Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography

In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method presented here, a potential function with edge-preserving properties is introduced as a regularized term in an objective function. With the minimization of this proposed objective function, an iterative method to solve this optimization problem is presented in which half-quadratic regularization is introduced to simplify the minimization task. Both numerical and experimental data are employed to justify the proposed technique. The reconstruction results indicate that edge-preserving regularization provides a superior performance over Tikhonov regularization.     

A gradient‐only line search method for the conjugate gradient method applied to constrained optimization problems with severe noise in the objective function

A new implementation of the conjugate gradient method is presented that economically overcomes the problem of severe numerical noise superimposed on an otherwise smooth underlying objective function of a constrained optimization problem. This is done by the use of a novel gradient‐only line search technique, which requires only two gradient vector evaluations per search direction and no explicit function evaluations. The use of this line search technique is not restricted to the conjugate gradient method but may be applied to any line search descent method. This method, in which the gradients may be computed by central finite differences with relatively large perturbations, allows for the effective smoothing out of any numerical noise present in the objective function. This new implementation of the conjugate gradient method, referred to as the ETOPC algorithm, is tested using a large number of well‐known test problems. For initial tests with no noise introduced in the objective functions, and with high accuracy requirements set, it is found that the proposed new conjugate gradient implementation is as robust and reliable as traditional first‐order penalty function methods. With the introduction of severe relative random noise in the objective function, the results are surprisingly good, with accuracies obtained that are more than sufficient compared to that required for engineering design optimization problems with similar noise. Copyright © 2004 John Wiley & Sons, Ltd.     

Use of non-negative constraint in Tikhonov regularization for particle sizing based on forward light scattering

Abstract

The set of linear equations in the inversion of particle size distribution (PSD) based on forward light scattering is an ill-posed problem. In order to solve the inverse problem of this kind, a number of inversion algorithms have been proposed. The regularization algorithm can reconstruct the PSD, but in usual case, the solution may contain negative values and is strongly oscillating. Owing to the natural reason, the solution should be non-negative and smooth. In this paper, a simple non-negative constraint (NNC) is used with a combination of the Tikhonov regularization. Simulations and experiments show that the regularization with NNC can achieve more reasonable results.     

An improved hybrid self-inertia weight adaptive particle swarm optimization algorithm with local search

As an evolutionary computing technique, particle swarm optimization (PSO) has good global search ability, but the swarm can easily lose its diversity, leading to premature convergence. To solve this problem, an improved self-inertia weight adaptive particle swarm optimization algorithm with a gradient-based local search strategy (SIW-APSO-LS) is proposed. This new algorithm balances the exploration capabilities of the improved inertia weight adaptive particle swarm optimization and the exploitation of the gradient-based local search strategy. The self-inertia weight adaptive particle swarm optimization (SIW-APSO) is used to search the solution. The SIW-APSO is updated with an evolutionary process in such a way that each particle iteratively improves its velocities and positions. The gradient-based local search focuses on the exploitation ability because it performs an accurate search following SIW-APSO. Experimental results verified that the proposed algorithm performed well compared with other PSO variants on a suite of benchmark optimization functions.     

A Bayesian inversion method for estimating the particle size distribution of latexes from multiangle dynamic light scattering measurements

A statistical Bayesian method is proposed for estimating the particle size distribution (PSD) of polymeric latexes from multiangle dynamic light scattering (MDLS) measurements. The procedure includes two main steps: 1) the calculation of the angle-dependent average diameters of the PSD from the MDLS autocorrelation measurements, and 2) the PSD estimation through a Bayesian method (that is solved with a Markov chain Monte Carlo sampling strategy implemented in the form of a Metropolis-Hasting algorithm). First, the method was evaluated through two simulated examples that involved unimodal and bimodal PSDs of different shapes. Then, the method was employed for estimating two bimodal PSDs obtained by mixing two narrow polystyrene standards. For comparison, all examples were also solved by numerical inversion of the raw MDLS autocorrelation measurements through a classical regularization technique typically used for inverting ill-conditioned linear problems. The proposed method appears as an effective and robust tool for characterizing unimodal or multimodal PSDs without requiring any a priori assumption on the number of modes or on their shapes. For unimodal PSDs exhibiting high asymmetries and for bimodal PSDs with modes of different particle concentration, the Bayesian method produced more accurate results than those obtained with the classical regularization technique.     

