Shaping the Wavefront of Incident Light with a Strong Robustness Particle Swarm Optimization Algorithm

We demonstrate a modified particle swarm optimization(PSO) algorithm to effectively shape the incident light with strong robustness and short optimization time. The performance of the modified PSO algorithm and genetic algorithm(GA) is numerically simulated. Then, using a high speed digital micromirror device, we carry out light focusing experiments with the modified PSO algorithm and GA. The experimental results show that the modified PSO algorithm has greater robustness and faster convergence speed than GA. This modified PSO algorithm has great application prospects in optical focusing and imaging inside in vivo biological tissue, which possesses a complicated background.

Integrated fire/flight control of armed helicopters based on C-BFGS and distributionally robust optimization

To meet the requirements of modern air combat,an integrated fire/flight control(IFFC)system is designed to achieve automatic precision tracking and aiming for armed helicopters and release the pilot from heavy target burden.Considering the complex dynamic characteristics and the couplings of armed helicopters,an improved automatic attack system is con-structed to integrate the fire control system with the flight con-trol system into a unit.To obtain the optimal command signals,the algorithm is investigated to solve nonconvex optimization problems by the contracting Broyden Fletcher Goldfarb Shanno(C-BFGS)algorithm combined with the trust region method.To address the uncertainties in the automatic attack system,the memory nominal distribution and Wasserstein distance are introduced to accurately characterize the uncertainties,and the dual solvable problem is analyzed by using the duality the-ory,conjugate function,and dual norm.Simulation results verify the practicality and validity of the proposed method in solving the IFFC problem on the premise of satisfactory aiming accu-racy.

Optimization of Uncertain Structures with Interval Parameters Considering Objective and Feasibility Robustness

For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust optimization model is constructed with both the center and halfwidth of the most important mechanical performance index described as objective functions and the other requirements on the mechanical performance indices described as constraint functions. To locate the optimal solution of objective and feasibility robustness, a new concept of interval violation vector and its calculation formulae corresponding to different constraint functions are proposed. The math?ematical formulae for calculating the feasibility and objective robustness indices and the robustness?based preferential guidelines are proposed for directly ranking various design vectors, which is realized by an algorithm integrating Kriging and nested genetic algorithm. The validity of the proposed method and its superiority to present interval optimization approaches are demonstrated by a numerical example. The robust optimization of the upper beam in a high?speed press with interval material properties demonstrated the applicability and effectiveness of the proposed method in engineering.

Robust Optimization Method of Cylindrical Roller Bearing by Maximizing Dynamic Capacity Using Evolutionary Algorithms

Optimization of cylindrical roller bearings(CRBs)has been performed using a robust design.It ensures that the changes in the objective function,even in the case of variations in design variables during manufacturing,have a minimum possible value and do not exceed the upper limit of a desired range of percentage variation.Also,it checks the feasibility of design outcome in presence of manufacturing tolerances in design variables.For any rolling element bearing,a long life indicates a satisfactory performance.In the present study,the dynamic load carrying capacity C,which relates to fatigue life,has been optimized using the robust design.In roller bearings,boundary dimensions(i.e.,bearing outer diameter,bore diameter and width)are standard.Hence,the performance is mainly affected by the internal dimensions and not the bearing boundary dimensions mentioned formerly.In spite of this,besides internal dimensions and their tolerances,the tolerances in boundary dimensions have also been taken into consideration for the robust optimization.The problem has been solved with the elitist non-dominating sorting genetic algorithm(NSGA-II).Finally,for the visualization and to ensure manufacturability of CRB using obtained values,radial dimensions drawing of one of the optimized CRB has been made.To check the robustness of obtained design after optimization,a sensitivity analysis has also been carried out to find out how much the variation in the objective function will be in case of variation in optimized value of design variables.Optimized bearings have been found to have improved life as compared with standard ones.

