Stochastic Optimization Procedure Research Articles

Multi-objective seismic optimization and evaluation of core-damper-frame tall buildings considering SSI effect

To control the seismic response of the core-frame (CF) structure and attenuate the stress level of the core tube, a novel core-damper-frame (CDF) system is proposed by decoupling the perimeter frame and the central core with flexible damper connectors. In this way, the large inertia force of the perimeter frame cannot be fully transmitted to the core, and the stress of the core is mitigated. In the meantime, the damper connectors would absorb a considerable amount of seismic energy, protecting the perimeter frame as the relative displacement between the two subsystems (perimeter frame and core tube) occurs. By incorporating the soil-structure-interaction (SSI) and the filtered Gaussian white-noise excitation model, the "excitation-soil-core-damper-frame" augmented system is established. Combing the augmented system and the genetic algorithm, a stochastic optimization procedure of the CDF considering the SSI effect is proposed. The optimization aims to minimize a series of performance objectives including displacement, acceleration, shear force, and overturning moment of the CDF system. The conflicting relationships between the multiple objectives are discussed; the influence of the SSI effect and the excitation parameters are evaluated. From an illustrative 40-story CDF structural example, the system shows great superiority in controlling the higher mode vibrations, and could significantly reduce the peak core acceleration (by 54.44 %), frame acceleration (by 56.48 %), core drift (by 28.83 %), frame drift (by 39.28 %), core shear (by 83.67 %), and frame moment (by 22.41 %), as compared to its conventional CF counterpart. In special, over 50 % of the input seismic energy is dissipated by the damper connectors in the CDF system.

A Two-Stage Flexibility-Oriented Stochastic Energy Management Strategy for Multi-Microgrids Considering Interaction With Gas Grid

Introduction of renewable energy sources (RESs) and independently operated multi-microgrid (MMG) systems have led to new issues in the management of power systems. In this context, uncertainty associated with RESs as well as intense ramps inflicted on the network called system flexibility constraints have raised new challenges in power systems. The new condition necessitates the implementation of novel frameworks that enable local system operators to efficiently manage the available resources to cope with the flexibility-ramp constraints. Moreover, the new framework should facilitate energy management in a system with an MMG structure considering uncertainty of RESs. Consequently, in this article, we aim to provide a novel framework that composes of a two-level stochastic optimization procedure to optimize the energy management in an MMG, considering uncertainty of RESs as well as grid flexibility constraints. In the proposed scheme, resource scheduling in microgrids (MGs) is conducted in the first level by their control units, while the second-level procedure focuses on the coordination of MGs, considering flexibility constraints. Furthermore, interaction with gas grid as a potential flexible resource is optimized in the second-level procedure. Finally, the provided flexibility-oriented management scheme is implemented to schedule the local resources in a three-MG test system, considering flexibility constraints.

A similarity-based Bayesian mixture-of-experts model

We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is especially advantageous in settings where inputs are of relatively high dimension in comparison to the data size, where input–output relationships are complex, and where predictive distributions may be skewed or multimodal. Computational studies on five datasets, of which two are synthetically generated, illustrate clear advantages of our mixture-of-experts method for high-dimensional inputs, outperforming competitor models both in terms of validation metrics and visual inspection.

Solving the Schrödinger Equation with Genetic Algorithms: A Practical Approach

The Schrödinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 1970s, the computer began to be used to solve this equation in elementary quantum systems, and, in the most complex case, a ‘hydrogen-like’ system. Obtaining the solution means finding the wave function, which allows predicting the physical and chemical properties of the quantum system. However, when a quantum system is more complex than a ‘hydrogen-like’ system, we must be satisfied with an approximate solution of the equation. During the last decade, application of algorithms and principles of quantum computation in disciplines other than physics and chemistry, such as biology and artificial intelligence, has led to the search for alternative techniques with which to obtain approximate solutions of the Schrödinger equation. In this work, we review and illustrate the application of genetic algorithms, i.e., stochastic optimization procedures inspired by Darwinian evolution, in elementary quantum systems and in quantum models of artificial intelligence. In this last field, we illustrate with two ‘toy models’ how to solve the Schrödinger equation in an elementary model of a quantum neuron and in the synthesis of quantum circuits controlling the behavior of a Braitenberg vehicle.

