Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

Hybrid Hierarchical Particle Swarm Optimization with Evolutionary Artificial Bee Colony Algorithm for Task Scheduling in Cloud Computing

Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.

Hierarchical Optimization of Landing Performance for Lander with Adaptive Landing Gear

A parameterized dynamics analysis model of legged lander with adaptive landing gear was established. Based on the analysis model, the landing performances under various landing conditions were analyzed by the optimized Latin hypercube experimental design method. In order to improve the landing performances, a hierarchical optimization method was proposed considering the uncertainty of landing conditions. The optimization problem was divided into a higher level(hereafter the "leader") and several lower levels(hereafter the "follower"). The followers took condition?ing factors as design variables to find out the worst landing conditions, while the leader took bu er parameters as design variables to better the landing performance under worst conditions. First of all, sensitivity analysis of landing conditioning factors was carried out according to the results of experimental design. After the sensitive factors were screened out, the response surface models were established to reflect the complicated relationships between sensi?tive conditioning factors, bu er parameters and landing performance indexes. Finally, the response surface model was used for hierarchical optimization iteration to improve the computational e ciency. After selecting the optimum bu er parameters from the solution set, the dynamic model with the optimum parameters was simulated again under the same landing conditions as the simulation before. After optimization, nozzle performance against damage is improved by 5.24%, the acceleration overload is reduced by 5.74%, and the primary strut improves its performance by 21.10%.

Crashworthiness Design and Multi-Objective Optimization for Bio-Inspired Hierarchical Thin-Walled Structures

Thin-walled structures have been used in many fields due to their superior mechanical properties.In this paper,two types of hierarchical multi-cell tubes,inspired by the self-similarity of Pinus sylvestris,are proposed to enhance structural energy absorption performance.The finite element models of the hierarchical structures are established to validate the crashworthiness performance under axial dynamic load.The theoreticalmodel of themean crushing force is also derived based on the simplified super folded element theory.The finite element results demonstrate that the energy absorption characteristics and deformation mode of the bionic hierarchical thin-walled tubes are further improved with the increase of hierarchical sub-structures.It can be also obtained that the energy absorption performance of corner self-similar tubes is better than edge self-similar tubes.Furthermore,multiobjective optimization of the hierarchical tubes is constructed by employing the response surface method and genetic algorithm,and the corresponding Pareto front diagram is obtained.This research provides a new idea for the crashworthiness design of thin-walled structures.

Explicit Isogeometric Topology Optimization Method with Suitably Graded Truncated Hierarchical B-Spline

This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.

Multi-Topology Hierarchical Collaborative Hybrid Particle Swarm Optimization Algorithm for WSN

Wireless sensor networks(WSN)are widely used in many situations,but the disordered and random deployment mode will waste a lot of sensor resources.This paper proposes a multi-topology hierarchical collaborative particle swarm optimization(MHCHPSO)to optimize sensor deployment location and improve the coverage of WSN.MHCHPSO divides the population into three types topology:diversity topology for global exploration,fast convergence topology for local development,and collaboration topology for exploration and development.All topologies are optimized in parallel to overcome the precocious convergence of PSO.This paper compares with various heuristic algorithms at CEC 2013,CEC 2015,and CEC 2017.The experimental results show that MHCHPSO outperforms the comparison algorithms.In addition,MHCHPSO is applied to the WSN localization optimization,and the experimental results confirm the optimization ability of MHCHPSO in practical engineering problems.

Multi-objective Hierarchical Optimization of Interior Permanent Magnet Synchronous Machines Based on Rotor Surface Modification

To solve the problem of large torque ripple of interior permanent magnet synchronous motor(IPMSM),the rotor surface notch design method was used for V-type IPMSM.In order to accurately obtain the optimal parameter values to improve the torque performance of the motor,this paper takes the output torque capacity and torque ripple as the optimization objectives,and proposes a multi-objective layered optimization method based on the parameter hierarchical design combined with Taguchi method and response surface method(RSM).The conclusion can be drawn by comparing the electromagnetic performance of the motor before and after optimization,the proposed IPMSM based on the rotor surface notch design can not only improve the output torque,but also play an obvious inhibition effect on the torque ripple.

Hierarchical Evolutionary Algorithms and Its Application in Transonic Airfoil Optimization in Aerodynamics

Hierarchical evolutionary algorithms based on genetic algorithms (GAs) and Nash strategy of game theory are proposed to accelerate the optimization process and implemented in transonic aerodynamic shape optimization problems Inspired from the natural evolution history that different periods with certain environments have different criteria for the evaluations of individuals’ fitness, a hierarchical fidelity model is introduced to reach high optimization efficiency The shape of an NACA0012 based airfoil is optimized in maximizing the lift coefficient under a given transonic flow condition Optimized results are presented and compared with the single model results and traditional GA

Strong Convergence Results for Hierarchical Circularly Iterative Method about Hierarchical Circularly Optimization

An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this paper. Under some suitable conditions, strong convergence results for the hierarchical circularly iterative sequence are proved in the setting of Hilbert spaces. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé.