A Metamodeling Method Based on Support Vector Regression for Robust Optimization

Metamodeling techniques have been used in robust optimization to reduce the high computational cost of the uncertainty analysis and improve the performance of robust optimization problems with computationally expensive simulation models. Existing metamodels main focus on polynomial regression（PR）, neural networks（NN） and Kriging models, these metamodels are not well suited for large-scale robust optimization problems with small size training sets and high nonlinearity. To address the problem, a reduced approximation model technique based on support vector regression（SVR） is introduced in order to improve the accuracy of metamodels. A robust optimization method based on SVR is presented for problems that involve high dimension and nonlinear. First appropriate design parameter samples are selected by experimental design theories, then the response samples are obtained from the simulations such as finite element analysis, the SVR metamodel is constructed and treated as the mean and the variance of the objective performance functions. Combining other constraints, the robust optimization model is formed which can be solved by genetic algorithm （GA）. The applicability of the method developed is demonstrated using a case of two-bar structure system study. The performances of SVR were compared with those of PR, Kriging and back-propagation neural networks（BPNN）, the comparison results show that the prediction accuracy of the SVR metamodel was higher than those of other metamodels under uncertainty. The robust optimization solutions are near to the real result, and the proposed method is found to be accurate and efficient for robust optimization. This reaserch provides an efficient method for robust optimization problems with complex structure.

Random Fuzzy Chance-constrained Programming Based on Adaptive Chaos Quantum Honey Bee Algorithm and Robustness Analysis

This paper proposes an adaptive chaos quantum honey bee algorithm （CQHBA） for solving chance-constrained program- ming in random fuzzy environment based on random fuzzy simulations. Random fuzzy simulation is designed to estimate the chance of a random fuzzy event and the optimistic value to a random fuzzy variable. In CQHBA, each bee carries a group of quantum bits representing a solution. Chaos optimization searches space around the selected best-so-far food source. In the marriage process, random interferential discrete quantum crossover is done between selected drones and the queen. Gaussian quantum mutation is used to keep the diversity of whole population. New methods of computing quantum rotation angles are designed based on grads. A proof of con- vergence for CQHBA is developed and a theoretical analysis of the computational overhead for the algorithm is presented. Numerical examples are presented to demonstrate its superiority in robustness and stability, efficiency of computational complexity, success rate, and accuracy of solution quality. CQHBA is manifested to be highly robust under various conditions and capable of handling most random fuzzy programmings with any parameter settings, variable initializations, system tolerance and confidence level, perturbations, and noises.

Novel Adaptive Memory Event-Triggered-Based Fuzzy Robust Control for Nonlinear Networked Systems via the Differential Evolution Algorithm

This article mainly investigates the fuzzy optimization robust control issue for nonlinear networked systems characterized by the interval type-2(IT2)fuzzy technique under a differential evolution algorithm.To provide a more reasonable utilization of the constrained communication channel,a novel adaptive memory event-triggered(AMET)mechanism is developed,where two event-triggered thresholds can be dynamically adjusted in the light of the current system information and the transmitted historical data.Sufficient conditions with less conservative design of the fuzzy imperfect premise matching(IPM)controller are presented by introducing the Wirtinger-based integral inequality,the information of membership functions(MFs)and slack matrices.Subsequently,under the IPM policy,a new MFs intelligent optimization technique that takes advantage of the differential evolution algorithm is first provided for IT2 TakagiSugeno(T-S)fuzzy systems to update the fuzzy controller MFs in real-time and achieve a better system control effect.Finally,simulation results demonstrate that the proposed control scheme can obtain better system performance in the case of using fewer communication resources.

Randomized Algorithms for Probabilistic Optimal Robust Performance Controller Design

Polynomial-time randomized algorithms were constructed to approximately solve optimal robust performance controller design problems in probabilistic sense and the rigorous mathematical justification of the approach was given. The randomized algorithms here were based on a property from statistical learning theory known as (uniform) convergence of empirical means (UCEM). It is argued that in order to assess the performance of a controller as the plant varies over a pre-specified family, it is better to use the average performance of the controller as the objective function to be optimized, rather than its worst-case performance. The approach is illustrated to be efficient through an example.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.

