Multi-source coordinated stochastic restoration for SOP in distribution networks with a two-stage algorithm

After suffering from a grid blackout, distributed energy resources(DERs), such as local renewable energy and controllable distributed generators and energy storage can be used to restore loads enhancing the system’s resilience. In this study, a multi-source coordinated load restoration strategy was investigated for a distribution network with soft open points(SOPs). Here, the flexible regulation ability of the SOPs is fully utilized to improve the load restoration level while mitigating voltage deviations. Owing to the uncertainty, a scenario-based stochastic optimization approach was employed,and the load restoration problem was formulated as a mixed-integer nonlinear programming model. A computationally efficient solution algorithm was developed for the model using convex relaxation and linearization methods. The algorithm is organized into a two-stage structure, in which the energy storage system is dispatched in the first stage by solving a relaxed convex problem. In the second stage, an integer programming problem is calculated to acquire the outputs of both SOPs and power resources. A numerical test was conducted on both IEEE 33-bus and IEEE 123-bus systems to validate the effectiveness of the proposed strategy.

Distributed Momentum-Based Frank-Wolfe Algorithm for Stochastic Optimization

This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.

A genetic algorithm based stochastic programming model for air quality management

This paper presents a model that can aid planners in defining the total allowable pollutant discharge in the planning region, accounting for the dynamic and stochastic character of meteorological conditions. This is accomplished by integrating Monte Carlo simulation and using genetic algorithm to solve the model. The model is demonstrated by using a realistic air urban scale SO 2 control problem in the Yuxi City of China. To evaluate effectiveness of the model, results of the approach are shown to compare with those of the linear deterministic procedures. This paper also provides a valuable insight into how air quality targets should be made when the air pollutant will not threat the residents' health. Finally, a discussion of the areas for further research are briefly delineated.

Archery Algorithm:A Novel Stochastic Optimization Algorithm for Solving Optimization Problems

Finding a suitable solution to an optimization problem designed in science is a major challenge.Therefore,these must be addressed utilizing proper approaches.Based on a random search space,optimization algorithms can find acceptable solutions to problems.Archery Algorithm(AA)is a new stochastic approach for addressing optimization problems that is discussed in this study.The fundamental idea of developing the suggested AA is to imitate the archer’s shooting behavior toward the target panel.The proposed algorithm updates the location of each member of the population in each dimension of the search space by a member randomly marked by the archer.The AA is mathematically described,and its capacity to solve optimization problems is evaluated on twenty-three distinct types of objective functions.Furthermore,the proposed algorithm’s performance is compared vs.eight approaches,including teaching-learning based optimization,marine predators algorithm,genetic algorithm,grey wolf optimization,particle swarm optimization,whale optimization algorithm,gravitational search algorithm,and tunicate swarm algorithm.According to the simulation findings,the AA has a good capacity to tackle optimization issues in both unimodal and multimodal scenarios,and it can give adequate quasi-optimal solutions to these problems.The analysis and comparison of competing algorithms’performance with the proposed algorithm demonstrates the superiority and competitiveness of the AA.

A New Stochastic Algorithm of Global Optimization ——Region's Walk and Contraction

This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum point to replace it, and in order to fit the level set well, this region would be walking and contracting in the running process. Thus, the new algorithm is named as region's walk and contraction(RWC). Some numerical experiments for the RWC were conducted, which indicate good property of the algorithm.

ANew Theoretical Framework forAnalyzing Stochastic Global Optimization Algorithms

In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.

Frequency modulated weak signal detection based on stochastic resonance and genetic algorithm

Stochastic resonance system is subject to the restriction of small frequency parameter in weak signal detection,in order to solve this problem,a frequency modulated weak signal detection method based on stochastic resonance and genetic algorithm is presented in this paper. The frequency limit of stochastic resonance is eliminated by introducing carrier signal,which is multiplied with the measured signal to be injected in the stochastic resonance system,meanwhile,using genetic algorithm to optimize the carrier signal frequency,which determine the generated difference-frequency signal in the lowfrequency range,so as to achieve the stochastic resonance weak signal detection. Results showthat the proposed method is feasible and effective,which can significantly improve the output SNR of stochastic resonance,in addition,the system has the better self-adaptability,according to the operation result and output phenomenon,the unknown frequency of the signal to be measured can be obtained,so as to realize the weak signal detection of arbitrary frequency.