A Bound Heuristic Technique for Solving DRAMA Spares Optimizations

1IntroductionTodaythePublicrequiresthatallcomplexellgilleering,suchasatomicPOwerplants,airCrafl,automobilesandcomputer,etc.,behighlyreliable.Generally,tilesystemsarerepairableinventorysystemsthatarecomposedofitemswhicharerepairedalldretUrnedtouseratherthandiscarded.TherepairableinventoryProblemistypicallyconcernedwilhtheoptimalstockingofpartsatbases(orforwardlocations)andacentereddelx)t1'llcilitywhichrepairedunitsreturnedfromthehaseswhileprovidingsomePredeterminedlevelofservice.Themathemati…     

Simultaneous reconstruction of the time-dependent Robin coefficient and heat flux in heat conduction problems

This paper aims to solve an inverse heat conduction problem in two-dimensional space under transient regime, which consists of the estimation of multiple time-dependent heat sources placed at the boundaries. Robin boundary condition (third type boundary condition) is considered at the working domain boundary. The simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with Tikhonov regularization. The properties of the continuous and discrete optimization problem are studied. Differentiability results and the adjoint problems are established. The numerical estimation is investigated using a modified conjugate gradient method. Furthermore, to verify the performance of the proposed algorithm, obtained results are compared with results obtained from the well-known finite-element software COMSOL Multiphysics under the same conditions. The numerical results show that the proposed algorithm is accurate, robust and capable of simultaneously representing the time effects on reconstructing the time-dependent Robin coefficient and heat flux.     

Constrained optimization using a multipoint type chaotic Lagrangian method with a coupling structure

This article proposes a new constrained optimization method using a multipoint type chaotic Lagrangian method that utilizes chaotic search trajectories generated by Lagrangian gradient dynamics with a coupling structure. In the proposed method, multiple search points autonomously implement global search using the chaotic search trajectory generated by the coupled Lagrangian gradient dynamics. These points are advected to elite points (which are chosen by considering their objective function values and their feasibility) by the coupling in order to explore promising regions intensively. In this way, the proposed method successfully provides diversification and intensification for constrained optimization problems. The effectiveness of the proposed method is confirmed through application to various types of benchmark problem, including the coil spring design problem, the benchmark problems used in the special session on constrained real parameter optimization in CEC2006, and a high-dimensional and multi-peaked constrained optimization problem.     

Combining kernel matrix optimization and regularization to improve particle size distribution retrieval

A new method combining Tikhonov regularization and kernel matrix optimization by multi-wavelength incidence is proposed for retrieving particle size distribution (PSD) in an independent model with improved accuracy and stability. In comparison to individual regularization or multi-wavelength least squares, the proposed method exhibited better anti-noise capability, higher accuracy and stability. While standard regularization typically makes use of the unit matrix, it is not universal for different PSDs, particularly for Junge distributions. Thus, a suitable regularization matrix was chosen by numerical simulation, with the second-order differential matrix found to be appropriate for most PSD types.     

基于天牛须改进粒子群算法的平面度误差评定研究

基于天牛须改进粒子群算法(BAS-PSO)对平面度误差进行了评定研究.首先,建立基于最小区域的平面度误差评定的数学模型,并将目标函数转化为非线性最优化问题;接着,在粒子群算法(PSO)的基础上,引人局部搜索能力较强的天牛须算法(BAS),加速全局搜索和局部搜索的并行计算,避免算法早熟收敛并陷入局部最优,提高平面度误差评...     