Analysis of the Application of the Integrated Catastrophe Risk Model Method for the Flood Insurance Program

As the flood rises continue to grow, well-designed insurance programs are becoming an important instrument in flood risk management. One of the obstacles in the flood insurance program is the method used to calculate the premium value. This thesis refers to the Integrated Catastrophe Risk Model (ICRM) which consists of two probability events and stochastic optimization procedures with respect to observation of site-specific risk. The application of the model is illustrated in the study area simulation data. In this thesis, analysis of various aspects of trade-off, new ex-post variables, opportunity occurrence 1 and 2 and minimization of loss function. From the results of research based on these four aspects it can be concluded that the use of Integrated Catastrophe Risk Model method in the optimal flood insurance program.

A Three-Component Additive Weibull Distribution and Its Reliability Implications

We consider a new failure time distribution by combining three Weibull distributions. The proposed distribution exhibits decreasing, increasing, and bathtub-shaped failure rate functions. Some statistical properties of the proposed distribution are presented. The maximum likelihood method is used to estimate the parameters, reliability, and failure rate functions of the proposed distribution, and the uncertainties of the estimates are obtained by using asymptotic confidence intervals. The cross-entropy method, a stochastic optimization procedure, is used to find the maximum of the log-likelihood function. The superiority of the proposed distribution is demonstrated on two benchmark datasets.

Stochastic Optimization of Multiple Tuned Inerter Dampers for Mitigating Seismic Responses of Bridges with Friction Pendulum Systems

Friction pendulum systems (FPSs) are increasingly being used for bridge seismic isolation, and the isolated response is generally achieved at the expense of inducing large bearing displacements. Setting up a tuned inerter damper (TID) is an approach for improving seismic performance. Nevertheless, the optimization and performance enhancement of multiple TIDs to mitigate the seismic responses of bridges isolated with the FPSs are limited. In this study, the stochastic optimization of multiple TIDs for controlling stochastically excited bridges with FPS bearings was pursued. By describing the hysteretic characteristics of the FPS using the Bouc–Wen model, augmented systems of the bridge model, FPS bearings, and TIDs were formulated and combined with the modeling of stochastic excitation as filtered Gaussian white noise. A stochastic optimization procedure of multiple TIDs for controlling the bridge response considering the nonlinearity of the FPS bearings is proposed and illustrated using examples of continuous bridges. The effects of FPS friction on the optimization and robustness of the TID parameters were identified. A parametric study was performed to determine the mechanism of TID performance enhancement depending on the number of TIDs, multiple modes of tuning, and inertance distribution. Numerical results indicate that the TIDs designed via stationary-stochastic-global (SSG) optimization significantly reduced the responses of the isolated bridge, and the performance was improved by increasing the TID number. Considering the multi-mode contributions to the transversal responses, the performance of spatially distributed TIDs can be substantially enhanced by adding the TID inertance as a design parameter.

Risk analysis of integrated biomass and concentrated solar system using downside risk constraint procedure

In the electric power industry, solar energy and bioenergy are two energy resources that produce near-zero emissions. In order to generate dispatchable electricity power and make increments in the role of the ever-growing renewable-dominated networks, the concentrated solar energy connected with biomass boiler and thermal storage unit could be used. In this regard, the model of day-ahead and intra-day dispatch is represented for an integrated biomass-concentrated solar (IBCS) system with the aim of maximizing the system profitability by a cooperative association of the elements of the system. Furthermore, to capture the impact of uncertainties on the system function, the investigation of the IBCS system is carried out based on a stochastic optimization procedure called the downside risk constraint (DRC) method, which is a scenario-based procedure. In this method, the function of the elements is explored thoroughly regarding the risk-averse and risk-neutral (under risky condition) strategies (risk is not considered). The simulation results demonstrated that the proposed model of the dispatch can achieve considerable profit for the decision-maker of the system. For instance, the obtained profit in the risk-averse model is 27074.5 $, while in the risk-neutral model, it is 31,347 $. This reveals that the system operator needs to increase %14 of its expenditure in the risk-averse strategy to increase the system's security.

