A constrained simultaneous perturbation stochastic approximation algorithm based on penalty functions

We present a stochastic approximation algorithm based on penalty function method and a simultaneous perturbation gradient estimate for solving stochastic optimisation problems with general inequality constraints. We present a general convergence result that applies to a class of penalty functions including the quadratic penalty function, the augmented Lagrangian, and the absolute penalty function. We also establish an asymptotic normality result for the algorithm with smooth penalty functions under minor assumptions. Numerical results are given to compare the performance of the proposed algorithm with different penalty functions.

Adaptive complementary filter using fuzzy logic and simultaneous perturbation stochastic approximation algorithm

This paper describes the implementation of a self- optimizing embedded control scheme for an induction motor drive. The online design problem is formulated as a search problem and solved with a stochastic optimization algorithm. The objective function takes in account the tracking error, and is directly measured on the hardware bench. The online optimization is performed with the simultaneous perturbation stochastic approximation (SPSA) algorithms, which offer a very effective tradeoff between simplicity of implementation, speed of convergence and quality of the final solutions. Among the known SPSA algorithms considered in this paper, we also propose a novel variant inspired to the concept of elitism frequently used in evolutionary computation. To assess the relative performances of the various algorithms, the paper carries out a comprehensive analysis of a control scheme for an induction motor drive subject to time-varying load disturbances.

Secondary path modeling is an important step in active noise control. Keeping the active noise control system stable, when the secondary path changes over time, is a widely studied problem. Using the simultaneous perturbation stochastic approximation algorithm, can update the control filter without secondary path modeling, avoiding the problem of increased noise caused by secondary path modeling. In this paper a variant of the simultaneous perturbation stochastic approximation algorithm is proposed, which incorporates historical coefficients of the control filter, to correct the direction of the gradient calculation. Based on an experimental setup with a realistic transfer path, this paper demonstrates that the proposed algorithm has superior performance in terms of convergence speed and noise reduction amount, than the general simultaneous perturbation stochastic approximation algorithm.

Rail simulation model calibration is a process of adjusting model parameters while comparing model output with observations from the real rail system. There is a lack of systematic methodology for calibrating urban rail simulation models. Based on a simulator developed for urban rail operations and control, the paper demonstrates a methodology of calibrating model parameters, and specifically, fine-tuning some of the simulation inputs. The calibration process is modeled as a multi-variate optimization problem and solved by the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. A case study of the Massachusetts Bay Transportation Authority (MBTA) Red Line shows that the methodology improves the simulation model dramatically in terms of replicating the track block runtimes. At the same time, it upgrades the station specific dwell time parameters and enhances a-priori boarding rates at stations fairly effectively.

The simultaneous perturbation stochastic approximation(SPSA) is an iterative gradient-free optimization algorithm. This algorithm approximates the optimal solution by estimating the gradient of the loss function and uses only 2 values of the loss function to estimate the gradient which is independent of the dimension of the problem. But for the high dimensional problem with large-scale, the convergence of classical SPSA algorithm is slow, even can not converge to the global minimum value. In order to accelerate the convergence of SPSA algorithm and improve the precision of the optimum solution, this paper proposes an improvement of SPSA algorithm based on the adaptive step sizes, which can adjust the step size of each iteration according to the gradient direction. The modified algorithm is implemented by Message Passing Interface (MPI) parallel in each iteration to widen the search scope for the better descending direction in order to accelerate the convergence. Numerical experiments of several classical nonlinear optimization problems shows that the modified SPSA algorithm can accelerate the convergence of nonlinear optimization problems and find the global extremum point of high-dimension for some optimization problems which the SPSA algorithm can not find. It proves that the modified algorithm with adaptive step sizes outperforms the classical SPSA algorithm.

In recent years, simulation optimization has attracted a great deal of attention because simulation can model the real systems in fidelity and capture complex dynamics. Among numerous simulation optimization algorithms, Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm is an attractive approach because of its simplicity and efficiency. Although SPSA has been applied in several problems, it does not converge for some. This research proposes Augmented Simultaneous Perturbation Stochastic Approximation (ASPSA) algorithm in which SPSA is augmented to include presearch, ordinal optimization, non-uniform gain, and line search. Performances of ASPSA are tested on complex discrete supply chain inventory optimization problems. The tests results show that ASPSA not only achieves speed up, but also improves solution quality and converges faster than SPSA. Experiments also show that ASPSA is comparable to Genetic Algorithms in solution quality (6% to 15% worse) but is much more efficient computationally (over 12x faster).Request access from your librarian to read this chapter's full text.

The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo process. The objective is to minimize the mean square error of the estimate. We also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric Bernoulli in both cases. We end the paper with a numerical study related to the area of experiment design.

