FPGA-based Acceleration of Davidon-Fletcher-Powell Quasi-Newton Optimization Method

Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithmetic cores, field programmable gate array(FPGA) has become an attractive alternative to the acceleration of scientific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton(DFP-QN) method by proposing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.

A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method

A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Research on Regulation Method of Energy Storage System Based on Multi-Stage Robust Optimization

To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

Optimization of Open-cast Mining Procedure Based on RSR Method

To explore the optimal evaluation mechanism of open-cast mining procedure,this paper takes the actual operation status of Huolinhe No.1 Open-cast Mine as the research basis,and makes a deep analysis of the four representative mining procedures proposed by this mine.A detailed and comprehensive evaluation system is constructed using rank-sum ratio(RSR)method.The system covers 17 key indicators and aims to evaluate the advantages and disadvantages of each scheme in an all-round and multi-angle manner.Through the calculation and analysis by RSR method,the comprehensive evaluation of the four types of mining procedure schemes is carried out,and finally the secondary river improvement project is determined as the optimal mining implementation scheme,and the joint mining scheme of the south and north areas is the alternative strategy.The research results of this paper are objective,clear and definite,can not only reveal the effectiveness and feasibility of RSR method in solving the problem of open-cast mining procedure optimization,but also provide a strong technical support and decision-making basis for the future production development of Huolinhe No.1 Open-cast Mine.Thus,this study is expected to further promote the scientific and refined process of mining operations.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

A Subdivision-Based Combined Shape and Topology Optimization in Acoustics

We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.

Development of Fixture Layout Optimization for Thin-Walled Parts:A Review

An increasing number of researchers have researched fixture layout optimization for thin-walled part assembly during the past decades.However,few papers systematically review these researches.By analyzing existing literature,this paper summarizes the process of fixture layout optimization and the methods applied.The process of optimization is made up of optimization objective setting,assembly variation/deformation modeling,and fixture layout optimization.This paper makes a review of the fixture layout for thin-walled parts according to these three steps.First,two different kinds of optimization objectives are introduced.Researchers usually consider in-plane variations or out-of-plane deformations when designing objectives.Then,modeling methods for assembly variation and deformation are divided into two categories:Mechanism-based and data-based methods.Several common methods are discussed respectively.After that,optimization algorithms are reviewed systematically.There are two kinds of optimization algorithms:Traditional nonlinear programming and heuristic algorithms.Finally,discussions on the current situation are provided.The research direction of fixture layout optimization in the future is discussed from three aspects:Objective setting,improving modeling accuracy and optimization algorithms.Also,a new research point for fixture layout optimization is discussed.This paper systematically reviews the research on fixture layout optimization for thin-walled parts,and provides a reference for future research in this field.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Gray code based gradient-free optimization algorithm for parameterized quantum circuit

A Gray code based gradient-free optimization(GCO)algorithm is proposed to update the parameters of parameterized quantum circuits(PQCs)in this work.Each parameter of PQCs is encoded as a binary string,named as a gene,and a genetic-based method is adopted to select the offsprings.The individuals in the offspring are decoded in Gray code way to keep Hamming distance,and then are evaluated to obtain the best one with the lowest cost value in each iteration.The algorithm is performed iteratively for all parameters one by one until the cost value satisfies the stop condition or the number of iterations is reached.The GCO algorithm is demonstrated for classification tasks in Iris and MNIST datasets,and their performance are compared by those with the Bayesian optimization algorithm and binary code based optimization algorithm.The simulation results show that the GCO algorithm can reach high accuracies steadily for quantum classification tasks.Importantly,the GCO algorithm has a robust performance in the noise environment.

An Efficient Optimization Design Framework for Low-Resistance Shape of Bionic Amphibious Robot

To realize the low-resistance shape optimization design of amphibious robots,an efficient optimization design framework is proposed to improve the geometric deformation flexibility and optimization efficiency.In the proposed framework,the free-form deformation parametric model of the flat slender body is established and an analytical calculation method for the height constraints is derived.CFD method is introduced to carry out the high-precision resistance calculation and a constrained Kriging-based optimization method is built to improve the optimization efficiency by circularly infilling the new sample points which satisfying the constraints.Finally,the shape of an amphibious robot example is optimized to get the low-resistance shape and the results demonstrate that the presented optimization design framework has the advantages of simplicity,flexibility and high efficiency.

Optimization of chemistry and process parameters for control of intermetallic formation in Mg sludges