Comparing the performance of a nested to a continuous evolution strategy with covariance matrix adaption for optimization of drilling EDM

Electrical discharge machining (EDM) is a complex manufacturing process where the correlation of the individual process parameters is not fully known. When introducing new materials or complex, individual geometries in EDM, a satisfactory vector of parameters for the process must be found. This challenge is often encountered in the aerospace industry as well as in mold and tool making. One previously successful method to tackle this challenge is the stochastic optimization procedure Evolutionary Strategy (ES). Utilizing an appropriately chosen objective function, the search for a suitable vector of input parameters may be formulated as a mathematical minimization problem over the parameter space. The ES with a covariance matrix adaption (CMA) was utilized to sample from this parameter space in a stochastic manner. Examining the impact of the CMA within an ES is a promising way to gain better insight into the performance of ES. For this purpose, a vector of input parameters was optimized for a drilling EDM process with a comma and a nested comma ES with CMA. It was found that the comma ES led to a reduction in erosion duration tero of 38 % compared to the initially chosen parameters and the nested comma ES led to a reduction in erosion duration tero of 27 % compared to the same initial parameters. The additional information stored in the covariance matrix enables the ES to find a local optimum of the parameter vector faster and more consistently. This fact is verified by use of visualizations of the covariance matrix on a two-dimensional subspace. From these findings it can be concluded, that for the application of the ES to the optimization of EDM processes the CMA should be performed continuously over all generations as opposed to resetting this matrix after a number of generations.

Economic power generation scheduling exploiting hill-climbed Sine–Cosine​ algorithm

This paper recommends a stochastic population-based optimization procedure named the hill-climbed Sine–Cosine algorithm (HcSCA) to solve the economic generation scheduling (EcGS) of thermal units. The sine–cosine algorithm creates a set of preliminary random individuals and needs them to change away from or near to the destination to create a new population-based on functions of sine and cosine. The sine–cosine algorithm finds the solution quickly while balancing exploration and exploitation but stagnates to a sub-optimal solution. To avoid stagnation, the sine–cosine optimization procedure coordinates local search and hill-climbing heuristics. The specific features i.e. valve-point loading effect, ramp-rate limits, generator limits for generation, prohibited operating zones, and power demand constraints with losses are assumed to resolve power economic thermal generation scheduling. The success of the recommended method is observed on small- and large-scale power test systems. The outcome of the recommended algorithm is matched with erstwhile algorithms. From the experimental results, it is experienced that HcSCA provides a competing solution to economic thermal generation scheduling problems.

Control problem for the impulse process under stochastic optimization procedure and Levy conditions

A stochastic approximation procedure and a limit generator of the original problem are constructed for a system of stochastic differential equations with Markov switching and impulse perturbation under Levy approximation conditions with control, which is determined by the condition for the extremum of the quality criterion function.The control problem using the stochastic optimization procedure is a generalization of the control problem with the stochastic approximation procedure, which was studied in previous works of the authors. This generalization is not simple and requires non-trivial approaches to solving the problem. In particular we discuss how the behavior of the boundary process depends on the prelimiting stochastic evolutionary system in the ergodic Markov environment. The main assumption is the condition for uniform ergodicity of the Markov switching process, that is, the existence of a stationary distribution for the switching process over large time intervals. This allows one to construct explicit algorithms for the analysis of the asymptotic behavior of a controlled process. An important property of the generator of the Markov switching process is that the space in which it is defined splits into the direct sum of its zero-subspace and a subspace of values, followed by the introduction of a projector that acts on the subspace of zeros.For the first time, a model of the control problem for the diffusion transfer process using the stochastic optimization procedure for control problem is proposed. A singular expansion in the small parameter of the generator of the three-component Markov process is obtained, and the problem of a singular perturbation with the representation of the limiting generator of this process is solved.

Simultaneous process parameters and heat integration optimization for industrial organosilicon production

Traditionally, the heat integrated schemes begin from the well-designed process, design parameters of a chemical process are first optimized based on various objectives (economic, environmental, sustainable, etc.), followed by the stiff heat integration. This may result in the omission of competitive solutions and unfair process comparisons. However, the reverse procedure, potential heat integrated structures prior to parameter optimization, require an exhaustive enumeration and is time-consuming. As a solution, this work proposes a simultaneous process parameter and heat integration optimization approach, by incorporating the consideration of heat integrated networks into a stochastic optimization procedure. Four complex industrial organosilicon production configurations with 4 or 5 columns, as illustrative examples, verify the feasibility of the proposed approach.