Previous studies show that parameter value for car following model, such as, maximum and minimum headway, acceleration, and gap are necessary but there is a big error found while comparing between original and simulated data. Therefore, it is not appropriately applicable to determine the real driver behavior for the different traffic systems. In this study, the calibration method has been proposed to estimate the model parameter and to find the best fit to the car following model. Here, Intelligent Driver Model (IDM) has been used for simulating car behavior and data have been collected from NGSIM eastbound I-80 in the San Francisco Bay area in Emeryville, CA, USA. Simultaneous perturbation stochastic approximation algorithm (SPSAA) has been used as the calibration model in the system to calculate parameters. The calculation has been made by using MATLAB software. SPSAA is proven to have a very much lower error between original simulation data and real trajectory observation I-80 data. Furthermore, this paper investigates that such kinds of estimated parameter are more appropriate to be used in different traffic system.

Considering the problem of the highly dependence on the accuracy model information of the industrial control process, an online PID parameter tuning method is proposed based on the simultaneous perturbation stochastic approximation (SPSA) algorithm and the traditional PID control only by the input and output data of the system. Interfering with each component of the PID controller parameters simultaneously, and the gradient information of the control performance loss function is estimated via the output value after disturbance by the global optimization method of stochastic approximation algorithm. The PID controller parameter is iterative updated according to the gradient estimation value. Finally, we applied this method to the control process of cement grinding particle size, and the simulation results by MATLAB shown it can lead a high control precision which proves the feasibility and effectiveness of this adaptive PID control method.

The purpose of this study is to determine the optimum design of arch longitudinal no prismatic single-cell section. The FE model of the Cetina open spandrel arch bridge was constructed using the ANSYS. In this present work the optimum design is carried out by taking total material volume of substructure of bridge as objective function. Substructure includes of column and reinforced concrete arch. Finally, the optimization technique is performed by Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. It is concluded that SPSA can be effectively used in the shape optimization of the bridges. Keywords: Long Span, Longitudinal Section Optimization, Open Spandrel Bridge, SPSA Algorithm, Substructure

In practical active noise control (ANC) systems, the primary path and the secondary path may be nonlinear and time-varying. It has been reported that the linear techniques used to control such ANC systems exhibit degradation in performance. In addition, the actuators of an ANC system very often have nonminimum-phase response. A linear controller under such situations yields poor performance. A novel functional link artificial neural network (FLANN)-based simultaneous perturbation stochastic approximation (SPSA) algorithm, which functions as a nonlinear mode-free (MF) controller, is proposed in this paper. Computer simulations have been carried out to demonstrate that the proposed algorithm outperforms the standard filtered-x least mean square (FXLMS) algorithm, and performs better than the recently proposed filtered-s least mean square (FSLMS) algorithm when the secondary path is time-varying. This observation implies that the SPSA-based MF controller can eliminate the need of the modeling of the secondary path for the ANC system.

Current hydraulic fracturing designs are based on equal fracturing intervals, ranging from 50 to 600 feet, along the horizontal well with an equal half-length, ranging from 100 to 600 feet. However, symmetric spacing designs are only suitable for homogeneous shale fracability or brittleness, which may not be the case in many shale plays. The efficiency of the fracturing process depends on the fracability of the underlying shale rock. Therefore, the heterogeneity in shale fracability can have an important role in designing and optimizing the hydraulic fracturing process, in particular in identifying the optimal number, location, and length of the fractures. In this paper, we develop an optimization approach for hydraulic fracturing design under geospatial variability in shale fracability and investigate several aspect of the design and optimization of the fracturing process. The optimization of the hydraulic fracturing design is performed using the Simultaneous Perturbation Stochastic Approximation algorithm to maximize the net present value of the shale asset that includes the cost of fracturing and revenue from gas production. The proposed optimization framework provides a systematic hydraulic fracturing design and treatment approach for unconventional reservoirs to improve production and reduce the cost and environmental impacts of hydraulic fracturing. We demonstrate the effectiveness and suitability of the proposed method with several numerical experiments in shale gas development.

Model-free PID control tuning methods have been widely reported for the case with the time-varying uncertain systems. A model-free control system is introduced in this paper with PID controller. This control design could be considered as a contribution to kernel wavelet neural network PID controllers in model-free system with a straightforward tuning by the simultaneous perturbation stochastic approximation algorithm. It is particularly well suited to problems involving the measurement data without prior inner structure knowledge of the unknown system. On the other hand, neural network activation functions are bounded which cause the outputs of neural network to be limited. Therefore, the T-S Fuzzy control method on basis of kernel wavelet neural network (KWNN) is introduced to improve the control parameter tuning adaptivity in terms of boundedness of the KWNN excitation function. Finally, simulation results are presented to exhibit the effectiveness of the proposed IPWR control system.

A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles