MONSS: A multi-objective nonlinear simplex search approach

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.     

Reducing the computational cost of local search in the hybrid evolutionary algorithm with application to electronic imaging

This article focuses on the efficiency problems associated with the use of local search in the hybrid evolutionary algorithm. A two-phase cyclic local search is proposed that alternates the random search and the downhill simplex method (DSM), and helps prevent the algorithm from converging to a sub-optimal solution in multidimensional optimization. The algorithm utilizes a novel micro-model of image local response, in order to reduce the number of fitness evaluations during the local DSM search, with the application to the global optimization problem arising in electronic imaging. The problem is stated as the search for the feasible transformation parameters that minimize the difference between two images. Image local response is defined as the variation of the fitness function that occurs because of a small variation of the parameters, and is computed over a small pixel area. The computed response coefficients specify a contraction transformation applied to the vector of the regular DSM coefficients that control the movement and the shape of the simplex. The transformation adjusts the length of the vector, making the step size of the simplex adaptive to the local properties of the fitness landscape. The computational experiments with two-dimensional grayscale images provide the experimental support and justification of the analytical model of image local response and its utilization for the reduction of the computational cost of local search, without the loss of the quality of the final solution.     

Guided particle swarm optimization method to solve general nonlinear optimization problems

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder–Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.     

Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions

This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodal functions.     

Performance comparison of several optimization algorithms in matched field inversion

Optimization efficiencies and mechanisms of simulated annealing, genetic algorithm, differential evolution and downhill simplex differential evolution are compared and analyzed. Simulated annealing and genetic algorithm use a directed random process to search the parameter space for an optimal solution. They include the ability to avoid local minima, but as no gradient information is used, searches may be relatively inefficient. Differential evolution uses information from a distance and azimuth between individuals of a population to search the parameter space, the initial search is effective, but the search speed decreases quickly because differential information between the individuals of population vanishes. Local downhill simplex and global differential evolution methods are developed separately, and combined to produce a hybrid downhill simplex differential evolution algorithm. The hybrid algorithm is sensitive to gradients of the object function and search of the parameter space is effective. These algorithms are applied to the matched field inversion with synthetic data. Optimal values of the parameters, the final values of object function and inversion time is presented and compared.     

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.     

几种优化算法在浅海匹配场反演中的性能比较

在分析模拟退火算法、遗传算法、差异进化算法、下山单纯形差异进化算法的优化机理的基础上,定量比较了上述算法在浅海匹配场反演中的效率差异。模拟退火算法与遗传算法只使用目标函数值信息在参数空间搜索全局最优值,效率低且易受参数间耦合的影响。差异进化算法使用种群中个体间的距离与方位信息在参数空间中搜索全局最优值,优化效率随着优化过程的进行而下降。下山单纯形差异进化算法将下山单纯形算法融入差异进化算法,增强了差异进化算法的寻优能力,混合算法对目标函数梯度信息敏感的特性使得这一算法具有较强的解耦能力。浅海匹配场反演仿真算例从最优参数反演结果、最终目标函数值、反演时间等方面检验了上述算法的反演效率。     

A new hybrid real-coded genetic algorithm and its application to parameters identification of soils

Inverse analysis using an optimization method based on a genetic algorithm (GA) is a useful tool for obtaining soil parameters in geotechnical fields. However, the performance of the optimization in identifying soil parameters mainly depends on the search ability of the GA used. This study aims to develop a new efficient hybrid real-coded genetic algorithm (RCGA) being applied to identify parameters of soils. In this new RCGA, a new hybrid strategy is proposed by adopting two crossovers with outstanding ability, namely the Simulated Binary Crossover and the simplex crossover. In order to increase the convergence speed, a chaotic local search technique is used conditionally. The performance of the proposed RCGA is first validated by optimizing mathematical benchmark functions. The results demonstrate that the RCGA has an outstanding search ability and faster convergence speed compared to other hybrid RCGAs. The proposed new hybrid RCGA is then further evaluated by identifying soil parameters based on both laboratory tests and field tests, for different soil models. All the comparisons demonstrate that the proposed RCGA has an excellent performance of inverse analysis in identifying soil parameters, and is thus recommended for use based on all the evaluations carried out in this paper.     