The Verification of Composite Position Tolerance

An algorithm for the verification of composite position tolerances is proposed and its computer implementation is described. It is shown that a prevalent graphical verification method does not adequately reflect the standard. Composite position tolerance requirements are mathematically formulated as a non-linear optimization problem with a linear objective function and quadratic constraints. The method of feasible directions is used as the basis for an efficient computer implementation. Its performance is evaluated under various test conditions as well as against a simplex pattern search.     

Integrated optimization of location assignment and sequencing in multi-shuttle automated storage and retrieval systems under modified 2n-command cycle pattern

This article explores the integrated optimization problem of location assignment and sequencing in multi-shuttle automated storage/retrieval systems under the modified 2n-command cycle pattern. The decision of storage and retrieval (S/R) location assignment and S/R request sequencing are jointly considered. An integer quadratic programming model is formulated to describe this integrated optimization problem. The optimal travel cycles for multi-shuttle S/R machines can be obtained to process S/R requests in the storage and retrieval request order lists by solving the model. The small-sized instances are optimally solved using CPLEX. For large-sized problems, two tabu search algorithms are proposed, in which the first come, first served and nearest neighbour are used to generate initial solutions. Various numerical experiments are conducted to examine the heuristics’ performance and the sensitivity of algorithm parameters. Furthermore, the experimental results are analysed from the viewpoint of practical application, and a parameter list for applying the proposed heuristics is recommended under different real-life scenarios.     

Stability assessment of earth slope using modified particle swarm optimization

This paper has proposed an effective method to determine the minimum factor of safety (FS) and associated critical failure surface in slope stability analysis. The search for the minimum FS based on limit equilibrium methods is a complex optimization problem as the objective function is non-smooth and non-convex. Recently, particle swarm optimization (PSO) as a meta-heuristic optimization algorithm has been developed with success in treating various types of problems. In the current study, a new approach of PSO is proposed to calculate the safety factor of earth slopes. The safety factors of the general slip surfaces are calculated using Spencer method of slices, and each new slip surface is randomly generated by straight line technique. The reliability and efficiency of the proposed algorithm are examined by considering a number of published cases. The results indicate that the new method can predict a more critical failure mechanism with a lower FS and can outperform the other methods in the literature as well as standard PSO. Finally, the proposed method will be validated by considering an existing slope failure in Ulu Klang, Malaysia.     

0-1型二次规划的光滑函数法

本文针对工程设计、经济分析及计算机辅助设计等领域出现的0-1型二次规划问题,提出了Newton型的光滑迭代算法.首先利用NCP函数将0-1规划转化为不可微优化问题,然后通过构造不可微问题的光滑一致逼近,将组合优化问题转化成了可微的无约束优化问题,克服了已有算法收敛速度慢且计算结构复杂的缺点.文中给出了算法的迭代格式,证...     

An uncertain multidisciplinary design optimization method using interval convex models

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.     

Parameter Identification Method of Large Macro-Micro Coupled Constitutive Models Based on Identifiability Analysis