Optimum design of hierarchical stiffened shells for low imperfection sensitivity

A concept of hierarchical stiffened shell is proposed in this study, aiming at reducing the imperfection sen- sitivity without adding additional weight. Hierarchical stiffened shell is composed of major stiffeners and minor stiff- eners, and the minor stiffeners are generally distributed between adjacent major stiffeners. For various types of geo- metric imperfections, e.g., eigenmode-shape imperfections, hierarchical stiffened shell shows significantly low imper- fection sensitivity compared to traditional stiffened shell. Furthermore, a surrogate-based optimization framework is proposed to search for the hierarchical optimum design. Then, two optimum designs based on two different opti- mization objectives （including the critical buckling load and the weighted sum of collapse loads of geometrically imperfect shells with small- and large-amplitude imperfections） are compared and discussed in detail. The illustrative example demonstrates the inherent superiority of hierarchical stiffened shells in resisting imperfections and the effectiveness of the proposed framework. Moreover, the decrease of imperfection sensitivity can finally be converted into a decrease of structural weight, which is particularly important in the development of large-diameter launch vehicles.

Hydrophilic bi-functional B-doped g-C_(3)N_(4) hierarchical architecture for excellent photocatalytic H_(2)O_(2) production and photoelectrochemical water splitting

Graphitic carbon nitride(g-C_(3)N_(4))has attracted great interest in photocatalysis and photoelectrocatalysis.However,their poor hydrophilicity poses a great challenge for their applications in aqueous environment.Here,we demonstrate synthesis of a hydrophilic bi-functional hierarchical architecture by the assembly of B-doped g-C_(3)N_(4)nanoplatelets.Such hierarchical B-doped g-C_(3)N_(4)material enables full utilization of their highly enhanced visible light absorption and photogenerated carrier separation in aqueous medium,leading to an excellent photocatalytic H_(2)O_(2)production rate of 4240.3μM g^(-1)h^(-1),2.84,2.64 and 2.13 times higher than that of the bulk g-C_(3)N_(4),g-C_(3)N_(4)nanoplatelets and bulk B doped g-C_(3)N_(4),respectively.Photoanodes based on these hierarchical architectures can generate an unprecedented photocurrent density of 1.72 m A cm^(-2)at 1.23 V under AM 1.5 G illumination for photoelectrochemical water splitting.This work makes a fundamental improvement towards large-scale exploitation of highly active,hydrophilic and stable metal-free g-C_(3)N_(4)photocatalysts for various practical applications.

The Synchronizability and Optimized Analysis of the Hierarchical Network

A large number of research results show that the synchronizability of complex networks is closely related to the topological structure. Some typical complex network models, such as random networks, small-world networks, BA scale-free network, etc, have totally different synchronizability. In this paper, a kind of hierarchical network synchronizability of self-similar module structures was studied, with more focus on the effect of the initial size of the module and network layer to the synchronizability and further research on the problem of network synchronous optimization. The Law of Segmentation Method was employed to reduce the maximum node betweenness and the Law of Parallel Reconnection employed to improve the ability of synchronizability of complex network by reducing the average path length of networks. Meanwhile, the effectiveness of proposed methods was verified through a lot of numerically simulative experiments.

Optimal Redundancy Allocation in Hierarchical Series-Parallel Systems Using Mixed Integer Programming

Reliability optimization plays an important role in design, operation and management of the industrial systems. System reliability can be easily enhanced by improving the reliability of unreliable components and/or by using redundant configuration with subsystems/components in parallel. Redundancy Allocation Problem (RAP) was studied in this research. A mixed integer programming model was proposed to solve the problem, which considers simultaneously two objectives under several resource constraints. The model is only for the hierarchical series-parallel systems in which the elements of any subset of subsystems or components are connected in series or parallel and constitute a larger subsystem or total system. At the end of the study, the performance of the proposed approach was evaluated by a numerical example.

Hierarchical Optimization Method for Federated Learning with Feature Alignment and Decision Fusion

In the realm of data privacy protection,federated learning aims to collaboratively train a global model.However,heterogeneous data between clients presents challenges,often resulting in slow convergence and inadequate accuracy of the global model.Utilizing shared feature representations alongside customized classifiers for individual clients emerges as a promising personalized solution.Nonetheless,previous research has frequently neglected the integration of global knowledge into local representation learning and the synergy between global and local classifiers,thereby limiting model performance.To tackle these issues,this study proposes a hierarchical optimization method for federated learning with feature alignment and the fusion of classification decisions(FedFCD).FedFCD regularizes the relationship between global and local feature representations to achieve alignment and incorporates decision information from the global classifier,facilitating the late fusion of decision outputs from both global and local classifiers.Additionally,FedFCD employs a hierarchical optimization strategy to flexibly optimize model parameters.Through experiments on the Fashion-MNIST,CIFAR-10 and CIFAR-100 datasets,we demonstrate the effectiveness and superiority of FedFCD.For instance,on the CIFAR-100 dataset,FedFCD exhibited a significant improvement in average test accuracy by 6.83%compared to four outstanding personalized federated learning approaches.Furthermore,extended experiments confirm the robustness of FedFCD across various hyperparameter values.