Задача керування для імпульсного процесу в умовах процедури стохастичної оптимізації та некласичних схем апроксимації

A stochastic approximation procedure and a limit generator of the original problem are constructed for a system of stochastic differential equations with Markov switching and impulse perturbation under noclassical approximation conditions with control, which is determined by the condition for the extremum of the quality criterion function. The control problem using the stochastic optimization procedure is a generalization of the control problem with the stochastic approximation procedure, which was studied in previous works of the authors. This generalization is not simple and requires non-trivial approaches to solving the problem. In particular we discuss how the behavior of the boundary process depends on the pre-limiting stochastic evolutionary system in the ergodic Markov environment. The main assumption is the condition for uniform ergodicity of the Markov switching process, that is, the existence of a stationary distribution for the switching process over large time intervals. This allows one to construct explicit algorithms for the analysis of the asymptotic behavior of a controlled process. An important property of the generator of the Markov switching process is that the space in which it is defined splits into the direct sum of its zero-subspace and a subspace of values, followed by the introduction of a projector that acts on the subspace of zeros. For the first time, a model of the control problem for the diffusion transfer process using the stochastic optimization procedure for control problem is proposed. A singular expansion in the small parameter of the generator of the three-component Markov process is obtained, and the problem of a singular perturbation with the representation of the limiting generator of this process is solved \KeywordsEng random evolution, nonclassical approximation conditions, stochastic optimization procedure, Markov process.

Stochastic optimization with momentum: Convergence, fluctuations, and traps avoidance

In this paper, a general stochastic optimization procedure is studied, unifying several variants of the stochastic gradient descent such as, among others, the stochastic heavy ball method, the Stochastic Nesterov Accelerated Gradient algorithm (S-NAG), and the widely used Adam algorithm. The algorithm is seen as a noisy Euler discretization of a non-autonomous ordinary differential equation, recently introduced by Belotto da Silva and Gazeau, which is analyzed in depth. Assuming that the objective function is non-convex and differentiable, the stability and the almost sure convergence of the iterates to the set of critical points are established. A noteworthy special case is the convergence proof of S-NAG in a non-convex setting. Under some assumptions, the convergence rate is provided under the form of a Central Limit Theorem. Finally, the non-convergence of the algorithm to undesired critical points, such as local maxima or saddle points, is established. Here, the main ingredient is a new avoidance of traps result for non-autonomous settings, which is of independent interest.

Analysis of energy efficient and network traffic delay in wireless networks using channel aware routing

AbstractThis article studies different analysis metrics of wireless networks using channel aware routing protocol. During communication the following characteristics are important performance metrics like network traffic delays and energy efficient. Energy Efficient is an important solution with limited buffer capacity and life time of battery in wireless environment. The status of each node can be identified by using co‐channel forwarding mechanism. The traffic delays can be measured by using Q‐Learning random early method and routing can be optimized by channel aware routing. The transmission changes in one node to another can be monitored by router database and energy level can be verified by additional changes in wireless network nodes. The network reliability is improved by reducing the communication delay, which uses various traditional routing protocols. Based on the demand of communication protocols, the router is designed to optimize the best network model. Based on the problem formation of open vehicle routing technique, it proves inherently NP‐hard. If it has reduced computation overhead, it will not perform well with the large scale framework. Therefore, the channel aware routing technique improves the performance by increasing the reliability of the network. The previous results are shown that efficient energy utilization and network traffic delays encountered the major and accuracy results are in below 60% In this article, we formulate to achieve analysis the energy performance and reduced traffic delay using co‐channels stochastic optimization procedure. The co‐channel method used to check various analytical bounds and check all the nodes are uniformly shares the energy level. The mathematical analysis report provides uniform distribution energy values and traffic delays. The simulation results are shows that efficient energy utilization and network traffic delays in wireless networks 75% achieved.

Asymptotics of Control Problem for the Diffusion Process in Markov Environment

A stochastic optimization procedure and a limit generator of the original problem are constructed for a system of stochastic differential equations with Markov switching and diffusion perturbation with control, which is determined by the condition for the extremum of the quality function. The complexity of the studied evolutionary model lies primarily in the fact that the system is in conditions of external random influence, which is modeled using a switching process. The main assumption is the condition for uniform ergodicity of the Markov switching process, that is, the existence of a stationary distribution for the switching process over large time intervals. This allows one to construct explicit algorithms for the analysis of the asymptotic behavior of a controlled process. An important property of the generator of the Markov switching process is that the space in which it is defined splits into the direct sum of its zero-subspace and a subspace of values, followed by the introduction of a projector that acts on the subspace of zeros. Another complexity of the model under study is the presence of an approximation scheme determined by normalization. The question of how the behavior of the limit process depends on the prelimit normalization by a small parameter of the stochastic system in an ergodic Markovian environment is studied. A stochastic differential equation is written for determining the limiting processes of transfer and control. For the first time, a model of the control problem for the diffusion transfer process using the stochastic optimization procedure for control is proposed. A singular expansion in the small parameter of the generator of the three-component Markov process is obtained, and the problem of a singular perturbation with the representation of the limiting generator of this process is solved.