Efficient Stochastic Simulation Algorithm for Chemically Reacting Systems Based on Support Vector Regression

The stochastic simulation algorithm （SSA） accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, a twin support vector regression based stochastic simulations algorithm （TS^3A） is proposed by combining the twin support vector regression and SSA, the former is a well-known robust regression method in machine learning. Numerical results indicate that this proposed algorithm can be applied to a wide range of chemically reacting systems and obtain significant improvements on efficiency and accuracy with fewer simulating runs over the existing methods.

Stochastic Design of Enhanced Network Management Architecture and Algorithmic Implementations

The paper is focused on available server management in Internet connected network environments. The local backup servers are hooked up by LAN and replace broken main server immediately and several different types of backup servers are also considered. The remote backup servers are hooked up by VPN (Virtual Private Network) with high-speed optical network. A Virtual Private Network (VPN) is a way to use a public network infrastructure and hooks up long-distance servers within a single network infrastructure. The remote backup servers also replace broken main severs immediately under the different conditions with local backups. When the system performs a mandatory routine maintenance of main and local backup servers, auxiliary servers from other location are being used for backups during idle periods. Analytically tractable results are obtained by using several mathematical techniques and the results are demonstrated in the framework of optimized networked server allocation problems. The operational workflow give the guidelines for the actual implementations.

A Modified Inhomogeneous Stochastic Simulation Algorithm to Model Reactive Boundary Conditions

The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.

Far and Near Optimization:A New Simple and Effective Metaphor-LessOptimization Algorithm for Solving Engineering Applications

In this article,a novel metaheuristic technique named Far and Near Optimization(FNO)is introduced,offeringversatile applications across various scientific domains for optimization tasks.The core concept behind FNO lies inintegrating global and local search methodologies to update the algorithm population within the problem-solvingspace based on moving each member to the farthest and nearest member to itself.The paper delineates the theoryof FNO,presenting a mathematical model in two phases:(i)exploration based on the simulation of the movementof a population member towards the farthest member from itself and(ii)exploitation based on simulating themovement of a population member towards the nearest member from itself.FNO’s efficacy in tackling optimizationchallenges is assessed through its handling of the CEC 2017 test suite across problem dimensions of 10,30,50,and 100,as well as to address CEC 2020.The optimization results underscore FNO’s adeptness in exploration,exploitation,and maintaining a balance between them throughout the search process to yield viable solutions.Comparative analysis against twelve established metaheuristic algorithms reveals FNO’s superior performance.Simulation findings indicate FNO’s outperformance of competitor algorithms,securing the top rank as the mosteffective optimizer across a majority of benchmark functions.Moreover,the outcomes derived by employing FNOon twenty-two constrained optimization challenges from the CEC 2011 test suite,alongside four engineering designdilemmas,showcase the effectiveness of the suggested method in tackling real-world scenarios.

Modified stochastic user-equilibrium assignment algorithm for urban rail transit under network operation

Based on the framework of method of successive averages(MSA), a modified stochastic user-equilibrium assignment algorithm was proposed, which can be used to calculate the passenger flow distribution of urban rail transit(URT) under network operation. In order to describe the congestion's impact to passengers' route choices, a generalized cost function with in-vehicle congestion was set up. Building on the k-th shortest path algorithm, a method for generating choice set with time constraint was embedded, considering the characteristics of network operation. A simple but efficient route choice model, which was derived from travel surveys for URT passengers in China, was introduced to perform the stochastic network loading at each iteration in the algorithm. Initial tests on the URT network in Shanghai City show that the methodology, with rational calculation time, promises to compute more precisely the passenger flow distribution of URT under network operation, compared with those practical algorithms used in today's China.

The Fuzzy Modeling Algorithm for Complex Systems Based on Stochastic Neural Network

A fuzzy modeling method for complex systems is studied. The notation of general stochastic neural network (GSNN) is presented and a new modeling method is given based on the combination of the modified Takagi and Sugeno's (MTS) fuzzy model and one-order GSNN. Using expectation-maximization(EM) algorithm, parameter estimation and model selection procedures are given. It avoids the shortcomings brought by other methods such as BP algorithm, when the number of parameters is large, BP algorithm is still difficult to apply directly without fine tuning and subjective tinkering. Finally, the simulated example demonstrates the effectiveness.

