Identification of material behavior via a Finite Element Model Updating strategy

In this paper an inverse and iterative method for the identification of material behavior is presented, based on the Finite Element Model Updating (FEMU) strategy. The FE simulations are performed with a commercial FE software code, using a self-implemented elastic material model at finite strain. The iterative identification procedure is based on an experimental test (numerical) whose measured kinematic values are compared to the corresponding simulated ones. Through an optimization algorithm the material parameters are varied in a way that the least-squares sum of the kinematic values is minimized and the optimal material parameters yielding the material behavior are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modified particle swarm optimization algorithm with simulated annealing behavior and its numerical verification

The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms.     

Synchronous and asynchronous Pareto-based multi-objective Artificial Bee Colony algorithms

Pareto-based multi-objective optimization algorithms prefer non-dominated solutions over dominated solutions and maintain as much as possible diversity in the Pareto optimal set to represent the whole Pareto-front. This paper proposes three multi-objective Artificial Bee Colony (ABC) algorithms based on synchronous and asynchronous models using Pareto-dominance and non-dominated sorting: asynchronous multi-objective ABC using only Pareto-dominance rule (A-MOABC/PD), asynchronous multi-objective ABC using non-dominated sorting procedure (A-MOABC/NS) and synchronous multi-objective ABC using non-dominated sorting procedure (S-MOABC/NS). These algorithms were investigated in terms of the inverted generational distance, hypervolume and spread performance metrics, running time, approximation to whole Pareto-front and Pareto-solutions spaces. It was shown that S-MOABC/NS is more scalable and efficient compared to its asynchronous counterpart and more efficient and robust than A-MOABC/PD. An investigation on parameter sensitivity of S-MOABC/NS was presented to relate the behavior of the algorithm to the values of the control parameters. The results of S-MOABC/NS were compared to some state-of-the art algorithms. Results show that S-MOABC/NS can provide good approximations to well distributed and high quality non-dominated fronts and can be used as a promising alternative tool to solve multi-objective problems with the advantage of being simple and employing a few control parameters.     

Algorithms for Unconstrained Optimization Problems via Control Theory

Existing algorithms for solving unconstrained optimization problems are generally only optimal in the short term. It is desirable to have algorithms which are long-term optimal. To achieve this, the problem of computing the minimum point of an unconstrained function is formulated as a sequence of optimal control problems. Some qualitative results are obtained from the optimal control analysis. These qualitative results are then used to construct a theoretical iterative method and a new continuous-time method for computing the minimum point of a nonlinear unconstrained function. New iterative algorithms which approximate the theoretical iterative method and the proposed continuous-time method are then established. For convergence analysis, it is useful to note that the numerical solution of an unconstrained optimization problem is none other than an inverse Lyapunov function problem. Convergence conditions for the proposed continuous-time method and iterative algorithms are established by using the Lyapunov function theorem.     

Factorization of moving-average spectral densities by state-space representations and stacking

To factorize a spectral density matrix of a vector moving average process, we propose a state space representation. Although this state space is not necessarily of minimal dimension, its associated system matrices are simple and most matrix multiplications involved are nothing but index shifting. This greatly reduces the complexity of computation. Moreover, in this article we stack every q consecutive observations of the original process MA(q) and generate a vector MA(1) process. We consider a similar state space representation for the stacked process. Consequently, the solution hinges on a surprisingly compact discrete algebraic Riccati equation (DARE), which involves only one Toeplitz and one Hankel block matrix composed of autocovariance functions. One solution to this equation is given by the so-called iterative projection algorithm. Each iteration of the stacked version is equivalent to q iterations of the unstacked one. We show that the convergence behavior of the iterative projection algorithm is characterized by the decreasing rate of the partial correlation coefficients for the stacked process. In fact, the calculation of the partial correlation coefficients via the Whittle algorithm, which takes a very simple form in this case, offers another solution to the problem. To achieve computational efficiency, we apply the general Newton procedure given by Lancaster and Rodman to the DARE and obtain an algorithm of quadratic convergence rate. One immediate application of the new algorithms is polynomial stabilization. We also discuss various issues such as check of positivity and numerical implementation.     

Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

After introducing briefly the principles of theerror linearization method, which is able to determine the coefficients of the first order error approximation, a collection of examples is presented to demonstrate its efficiency as a test bench for analyzing numerical algorithms. These examples illustrate the propagation of initial errors, the effect of cancellation, the easy location of the most unstable parts of an algorithm, calculation of condition numbers, approximating the statistical behavior of accumulated errors and the convergence of iterative methods.     