An improved harmony search minimization algorithm using different slip surface generation methods for slope stability analysis

An improved harmony search algorithm is proposed which is found to be more efficient than the original harmony search algorithm for slope stability analysis. The effectiveness of the proposed algorithm is examined by considering several published cases. The improved harmony search method is applied to slope stability problems with five types of procedure for generating trial slip surfaces. It is demonstrated that the improved harmony search algorithm is efficient and effective for the minimization of factors of safety for various difficult problems, and the method of generating the trial failure surfaces can be important in the minimization process.     

Imperfection sensitivity due to coupled local instability: a non‐convex QP solution algorithm

The paper deals with the collapse safety of slender elastic structures subjected to local buckling interaction. Using Koiter's asymptotic approach, the mechanical problem is reduced to the search for all the local minima of an indefinite quadratic form over the unit simplex. An efficient recursive branch‐and‐cut algorithm is proposed for solving this non‐convex QP problem, allowing a numerical procedure providing statistical information about the collapse load for a given distribution of random imperfections to be set up. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical identification of material model for C–Mn steel using micro-indentation test

Abstract

Identification of the elastoplastic material model for C–Mn steel, using finite element model of micro-indentation test developed by the authors and proposed algorithm of inverse analysis, is one of the objectives of the project. The micro-indentation experiment is widely described in the present paper, especially those parts, which are meaningful in getting input data for direct, further application in the numerical model of micro-indentation test and in the inverse procedure. Finite element solution connected with the inverse algorithm, which is based on the simplex method, is used to search for the unknown parameters of material model. Validation of the developed inverse algorithm is the particular objective of the present work. The present paper shows that material model determined using the inverse analysis is in agreement with that obtained from the tensile test. The results coincide also with the data available in the literature.     

结构逆可靠度最可能失效点的改进搜索算法

确定逆可靠度最可能失效点(MPPIR)是结构逆可靠度分析的核心问题,以改进均值法(AMV)及其改进方法应用最广泛。但当功能函数非线性程度较高或为非凸非凹函数时,AMV易出现周期振荡等不收敛问题。以现有的AMV改进方法为基础,通过迭代过程中控制搜索方向和步长,提出一种MPPIR的改进搜索算法,并结合不精确一维搜索方法给出了具体的计算流程。数值算例分析表明:提出的算法与AMV相比具有更好的收敛性,与弧长搜索法相比不需要采用优化方法确定最优步长,且对于非凸非凹功能函数以及高度非线性功能函数都具有良好的收敛性。     

一种新的人脸图像本征维数估计方法

利用拓扑理论中的单形定义,本文提出了一种针对人脸图像本征维数的估计方法.首先给出一个简单的几何模型,说明在不同的姿态和光照条件下人脸图像可看成一个弯曲流形;然后把人脸流形模型近似为一个单纯复形,获得相应的单形数目;最后,利用单纯复形中单形的最大维数是单纯复形的维数的性质,从而估计出人脸图像的本征维数.实验结果表明,本文方法跟经典方法,如分形方法、熵估计方法及k-近邻图方法等相比较,在人脸图像本征维数估计方面是有效的和准确的.     

四参数正弦波组合式拟合算法

提出了一种组合式四参数正弦曲线拟合方法。首先,使用已知频率的三参数正弦拟合算法进行频率搜索,构造出一维搜索迭代正弦拟合算法,获得幅度、频率、相位、直流分量4个参数。然后,以其作为初始值,使用四参数搜索迭代方式,获得最终的正弦拟合结果。该方法可以适用于多周期和残周期序列情况,具有明确的收敛域,可以保证在任何情况下获得总体最优的收敛拟合结果。仿真和实测实验,均验证了所述方法的有效性与可行性。     

Bacterial foraging optimisation: Nelder?Mead hybrid algorithm for economic load dispatch

A novel stochastic optimisation approach to solve constrained economic load dispatch problem using hybrid bacterial foraging (BF) technique is presented. in order to explore the search space for finding the local minima of the current location, the simplex algorithm called nelder-mead is used along with BF algorithm. the proposed methodology easily takes care of solving non-convex economic dispatch problems along with different constraints such as transmission losses, dynamic operation constraints (ramp rate limits) and prohibited zones. simulations were performed over various standard test systems with different number of generating units and comparisons are performed with other existing relevant approaches. the findings affirmed the robustness and proficiency of proposed methodology over other existing techniques.     