Gaining-Sharing Knowledge Based Algorithm for Solving Stochastic Programming Problems

This paper presents a novel application of metaheuristic algorithmsfor solving stochastic programming problems using a recently developed gaining sharing knowledge based optimization (GSK) algorithm. The algorithmis based on human behavior in which people gain and share their knowledgewith others. Different types of stochastic fractional programming problemsare considered in this study. The augmented Lagrangian method (ALM)is used to handle these constrained optimization problems by convertingthem into unconstrained optimization problems. Three examples from theliterature are considered and transformed into their deterministic form usingthe chance-constrained technique. The transformed problems are solved usingGSK algorithm and the results are compared with eight other state-of-the-artmetaheuristic algorithms. The obtained results are also compared with theoptimal global solution and the results quoted in the literature. To investigatethe performance of the GSK algorithm on a real-world problem, a solidstochastic fixed charge transportation problem is examined, in which theparameters of the problem are considered as random variables. The obtainedresults show that the GSK algorithm outperforms other algorithms in termsof convergence, robustness, computational time, and quality of obtainedsolutions.

A Novel Stochastic Algorithm Using Pythagorean Means for Minimization

In this paper, A Novel Stochastic Algorithm using Pythagorean means for minimization of the objective function is described. The algorithm is initially tested with Rastrigin’s function and compared with Genetic algorithm results for the function with the same initial conditions. After this, it is used in tuning the gains of fuzzy PD + I controller for trajectory control of PUMA 560 robot manipulator. The results are again verified with the results of genetic algorithm.

A Complex Algorithm for Solving a Kind of Stochastic Programming

Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of two-stage stochastic programming problems modeling with maximum minimum expectation compensation criterion (MaxEMin) under the probability distribution having linear partial information (LPI). In view of the nondifferentiability of this kind of stochastic programming modeling, an improved complex algorithm is designed and analyzed. This algorithm can effectively solve the nondifferentiable stochastic programming problem under LPI through the variable polyhedron iteration. The calculation and discussion of numerical examples show the effectiveness of the proposed algorithm.

Multicut L-Shaped Algorithm for Stochastic Convex Programming with Fuzzy Probability Distribution

Two-stage problem of stochastic convex programming with fuzzy probability distribution is studied in this paper. Multicut L-shaped algorithm is proposed to solve the problem based on the fuzzy cutting and the minimax rule. Theorem of the convergence for the algorithm is proved. Finally, a numerical example about two-stage convex recourse problem shows the essential character and the efficiency.

TWO-DIMENSIONAL STOCHASTIC AIRFOIL OPTIMIZATION DESIGN METHOD BASED ON NEURAL NETWORKS

To avoid the aerodynamic performance loss of airfoil at non-design state which often appears in single point design optimization, and to improve the adaptability to the uncertain factors in actual flight environment, a two-dimensional stochastic airfoil optimization design method based on neural networks is presented. To provide highly efficient and credible analysis, four BP neural networks are built as surrogate models to predict the airfoil aerodynamic coefficients and geometry parameter. These networks are combined with the probability density function obeying normal distribution and the genetic algorithm, thus forming an optimization design method. Using the method, for GA（W）-2 airfoil, a stochastic optimization is implemented in a two-dimensional flight area about Mach number and angle of attack. Compared with original airfoil and single point optimization design airfoil, results show that the two-dimensional stochastic method can improve the performance in a specific flight area, and increase the airfoil adaptability to the stochastic changes of multiple flight parameters.

Stability and performance analysis of the compressed Kalman filter algorithm for sparse stochastic systems

This paper considers the problem of estimating unknown sparse time-varying signals for stochastic dynamic systems.To deal with the challenges of extensive sparsity,we resort to the compressed sensing method and propose a compressed Kalman filter(KF)algorithm.Our algorithm first compresses the original high-dimensional sparse regression vector via the sensing matrix and then obtains a KF estimate in the compressed low-dimensional space.Subsequently,the original high-dimensional sparse signals can be well recovered by a reconstruction technique.To ensure stability and establish upper bounds on the estimation errors,we introduce a compressed excitation condition without imposing independence or stationarity on the system signal,and therefore suitable for feedback systems.We further present the performance of the compressed KF algorithm.Specifically,we show that the mean square compressed tracking error matrix can be approximately calculated by a linear deterministic difference matrix equation,which can be readily evaluated,analyzed,and optimized.Finally,a numerical example demonstrates that our algorithm outperforms the standard uncompressed KF algorithm and other compressed algorithms for estimating high-dimensional sparse signals.

A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.