Large and complex macro-micro coupled constitutive models, which describe metal flow and microstructure evolution during metal forming, are sometimes overparameterized with respect to given sets of experimental datum. This results in poorly identifiable or non-identifiable model parameters. In this paper, a systemic parameter identification method for the large macro-micro coupled constitutive models is proposed. This method is based on the global and local identifiability analysis, in which two identifiability measures are adopted. The first measure accounts for the sensitivity of model results with respect to single parameters, and the second measure accounts for the degree of near-linear dependence of sensitivity functions of parameter subsets. The global identifiability analysis adopts a sampling strategy with only a limited number of model evaluations, and the strategy is a combination of Latin-hypercube sampling, one-factor-at-a-time sampling and elitism preservation strategy. The global identifiability index is the integration of the corresponding local index. A hybrid global optimization method is designed to identify the parameter. Firstly, the genetic algorithm is adopted to identify the model parameter rudely, and then the obtained parameter is further refined through the improved Levenberg-Marquardt algorithm. The niching method is used to maintain the population diversity and to choose the initial value for the Levenberg-Marquardt algorithm. A transition criterion between the genetic algorithm and the Levenberg-Marquardt algorithm is proposed, through the improvement on the average objective function value of the chromosomes and the objective function value of the best chromosome. During optimization by the Levenberg-Marquardt algorithm, the local identifiability analysis is taken at the beginning stage of each iteration, and then the variable with poor identifiability remains unchanged in this iteration; the problem of violation constraint for some solution is solved through adjusting the search step length. At last, taking Ti-6Al-4V as an example, a set of satisfactory material parameters is obtained. The calculated results agree with the experimental results well. The identified results show that some parameters involved in the model are poorly identifiable; at the same time, the identifiability analysis method can provide a guide to experiment design.     

缓冲区容量约束下发动机混流装配线排序研究

为解决缓冲区容量约束下发动机混流装配排序问题,以关键部件消耗均匀化和最大完工时间最小化为目标,建立了优化数学模型,设计了一种多目标遗传算法,采用了混合交叉算子和启发式变异方法,并设计了基于帕累托分级和共享函数的适应度函数,将多目标遗传算法和多目标模拟退火算法的优化结果进行了比较。研究结果表明,多目标遗传算法在满意度和计算效率方面均优于多目标模拟退火算法,是一种有效的混流装配线排序问题求解算法。     

一种电容层析成像图像重建优化算法

提出一种电学层析成像(ECT)图像重建优化算法。通过将传统正则化算法转化为最小二乘问题进行求解,结合lp范数逼近正则化最小化问题,利用重新加权的方法进行迭代计算。以油-气两相流模型进行仿真及静态实验,将所提出的优化算法与常用的LBP、Landweber迭代及Tikhonov正则化算法进行对比。结果表明,与常用算法相比,采用该优化算法对管道中心物体及多物体分布流型进行图像重建,其图像相对误差均为最低,且重建图像的形状保真度明显提高。     

A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation

In this paper, an efficient numerical technique is developed to approximate the solution of two-dimensional cubic nonlinear Schrödinger equations. The method is based on the nonsymmetric radial basis function collocation method (Kansa's method), within an operator Newton algorithm. In the proposed process, three-dimensional radial basis functions (especially, three-dimensional Multiquadrics (MQ) and Inverse multiquadrics (IMQ) functions) are used as the basis functions. For solving the resulting nonlinear system, an algorithm based on the Newton approach is constructed and applied. In the multilevel Newton algorithm, to overcome the instability of the standard methods for solving the resulting ill-conditioned system an interesting and efficient technique based on the Tikhonov regularization technique with GCV function method is used for solving the ill-conditioned system. Finally, the presented method is used for solving some examples of the governing problem. The comparison between the obtained numerical solutions and the exact solutions demonstrates the reliability, accuracy and efficiency of this method.     

Improved artificial bee colony algorithm for crack identification in beam using natural frequencies only

An improved artificial bee colony algorithm (I-ABC) is proposed for crack identification in beam structures. ABC is a heuristic algorithm and swarm technique with simple structure, which is easy to implement but with slow convergence rate. In the I-ABC, the differential evolution (DE) mechanism is introduced to employed bee phase, roulette selection strategy is replaced by tournament selection strategy and a new formula is used to simulate onlooker bee’s behaviour. A discrete open crack is used for vibration analysis of the cracked beam and only the changes in the first few natural frequencies are utilized to establish the objective function of the optimization problem for crack identification. A numerical simulation and an experimental work are studied to illustrate the efficiency of the proposed method. Studies show that the present techniques can produce more accurate damage identification results when compared with original ABC, DE algorithm, particle swarm optimization and genetic algorithm.