Optimization of elastic material parameters of sheet metal with FEMU and DIC

In this paper a deep-drawing sheet steel is characterized through tensile tests with samples taken in different angles to the rolling direction. The displacement field is recorded with an optical full-field measurement system and the deformation field is calculated by Digital Image Correlation (DIC). The orthotropic elastic material parameters are identified through an iterative parameter optimization via Finite Element Model Updating (FEMU). In this procedure the material parameters are modified in every iteration so that the numerically computed deformation field and forces match the measured values as well as possible. Depending on the objective function and the input values used in the optimization routine, global or only local minima exist. To show the convergence of the applied technique, two different optimization algorithms, one gradient-based and one gradient-free with different initial starting points were used. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study on network traffic forecast model of SVR optimized by GAFSA

There are some problems, such as low precision, on existing network traffic forecast model. In accordance with these problems, this paper proposed the network traffic forecast model of support vector regression (SVR) algorithm optimized by global artificial fish swarm algorithm (GAFSA). GAFSA constitutes an improvement of artificial fish swarm algorithm, which is a swarm intelligence optimization algorithm with a significant effect of optimization. The optimum training parameters used for SVR could be calculated by optimizing chosen parameters, which would make the forecast more accurate. With the optimum training parameters searched by GAFSA algorithm, a model of network traffic forecast, which greatly solved problems of great errors in SVR improved by others intelligent algorithms, could be built with the forecast result approaching stability and the increased forecast precision. The simulation shows that, compared with other models (e.g. GA-SVR, CPSO-SVR), the forecast results of GAFSA-SVR network traffic forecast model is more stable with the precision improved to more than 89%, which plays an important role on instructing network control behavior and analyzing security situation.     

Dealing with singularities in nonlinear unconstrained optimization

We propose a new trust region based optimization algorithm for solving unconstrained nonlinear problems whose second derivatives matrix is singular at a local solution. We give a theoretical characterization of the singularity in this context and we propose an iterative procedure which allows to identify a singularity in the objective function during the course of the optimization algorithm, and artificially adds curvature to the objective function. Numerical tests are performed on a set of unconstrained nonlinear problems, both singular and non-singular. Results illustrate the significant performance improvement compared to classical trust region and filter algorithms proposed in the literature. The approach is also shown to be competitive with tensor methods in terms of efficiency while reaching a higher level of robustness.     

Three-term conjugate gradient method for the convex optimization problem over the fixed point set of a nonexpansive mapping

Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm.     

基于正弦控制因子的Lateral变异鲨鱼优化算法

针对传统鲨鱼优化算法在求解高维目标函数时,易早熟收敛,陷入局部最优的缺陷.提出一种基于正弦控制因子的Lateral变异鲨鱼优化算法.通过正弦曲线的特性和自适应惯性权重,改善了传统鲨鱼优化算法中由于随机选取控制因子数值大小可能导致算法在迭代后期全局搜索能力降低的问题,提高了算法在迭代后期的全局收敛能力,并对最佳鲨鱼位置引入Lateral变异策略,加强了算法跳出局部最优的可能性.改进后的算法对多个shifted单峰,多峰以及固定维测试函数进行求解,实验结果表明,对比多种不同优化算法而言,本文所提LSSO算法具有更高的收敛精度和搜索速度.     

An Adapted Step Size Algorithm for a 0-1 Biknapsack Lagrangean Dual

This paper deals with a new algorithm for a 0-1 bidimensional knapsack Lagrangean dual which relaxes one of the two constraints. Classical iterative algorithms generate a sequence of multipliers which converges to an optimal one. In this way, these methods generate a sequence of 0-1 one-dimensional knapsack instances. Generally, the procedure for solving each instance is considered as a black box. We propose to design a new iterative scheme in which the computation of the step size takes into account the algorithmic efficiency of each instance. Our adapted step size iterative algorithm is compared favorably with several other algorithms for the 0-1 biknapsack Lagrangean dual over difficult instances for CPLEX 7.0.     

Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming

In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the preconditioner, and how many updates to apply. These decisions are based on predictions of the cost of using the different solvers to determine the next search direction, given costs in determining earlier directions. We summarize earlier results using a modified version of the OB1-R code of Lustig, Marsten, and Shanno, and we present results from a predictor–corrector code PCx modified to use adaptive iteration. If a direct method is appropriate for the problem, then our procedure chooses it, but when an iterative procedure is helpful, substantial gains in efficiency can be obtained.     