Control of dead-time systems using derivative free local search guided population based incremental learning algorithms

This paper introduces two improved forms of population based incremental learning (PBIL) algorithm applied to proportional integral derivative (PID) controller and Smith predictor design. Derivative free optimization methods, namely simplex derivative pattern search (SDPS) and implicit filtering (IMF) are used to intensify search mechanism in PBIL algorithm with improved convergence than that of the original PBIL. Although the idea of combining local methods and global methods is not new, this paper focuses application of hybrid heuristics to the vast field of control design especially, control of systems having dead-time. The effectiveness of the controller schemes arrived using the developed algorithms namely simplex derivative pattern search guided population based incremental learning (SDPS-PBIL) and implicit filtering guided population based incremental learning (IMF-PBIL) are demonstrated using unit step set point response for a class of dead-time systems. The results are compared with some existing methods of controller tuning.     

基于自适应引力算法的桥梁监测传感器优化布置

针对桥梁健康监测中传感器布置优化问题,提出了一种基于自适应引力算法的传感器优化布置方法。以模态置信准则为基础,构造满足传感器优化布置的适应度函数;针对引力搜索算法开发能力不足,对衰减因子α进行了自适应改进。搜索初期α较小,粒子以较大步长进行全局搜索,增强了算法的搜索效率;搜索后期α较大,粒子以较小的步长进行局部搜索,提高了算法的搜索能力,避免落入局部极值点。改进后的自适应引力算法通过双重编码的方式,使算法可以解决离散型的传感器布置问题;以马水河大桥为例,验证算法的可行性。结果表明,改进后的算法有很好的寻优能力,能够准确高效的确定传感器优化位置。     

Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm

We present a novel algorithm based on the extended finite element method (XFEM) and an enhanced artificial bee colony (EABC) algorithm to detect and quantify multiple flaws in structures. The concept is based on recent work that have shown the excellent synergy between XFEM, used to model the forward problem, and a genetic‐type algorithm to solve an inverse identification problem and converge to the ‘best’ flaw parameters. In this paper, an adaptive algorithm that can detect multiple flaws without any knowledge on the number of flaws beforehand is proposed. The algorithm is based on the introduction of topological variables into the search space, used to adaptively activate/deactivate flaws during run time until convergence is reached. The identification is based on a limited number of strain sensors assumed to be attached to the structure surface boundaries. Each flaw is approximated by a circular void with the following three variables: center coordinates (x_c, y_c) and radius (r_c), within the XFEM framework. In addition, the proposed EABC scheme is improved by a guided‐to‐best solution updating strategy and a local search (LS) operator of the Nelder–Mead simplex type that show fast convergence and superior global/LS abilities compared with the standard ABC or classic genetic algorithms. Several numerical examples, with increasing level of difficulty, are studied in order to evaluate the proposed algorithm. In particular, we consider identification of multiple flaws with unknown a priori information on the number of flaws (which makes the inverse problem harder), the proximity of flaws, flaws having irregular shapes (similar to artificial noise), and the effect of structured/unstructured meshes. The results show that the proposed XFEM–EABC algorithm is able to converge on all test problems and accurately identify flaws. Hence, this methodology is found to be robust and efficient for nondestructive detection and quantification of multiple flaws in structures. Copyright © 2013 John Wiley & Sons, Ltd.     

基于亚像素综合定位匹配算法的MEMS平面运动测量

动态测试对MEMS的设计、制造和可靠性具有非常重要的意义．提出了快速高精度的综合亚像素定位匹配算法,应用于MEMS平面运动测量．该综合算法把标准化协方差相关法、亚像素步长相关法、曲面拟合法、序惯相似性检测算法和单纯形法有机结合,综合运用各算法的优点,达到了提高亚像素定位速度和精度的目的．通过位移测量实验和对硅微陀螺仪质量块面内振动及谐振频率的测量,验证了该综合算法的可行性和有效性．     

基于文化基因算法的开放车间调度问题研究

针对开放车间调度问题,运用了文化基因算法进行优化求解。在文化基因算法的框架中,既有种群中的全局搜索,又包含针对问题自身特点的局部搜索,为解决开放车间调度问题提供了一种新的算法。按照文化基因算法的思想和特点,将爬山法作为局部搜索策略加入到全局搜索策略所用到的遗传算法中,通过对开放车间调度问题的邻域结构进行研究,加入爬山搜索法进行优化求解。基于40个标准算例,通过与下界值的比较,验证了所提算法在解决具有较大搜索空间的调度问题时,其拥有更出色的算法性能。