Application of a second-order stochastic optimization algorithm for fitting stochastic epidemiological models

The most widely used method applied in the context of off-line dynamic demand calibration is Simultaneous Perturbation Stochastic Approximation (SPSA). In the research following the SPSA approach single origin-destination (O-D) demand components were mostly considered as calibration parameters. However, basic SPSA, especially in high dimensions, shows convergence issues, as proven by various authors. To overcome this drawback, some authors suggested modifications of basic SPSA to improve its performance. In this paper, we investigate various techniques and approaches to improve the SPSA performance, and overcome, or at least alleviate, its shortcomings. We concentrate our analysis mostly on SPSA coefficients and gradient control. The comparison of investigated settings is conducted on a real-world network. This establishes a path to identify critical aspects that influence the calibration process and suggests an optimal SPSA configuration for practice. The contribution of this paper is to provide a detailed analysis of the SPSA behavior in cases its configuration is subject to various modifications. The findings are primarily intended for the offline context. However, the insights can also be used for the selection of the most efficient SPSA configuration given time constraint, particularly suitable for on-line applications.

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.

B034 PARALLEL WELL LOCATION OPTIMIZATION USING STOCHASTIC ALGORITHMS ON THE GRID COMPUTATIONAL FRAMEWORK 1 Hector Klie 1 Wolfgang Bangerth 1 2 Mary F. Wheeler 1 Manish Parashar 3 and Vincent Matossian 3 1 Center for Subsurface Modeling The University of Texas at Austin Austin TX. 2 Institute for Geophysics The University of Texas at Austin Austin TX. 3 The Applied Software Systems Laboratory Rutgers University Piscataway NJ. Abstract The determination of optimal well locations is a challenging problem in oil production since it depends on geological and fluid properties as well as on economic parameters. This work addresses the efficient

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.

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.

Aerodynamic optimization design of wing shape is a complicated problem, so the computational efficiency of the method is very important. Genetic Algorithms (GAs) are strong tools for solving the large-scale optimization problems. They have very strong global search capability, but poor local search capability. This makes GAs converge very slowly especially when they are used for such complex question as the inverse design of 3d wing shape. The genetic operators are specially designed and Simultaneous Perturbation Stochastic Approximation (SPSA) is introduced into Stochastic Gradient Genetic Algorithm (SGGA). In fact, SPSA is a simple, easily implemented and efficient stochastic approximation algorithm. Also SGGA is used for the inverse design of wing shape. And flow field is calculated by means of wing supercritical analysis program-the software of simplification version of FLO22VSE. The paper explores a high efficient method for the inverse design of wing shape. The experiments show satisfactory results.

The parameters of a transportation simulation model need to pass through a careful calibration process to ensure that the model’s output is as close as possible to the actual system. Owing to the computationally expensive and black-box nature of a simulation model, there is a need for robust and efficient calibration algorithms. This paper proposes a Bayesian optimization framework for the high-dimensional calibration problem of transportation simulation models. Bayesian optimization uses acquisition functions to determine more promising values for future evaluation, instead of relying on local gradient approximations. It guarantees convergence to the global optimum with a reduced number of evaluations, therefore is very computationally efficient. The proposed algorithm is applied to the calibration of a simulation network coded in simulation of urban mobility (SUMO), an open-source microscopic transportation simulation platform, and compared with a well-known method named simultaneous perturbation stochastic approximation (SPSA). To assess the calibration accuracy, speed distributions obtained from the two models calibrated using these two different methods are compared with the observation. For both the Bayesian optimization and SPSA results, the simulated and observed distributions are validated to be from the same distribution at a 95% confidence level for multiple sensor locations. Thus, the calibration accuracy of the two approaches are both acceptable for a stochastic transportation simulation model. However, Bayesian optimization shows a better convergence and a higher computational efficiency than SPSA. In addition, the comparative results of multiple implementations validate its robustness for a noisy objective function, unlike SPSA which may sometimes get stuck in a local optimum and fail to converge in a global solution.

