A simultaneous perturbation stochastic approximation algorithm for coupled well placement and control optimization under geologic uncertainty

2012 ◽  
Vol 17 (1) ◽  
pp. 167-188 ◽  
Author(s):  
Lianlin Li ◽  
Behnam Jafarpour ◽  
M. Reza Mohammad-Khaninezhad
Keyword(s):  
Approximation Algorithm ◽  
Stochastic Approximation ◽  
Well Placement ◽  
Simultaneous Perturbation Stochastic Approximation ◽  
Stochastic Approximation Algorithm ◽  
Control Optimization ◽  
Geologic Uncertainty ◽  
And Control

scholarly journals An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 174
Author(s):  
Wenxiao Zhao
Keyword(s):  
Approximation Algorithm ◽  
Stochastic Approximation ◽  
Probabilistic Method ◽  
Principal Component ◽  
Stochastic Approximation Algorithm ◽  
The Past ◽  
Systems And Control ◽  
Ode Method ◽  
Centralized Algorithm ◽  
And Control

The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).

Simultaneous Perturbation Stochastic Approximation Algorithm for Solving Stochastic Problems of Transportation Network Analysis

2008 ◽  
Vol 2085 (1) ◽  
pp. 12-20 ◽  
Author(s):  
Eren Erman Ozguven ◽  
Kaan Ozbay
Keyword(s):  
Network Analysis ◽  
Approximation Algorithm ◽  
Stochastic Approximation ◽  
Traffic Assignment ◽  
Transportation Network ◽  
Assignment Problems ◽  
Worst Case ◽  
Simultaneous Perturbation Stochastic Approximation ◽  
Stochastic Approximation Algorithm ◽  
Number Of Iterations

Stochastic optimization has become one of the important modeling approaches in transportation network analysis. For example, for traffic assignment problems based on stochastic simulation, it is necessary to use a mathematical algorithm that iteratively seeks out the optimal, the suboptimal solution, or both, because an analytical (closed-form) objective function is not available. Therefore, efficient stochastic approximation algorithms that can find optimal or suboptimal solutions to these problems are needed. The method of successive averages (MSA), a well-known algorithm, is used to solve both deterministic and stochastic equilibrium assignment problems. As found in previous studies, the MSA has questionable convergence characteristics, especially when the number of iterations is not sufficiently large. In fact, the stochastic approximation algorithm is of little practical use if the number of iterations to reduce the errors to within reasonable bounds is arbitrarily large. An efficient method to solve stochastic approximation problems is the simultaneous perturbation stochastic approximation (SPSA), which can be a viable alternative to the MSA because of its proven power to converge to sub-optimal solutions in the presence of stochasticities and its ease of implementation. The performance of MSA and SPSA algorithms is compared for solving traffic assignment problems with varying levels of stochastic-ities on a small network. The utmost importance is given to comparison of the convergence characteristics of the two algorithms as well as to the computational times. A worst-case scenario is also studied to check the efficiency and practicality of both algorithms in terms of computational times and accuracy of results.

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