Robust optimization for volume variation in timber processing

Volume variation is an uncertainty element which affects timber processing. We studied the volume variation of logs caused by quality defects in traditional timber processing and set up an optimization approach,using a robust optimization method. We used total number of acceptable boards produced to study the relationship between board thickness and raw material logs, using a heuristic search algorithm to control the variation of board volume to improve the output of boards, reduce the quantity of by-products, and lower production costs. The robust optimization method can effectively control the impact of volume variations in timber processing, reduce cutting waste as far as possible using incremental processing and increase profits, maximize the utilization ratio of timber, prevent waste in processing, cultivate the productive type of tree species and save forest resources.

Temperature prediction model for a high-speed motorized spindle based on back-propagation neural network optimized by adaptive particle swarm optimization

To predict the temperature of a motorized spindle more accurately,a novel temperature prediction model based on the back-propagation neural network optimized by adaptive particle swarm optimization(APSO-BPNN)is proposed.First,on the basis of the PSO-BPNN algorithm,the adaptive inertia weight is introduced to make the weight change with the fitness of the particle,the adaptive learning factor is used to obtain different search abilities in the early and later stages of the algorithm,the mutation operator is incorporated to increase the diversity of the population and avoid premature convergence,and the APSO-BPNN model is constructed.Then,the temperature of different measurement points of the motorized spindle is forecasted by the BPNN,PSO-BPNN,and APSO-BPNN models.The experimental results demonstrate that the APSO-BPNN model has a significant advantage over the other two methods regarding prediction precision and robustness.The presented algorithm can provide a theoretical basis for intelligently controlling temperature and developing an early warning system for high-speed motorized spindles and machine tools.

Optimized Robust Filter for Uncertain Discrete Time System and Its Application to Flight Test

An optimized robust filtering algorithm for uncertain discrete-time systemsis presented. To get a series of computational equations, the uncertain part generated by theuncertain systematic matrix in the expression of the error-covariance matrix of time update stateestimation is optimized and the least upper bound of the uncertain part is given. By means of theseresults, the equivalent systematic matrix is obtained and a robust time update algorithm is builtup. On the other hand, uncertain parts generated by the uncertain observation matrix in theexpression of the error-covariance matrix of measurement update state estimation are optimized, andthe largest lower bound of the uncertain part is given. Thus both the time update and measurementupdate algorithms are developed. By means of the matrix inversion formula, the expression structuresof both time update and measurement update algorithms are all simplified. Moreover, the convergencecondition of a robust filter is developed to make the results easy to application. The results offlight data processing show that the method presented in this paper is efficient.

A scenario relaxation algorithm for finite scenario based robust assembly line balancing

A balancing problem for a mixed model assembly line with uncertain task processmg Ume anO daily model mixed changes is considered, and the objective is to minimize the work variances between stations in the line. For the balancing problem for the scenario-based robust assembly line with a finitely large number of potential scenarios, the direct solution methodology considering all potential scenarios is quite time-consuming. A scenario relaxation algorithm that embeds genetic al- gorithm is developed. This new algorithm guarantees termination at an optimal robust solution with relatively short running time, and makes it possible to solve robust problems with large quantities of potential scenarios. Extensive computational results are reported to show the efficiency and effectiveness of the proposed algorithm.

Optimal hydrogen-battery energy storage system operation in microgrid with zero-carbon emission

To meet the greenhouse gas reduction targets and address the uncertainty introduced by the surging penetration of stochastic renewable energy sources,energy storage systems are being deployed in microgrids.Relying solely on short-term uncertainty forecasts can result in substantial costs when making dispatch decisions for a storage system over an entire day.To mitigate this challenge,an adaptive robust optimization approach tailored for a hybrid hydrogen battery energy storage system(HBESS)operating within a microgrid is proposed,with a focus on efficient state-of-charge(SoC)planning to minimize microgrid expenses.The SoC ranges of the battery energy storage(BES)are determined in the day-ahead stage.Concurrently,the power generated by fuel cells and consumed by electrolysis device are optimized.This is followed by the intraday stage,where BES dispatch decisions are made within a predetermined SoC range to accommodate the uncertainties realized.To address this uncertainty and solve the adaptive optimization problem with integer recourse variables in the intraday stage,we proposed an outer-inner column-and-constraint generation algorithm(outer-inner-CCG).Numerical analyses underscored the high effectiveness and efficiency of the proposed adaptive robust operation model in making decisions for HBESS dispatch.