Structured FISTA for image restoration

In this paper, we propose an efficient numerical scheme for solving some large‐scale ill‐posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited. First, the coefficient matrix is approximated as the sum of a small number of Kronecker products. This procedure not only introduces one more level of parallelism into the computation but also enables the usage of computationally intensive matrix–matrix multiplications in the subsequent optimization procedure. We then derive the corresponding Tikhonov regularized minimization model and extend the fast iterative shrinkage‐thresholding algorithm (FISTA) to solve the resulting optimization problem. Because the matrices appearing in the Kronecker product approximation are all structured matrices (Toeplitz, Hankel, etc.), we can further exploit their fast matrix–vector multiplication algorithms at each iteration. The proposed algorithm is thus called structured FISTA (sFISTA). In particular, we show that the approximation error introduced by sFISTA is well under control and sFISTA can reach the same image restoration accuracy level as FISTA. Finally, both the theoretical complexity analysis and some numerical results are provided to demonstrate the efficiency of sFISTA.     

Numreical solutoin of a class of parabolic partial differential equation arising in optimal control problems with uncertainty

In this paper the optimal control of uncertain parabolic systems of partial differential equations is investigated. In order to search for controllers that are insensitive to uncertainties in these systems, an iterative optimization procedure is proposed. This procedure involves the solution of a set of operator valued parabolic partial differential equations. The existence and uniqueness of solutions to these operator equations is proved, and a stable numerical algorithm to approximate the uncertain optimal control problem is proposed. The viability of the proposed algorithm is demonstrated by applying it to the control of parabolic systems having two different types of uncertainty.     

A numerical method for solving optimal control problems using state parametrization

A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.     

Constraints on the convergence behavior of algorithms via reachable set analysis

Many iterative algorithms can be interpreted as discrete-time control systems evolving on manifolds. Here, shift parameters act as control inputs. The Adherence structure of the reachable sets provides fundamental limitations on the possible convergence behavior of the algorithm. We analyse the reachable sets of inverse iteration schemes and rational iteration schemes. In particular we show a necessary conditions for the existence of local convergent shift strategies for inverse iteration. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On-line identification of language measure parameters for discrete-event supervisory control

The discrete-event dynamic behavior of physical plants is often represented by regular languages that can be realized as deterministic finite state automata (DFSA). The concept and construction of signed real measures of regular languages have been recently reported in literature. Major applications of the language measure are: quantitative evaluation of the discrete-event dynamic behavior of unsupervised and supervised plants; and analysis and synthesis of optimal supervisory control algorithms in the discrete-event setting. This paper formulates and experimentally validates an on-line procedure for identification of the language measure parameters based on a DFSA model of the physical plant. The recursive algorithm of this identification procedure relies on observed simulation and/or experimental data. Efficacy of the parameter identification procedure is demonstrated on the test bed of a mobile robotic system, whose dynamic behavior is modelled as a DFSA for discrete-event supervisory control.     

Meta-control of an interacting-particle algorithm for global optimization

A common issue for stochastic global optimization algorithms is how to set the parameters of the sampling distribution (e.g. temperature, mutation/cross-over rates, selection rate, etc.) so that the samplings converge to the optimum effectively and efficiently. We consider an interacting-particle algorithm and develop a meta-control methodology which analytically guides the inverse temperature parameter of the algorithm to achieve desired performance characteristics (e.g. quality of the final outcome, algorithm running time, etc.). The main aspect of our meta-control methodology is to formulate an optimal control problem where the fractional change in the inverse temperature parameter is the control variable. The objectives of the optimal control problem are set according to the desired behavior of the interacting-particle algorithm. The control problem considers particles’ average behavior, rather than treating the behavior of individual particles. The solution to the control problem provides feedback on the inverse temperature parameter of the algorithm.     

Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization

Due to the vagaries of optimization problems encountered in practice, users resort to different algorithms for solving different optimization problems. In this paper, we suggest and evaluate an optimization procedure which specializes in solving a wide variety of optimization problems. The proposed algorithm is designed as a generic multi-objective, multi-optima optimizer. Care has been taken while designing the algorithm such that it automatically degenerates to efficient algorithms for solving other simpler optimization problems, such as single-objective uni-optimal problems, single-objective multi-optima problems and multi-objective uni-optimal problems. The efficacy of the proposed algorithm in solving various problems is demonstrated on a number of test problems chosen from the literature. Because of its efficiency in handling different types of problems with equal ease, this algorithm should find increasing use in real-world optimization problems.