ОПТИМАЛЬНОЕ ПРОЕКТИРОВАНИЕ СТАЛЬНЫХ РАМНЫХ КОНСТРУКЦИЙ С УЧЕТОМ УРОВНЯ МЕХАНИЧЕСКОЙ БЕЗОПАСНОСТИ

The approach to the design of steel frame structures is considered, taking into account the potential risk of occurrence of emergencies associated with their mechanical local damage, and possible material losses. It is proposed to classify these systems according to the safety level of the solution. In accordance with the introduced classification, methods for finding solutions are proposed based on the use of evolutionary modeling with subsequent risk assessment from the onset of an emergency. These methods include a combination of two-level stochastic optimization procedures. At the first level, a search is performed on discrete sets of design parameters of a design variant with a minimum cost. As constraints in the absence of emergencies, regulatory requirements of limit states are accepted, and the strength ratio is regulated. In a possible emergency for the construction is considered a limitation on survivability. At the second level, a heuristic search is performed for the design variant for which the risks of receiving material damage from an accident are minimal while ensuring a minimum of capital investments on the considered stages at building life cycle. Examples of the steel frame design with different levels of safety are given, which demonstrate the efficiency of the proposed approach.

Constructing transformation paths for conformational changes in (MgF2) n clusters using a stochastic procedure

We present a stochastic optimisation procedure using simulated annealing for studying conformational changes in ( MgF 2 ) n clusters. The pathways for transformation between stable geometries through a transition state is studied for cluster sizes n=3−12. The work uses an objective function which exploits the sign of the eigenvalues of the Hessian matrix to locate transition states. Once it is located for a specific size it is examined if one minimum geometry can be converted to another through the transition state. The potential energy surface for the system is searched using the stochastic optimisation procedure of simulated annealing. The ruggedness of the surface makes the choice of the optimiser an ideal one. To complete the results the progress of the pathway is depicted as the function of the path coordinates at intermediate geometries.

Optimization of damped outrigger systems subject to stochastic excitation

High-rise buildings have attracted much attention with the continuing growth of world population and increasing urbanization. As buildings become taller, suppressing excessive vibration due to lateral excitation becomes more challenging. One of the promising solutions that has been proposed is the damped outrigger system, where dampers are vertically installed between outriggers attached to the core and perimeter columns, leading to a significant increment of structural damping. To gain insight into the design of damped outrigger systems subject to seismic excitation, a stochastic optimization procedure is proposed. The seismic excitation is modeled as a filtered white noise, following the Kanai-Tajimi spectrum. To better represent the interstory drift, the core of the building is modeled using a Timoshenko beam, and a Kelvin model of the damper is considered. The equations of motion of the structure-damper-excitation system are combined into an augmented state space representation. The variance of the responses of the structure are calculated via solution of the Lyapunov equation. A genetic algorithm is used to determine the damper placement and associated parameters so as to minimize objective function, which is in terms of the structural responses. A Pareto optimal front is used to examine the tradeoffs with respect to minimizing interstory drift, floor accelerations, base shear, and base overturning moment. The results demonstrate the efficacy of the proposed approach, reveal the range of application for such damped outrigger systems, and provide insight into the system design in the presence of seismic excitation.

Modeling of the Penultimate Unit Effect in Chain-Growth Copolymerizations

The present work addresses the modeling and simulation of the addition of copolymerizations of styrene and methyl methacrylate in batch mode, and the formation of tailored vinyl acetate/acrylic acid copolymers is evaluated through stochastic optimization procedures based on the Monte Carlo method. A kinetic model of the free-radical reaction was proposed in order to predict the behavior of the reaction system taking into consideration the presence of the penultimate unit effect. The profiles of conversion and copolymer composition were also evaluated considering the effect of the medium viscosity (kinetic phenomena related to gel and glass effects) on the reaction performance. It was shown that the proposed model for chain-growth copolymerization is able to describe strong nonlinear behaviors such as autoacceleration of the polymerization and drift of copolymer composition. It was also shown that copolymers with homogeneous composition can be successfully synthesized through manipulation of the monomer feed flow rate based on a stochastic optimization procedure.