基于改进粒子群优化权函数的直流微电网H_(∞)控制策略

直流微电网中常常含有恒功率负载(constant power loads,CPLs),其负阻抗特性会降低系统的稳定性,造成直流母线电压波动甚至崩溃。因此,首先建立了直流微电网的小信号模型,使用根轨迹法分析了恒功率负载对系统稳定性的影响;其次提出一种基于混合灵敏度优化的电压控制策略,提升了直流微电网系统的稳定性,并采用改进粒子群优化(particle swarm optimization,PSO)算法对权函数进行了优化,进一步提升了鲁棒控制器的性能;最后采用Matlab/Simulink仿真算例进行验证,仿真结果表明提出的鲁棒控制器减小了母线电压的波动,有效提升了直流微电网系统的稳定性。

Green and efficient epoxidation of methyl oleate over hierarchical TS-1

The epoxidation of methyl oleate(MO)was conducted in the presence of aqueous H2O2 as the oxidant and hierarchical TS-1(HTS-1)as the catalyst;the catalyst was synthesized using polyquaternium-6 as the mesopore template.The effects of various parameters,i.e.,H2O2/C=C molar ratio,oxidant concentration,amount of the catalyst,reaction temperature,and time,were systematically studied.Furthermore,response surface methodology(RSM)was used to optimize the conditions to maximize the yield of epoxy MO and to evaluate the significance and interplay of the factors affecting the epoxy MO production.The H2O2/C=C molar ratio and catalyst amount were the determining factors for MO epoxidation,wherein the maximum yield of epoxy MO reached 94.9%over HTS-1 under the optimal conditions.

Evaluation and optimization of secondary water supply system renovation

Due to pollution in second water supply system (SWSS),nine renovation alternative plans were proposed and com-prehensive evaluations of different plan based on Analytical Hierarchy Process (AHP) were presented in this paper. Comparisons of advantages and disadvantages among the plans of SWSS renovations provided solid foundation for selecting the most appro-priate plan for engineering projects. In addition,a mathematical model of the optimal combination of renovation plans has been set up and software Lingo was used to solve the model. As a case study,the paper analyzed 15 buildings in Tianjin City. After simulation of the SWSS renovation system,an optimal scheme was obtained,the result of which indicates that 10 out of those 15 buildings need be renovated in priority. The renovation plans selected for each building are the ones ranked higher in the com-prehensive analysis. The analysis revealed that the optimal scheme,compared with two other randomly calculated ones,increased the percentage of service population by 19.6% and 13.6% respectively,which significantly improved social and economical benefits.

Hierarchical Algorithms of Large-Scale Systems with Nonseparable Multiobjective

A class of large-scale hierarchical control systems is considered, the overall objective function is a nonlinear and nonseparable function of multiple quadratic performance indices.The separation strategy of the multiobjective optimization technique and the three-level objective coordination method are applied to the large -sacle systems, and a four-level hierarchical algorithms of optimization control is obtained.

A HIERARCHICAL IDENTIFICATION ALGORITHM FOR THE EXTENDED EXPONENTIAL MODEL

A new hierarchical identification algorithm is proposed for solving the identi-fication problem of the extended exponential model,which is used frequently in ecological,social and economical systems.By using the zero character of the optimal Lagrangianmultipliers of the equivalent identification problem,a two-level structure of the algorithmis derived first.Then,the convergence and the correspondence with the conventionalnonlinear approaches of the algorithm are proved.The results of simulation and applica-tion show that its convergent rate is greatly higher than that of the L-Mmethod.

Hierarchical Control for Large-Scale Systems

A class of large-scale systems, where the overall objective function is a nonlinear function of performance index of each subsystem, is investigated in this paper. This type of large-scale control problem is non-separable in the sense of conventional hierarchical control. Hierarchical control is extended in the paper to large-scale non-separable control problems, where multiobjective optimization is used as separation strategy. The large-scale non-separable control problem is embedded, under certain conditions, into a family of the weighted Lagrangian formulation. The weighted Lagrangian formulation is separable with respect to subsystems and can be effectively solved using the interaction balance approach at the two lower levels in the proposed three-level solution structure. At the third level, the weighting vector for the weighted Lagrangian formulation is adjusted iteratively to search the optimal weighting vector with which the optimal of the original large-scale non-separable control problem is obtained. Theoretical base of the algorithm is established. Simulation shows that the algorithm is effective.