An effective digital audio watermarking using a deep convolutional neural network with a search location optimization algorithm for improvement in Robustness and Imperceptibility

Watermarking is the advanced technology utilized to secure digital data by integrating ownership or copyright protection.Most of the traditional extracting processes in audio watermarking have some restrictions due to low reliability to various attacks.Hence,a deep learning-based audio watermarking system is proposed in this research to overcome the restriction in the traditional methods.The implication of the research relies on enhancing the performance of the watermarking system using the Discrete Wavelet Transform(DWT)and the optimized deep learning technique.The selection of optimal embedding location is the research contribution that is carried out by the deep convolutional neural network(DCNN).The hyperparameter tuning is performed by the so-called search location optimization,which minimizes the errors in the classifier.The experimental result reveals that the proposed digital audio watermarking system provides better robustness and performance in terms of Bit Error Rate(BER),Mean Square Error(MSE),and Signal-to-noise ratio.The BER,MSE,and SNR of the proposed audio watermarking model without the noise are 0.082,0.099,and 45.363 respectively,which is found to be better performance than the existing watermarking models.

生产-分销物流系统的Robust优化模型与算法

讨论不确定情况下的生产-分销三级物流系统的优化设计问题。我们首先提出一个生产-分销系统的确定性模型,通过引入R obust优化理论,将该模型进一步拓展为包含不确定需求因素的R obust优化模型,最后运用L agrang ian松弛算法得到了原问题的近似最优解,并通过算例对模型和算法的性能进行了分析与评价。

Robust极点配置及其优化算法

本文提出了一个线性系统极点配置的有效算法,首先利用正交变换将能控系统简化成上Hessenberg能控标准型,然后利用(A,B)特征子空间找出闭环系统关于指定复数集所有可能的特征向量,从中选取一组线性无关的向量{x_1,…x_n}作为闭环系统的特征向量,使得max{c_k,k∈n}极小,最后由x={x_1,…x_n}找出反馈阵F,使得闭环系统(A+BF,B)的极点集等于L。

多产消者的两阶段四层主从-合作博弈鲁棒模型及求解

针对含可再生能源和柔性负荷的产消者参与电力市场的主从-合作交易过程,提出一种多产消者两阶段四层主从-合作博弈鲁棒模型。通过引入“最大波动幅度”的概念以及定义波动比例系数,建立可再生能源不确定性集;考虑可再生能源的不确定性和柔性负荷对交易策略的影响,建立max-max-min-max形式的两阶段四层主从-合作鲁棒模型;提出一种交替迭代的列约束生成算法,通过解耦子问题加速求解;将共识乘子交替方向法与改进的动态自适应交替优化法相结合,克服非凸的主从-合作鲁棒模型收敛困难的问题。基于某智慧能源示范项目的仿真验证了所提模型和方法的有效性。

Optimal variable structure control with sliding modes for unstable processes

In this work,a variable structure control(VSC)technique is proposed to achieve satisfactory robustness for unstable processes.Optimal values of unknown parameters of VSC are obtained using Whale optimization algorithm which was recently reported in literature.Stability analysis has been done to verify the suitability of the proposed structure for industrial processes.The proposed control strategy is applied to three different types of unstable processes including non-minimum phase and nonlinear systems.A comparative study ensures that the proposed scheme gives superior performance over the recently reported VSC system.Furthermore,the proposed method gives satisfactory results for a cart inverted pendulum system in the presence of external disturbance and noise.