies the Monte Carlo method for representing the hourly wind energy and system load forecast errors. A 6-bus, 118-bus, and the Northwest region of Turkish electric power network are considered to demonstrate the effectiveness of the proposed day-ahead stochastic scheduling method in power systems.
138 citations