The minimization of a convex function defined over the grid Z/sup p/ is considered. A few relevant mathematical devices such as integer convexity, Markov chain Monte Carlo (MCMC) methods, including stochastic comparison (SC), and simultaneous perturbation stochastic approximation (SPSA) are summarized. A truncated fixed gain SPSA method is proposed and investigated in combination with devices borrowed from the MCMC literature. The main contribution of the paper is the development and testing a number of devices that may eventually improve the convergence properties of the algorithm, such as various truncation techniques, averaging and choices of acceptance probabilities. The basis for comparison of performances is accuracy vs. number of function evaluations. We present experimental evidence for the superiority of an SC method allowing moves in wrong directions with small probability, where the underlying method is an SPSA method using averaging and adaptive truncation.

Calibration and validation have long been a significant topic in traffic model development. In fact, when moving to dynamic traffic assignment (DTA) models, the need to dynamically update the demand and supply components creates a considerable burden on the existing calibration algorithms, often rendering them impractical. These calibration approaches are mostly restricted either due to non-linearity or increasing problem dimensionality. Simultaneous perturbation stochastic approximation (SPSA) has been proposed for the DTA model calibration, with encouraging results, for more than a decade. However, it often fails to converge reasonably with the increase in problem size and complexity. In this paper, we combine SPSA with principal components analysis (PCA) to form a new algorithm, we call, PC–SPSA. The PCA limits the search area of SPSA within the structural relationships captured from historical estimates in lower dimensions, reducing the problem size and complexity. We formulate the algorithm, demonstrate its operation, and explore its performance using an urban network of Vitoria, Spain. The practical issues that emerge from the scale of different variables and bounding their values are also analyzed through a sensitivity analysis using a non-linear synthetic function.

In this paper we consider a possible application of simultaneous perturbation stochastic approximation (SPSA) method to problems of control of educational processes. SPSA is an efficient tool for optimization problems and uncertain parameters estimation. What is more important, such SPSA procedures actually work under arbitrary external observation noise, while most other optimization methods work only with Gaussian noises. The illustrative example is also presented.

Arriving at optimal signal timing parameters to improve the efficiency of traffic flow has been one of the major challenges faced by traffic engineers. The choice of a robust optimization framework and an accurate traffic model plays a significant role in determining optimal signal timing parameters. Though traffic flow is intuitively stochastic, few studies incorporate stochasticity in their optimization framework for traffic signal design. This study proposes two simulation-based stochastic optimization algorithms—an evolutionary algorithm-based framework and a simultaneous perturbation stochastic approximation (SPSA) algorithm-based framework for the optimal signal design of an isolated intersection using a calibrated microsimulation environment with reasonable accuracy. A software-in-the loop approach is used to control the traffic signals in the microsimulation environment. SPSA is a gradient descent algorithm with a powerful approach for approximating the gradient with just two function evaluations per gradient approximation. To evaluate the performance of the two frameworks, the study optimizes the signal timings for a case study on an isolated intersection in an urban arterial in Chennai. On comparing the two algorithms, it is found that SPSA performed better and took 100 function evaluations less than that taken by GA. A better (near optimal) initial solution is found to yield a faster rate of convergence for both algorithms. As the proposed optimization framework incorporates the stochastic nature of traffic in the optimization algorithm, it can accommodate the temporal variations in traffic and thereby provide traffic engineers a robust signal control strategy for improving the efficiency of traffic flow.

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.

This study proposes a data-driven PID tuning for liquid slosh suppression based on enhanced stochastic approximation. In particular, a new version of Simultaneous Perturbation Stochastic Approximation (SPSA) based on memory type function is introduced. This memory-based SPSA (M-SPSA) algorithm has the capability to obtain a better optimization accuracy than the conventional SPSA since it is able to keep the best design parameter during the tuning process. The effectiveness of this algorithm is tested to data-drive PID tuning for liquid slosh problem. The achievement of the M-SPSA based algorithm is assessed in terms of trajectory tracking of trolley position, slosh angle reduction and also computation time. The outcome of this study shows that the PID-tuned M-SPSA is able to provide better control performance accuracy than the other variant of SPSA based 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

A novel data based control method is proposed by modifying the cost function of a model-free control method based on Simultaneous Perturbation Stochastic Approximation (SPSA). The controller is constructed through use of a Function Approximator (FA), which is fixed as a neural network here. In the novel approach, the ability of the controller has been greatly improved. At last, the proposed modified control method is applied to solve non-linear tracking problems. Simulation comparison tests were done on typical non-linear plants, through which, the effectiveness of the novel data based control method is fully illustrated.