Intermetallic formation in sludge during magnesium(Mg)melting,holding and high pressure die casting practices is a very important issue.But,very often it is overlooked by academia,original equipment manufacturers(OEM),metal ingot producers and even die casters.The aim of this study was to minimize the intermetallic formation in Mg sludge via the optimization of the chemistry and process parameters.The Al8Mn5 intermetallic particles were identified by the microstructure analysis based on the Al and Mn ratio.The design of experiment(DOE)technique,Taguchi method,was employed to minimize the intermetallic formation in the sludge of Mg alloys with various chemical compositions of Al,Mn,Fe,and different process parameters,holding temperature and holding time.The sludge yield(SY)and intermetallic size(IS)was selected as two responses.The optimum combination of the levels in terms of minimizing the intermetallic formation were 9 wt.%Al,0.15 wt.%Mn,0.001 wt.%(10 ppm)Fe,690℃ for the holding temperature and holding at 30 mins for the holding time,respectively.The best combination for smallest intermetallic size were 9 wt.%Al,0.15 wt.%Mn,0.001 wt.%(10 ppm)Fe,630℃ for the holding temperature and holding at 60 mins for the holding time,respectively.Three groups of sludge factors,Chemical Sludge(CSF),Physical Sludge(PSF)and Comprehensive Sludge Factors(and CPSF)were established for prediction of sludge yields and intermetallic sizes in Al-containing Mg alloys.The CPSF with five independent variables including both chemical elements and process parameters gave high accuracy in prediction,as the prediction of the PSF with only the two processing parameters of the melt holding temperature and time showed a relatively large deviation from the experimental data.The Chemical Sludge Factor was primarily designed for small ingot producers and die casters with a limited melting and holding capacity,of which process parameters could be fixed easily.The Physical Sludge Factor could be used for mass production with a single type of Mg alloy,in which the chemistry fluctuation might be negligible.In large Mg casting suppliers with multiple melting and holding furnaces and a number of Mg alloys in production,the Comprehensive Sludge Factor should be implemented to diminish the sludge formation.

Multi-objective optimization and evaluation of supercritical CO_(2) Brayton cycle for nuclear power generation

The supercritical CO_(2) Brayton cycle is considered a promising energy conversion system for Generation IV reactors for its simple layout,compact structure,and high cycle efficiency.Mathematical models of four Brayton cycle layouts are developed in this study for different reactors to reduce the cost and increase the thermohydraulic performance of nuclear power generation to promote the commercialization of nuclear energy.Parametric analysis,multi-objective optimizations,and four decision-making methods are applied to obtain each Brayton scheme’s optimal thermohydraulic and economic indexes.Results show that for the same design thermal power scale of reactors,the higher the core’s exit temperature,the better the Brayton cycle’s thermo-economic performance.Among the four-cycle layouts,the recompression cycle(RC)has the best overall performance,followed by the simple recuperation cycle(SR)and the intercooling cycle(IC),and the worst is the reheating cycle(RH).However,RH has the lowest total cost of investment(C_(tot))of$1619.85 million,and IC has the lowest levelized cost of energy(LCOE)of 0.012$/(kWh).The nuclear Brayton cycle system’s overall performance has been improved due to optimization.The performance of the molten salt reactor combined with the intercooling cycle(MSR-IC)scheme has the greatest improvement,with the net output power(W_(net)),thermal efficiencyη_(t),and exergy efficiency(η_(e))improved by 8.58%,8.58%,and 11.21%,respectively.The performance of the lead-cooled fast reactor combined with the simple recuperation cycle scheme was optimized to increase C_(tot) by 27.78%.In comparison,the internal rate of return(IRR)increased by only 7.8%,which is not friendly to investors with limited funds.For the nuclear Brayton cycle,the molten salt reactor combined with the recompression cycle scheme should receive priority,and the gas-cooled fast reactor combined with the reheating cycle scheme should be considered carefully.

The study of a neutron spectrum unfolding method based on particle swarm optimization combined with maximum likelihood expectation maximization

The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric Boundary Element Method

In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.

A Spacecra Equipment Layout Optimization Method for Diverse and Competitive Design

The spacecraequipment layout optimization design(SELOD)problems with complicated performance con-straints and diversity are studied in this paper.The previous literature uses the gradient-based algorithm to obtain optimized non-overlap layout schemes from randomly initialized cases eectively.However,these local optimal solutions are too dicult to jump out of their current relative geometry relationships,signi􀀀cantly limiting their further improvement in performance indicators.Therefore,considering the geometric diversity of layout schemes is put forward to alleviate this limitation.First,similarity measures,including modi􀀀ed cosine similarity and gaussian kernel function similarity,are introduced into the layout optimization process.Then the optimization produces a set of feasible layout candidates with the most remarkable dierence in geometric distribution and the most representative schemes are sampled.Finally,these feasible geometric solutions are used as initial solutions to optimize the physical performance indicators of the spacecra,and diversi􀀀ed layout schemes of spacecraequipment are generated for the engineering practice.The validity and eectiveness of the proposed methodology are demonstrated by two SELOD applications.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Cooperative trajectory optimization of UAVs in approaching stage using feedback guidance methods

This paper mainly studies the problem of using UAVs to provide accurate remote target indication for hypersonic projectiles.Based on the optimal trajectory trends and feedback guidance methods,a new cooperative control algorithm is proposed to optimize trajectories of multi-UAVs for target tracking in approaching stage.Based on UAV kinematics and sensor performance models,optimal trajectory trends of UAVs are analyzed theoretically.Then,feedback guidance methods are proposed under the optimal observation trends of UAVs in the approaching target stage,producing trajectories with far less computational complexity and performance very close to the best-known trajectories.Next,the sufficient condition for the UAV to form the optimal observation configuration by the feedback guidance method is presented,which guarantees that the proposed method can optimize the observation trajectory of the UAV in approaching stage.Finally,the feedback guidance method is numerically simulated.Simulation results demonstrate that the estimation performance of the feedback guidance method is superior to the Lyapunov guidance vector field(LGVF)method and verify the effectiveness of the proposed method.Additionally,compared with the receding horizon optimization(RHO)method,the proposed method has the same optimization ability as the RHO method and better real-time performance.

Bi-Objective Optimization: A Pareto Method with Analytical Solutions

Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.