Design of code division multiple access filters based on sampled fiber Bragg grating by using global optimization algorithms

In this article, we focus on the design of code division multiple access filters (used in data transmission) composed of a particular optical fiber called sampled fiber Bragg grating (SFBG). More precisely, we consider an inverse problem that consists in determining the effective refractive index profile of an SFBG that produces a given reflected spectrum. In order to solve this problem, we use an original multi-layers semi-deterministic global optimization method based on the search of suitable initial conditions for a given optimization algorithm. The results obtained with our optimization algorithms are compared, in term of complexity and final design, with those given by an hybrid genetic algorithm (the method generally considered in the literature for designing SFBGs).     

Multiple colony ant algorithm for job-shop scheduling problem

Ant colony optimization (ACO) is a metaheuristic that takes inspiration from the foraging behaviour of a real ant colony to solve the optimization problem. This paper presents a multiple colony ant algorithm to solve the Job-shop Scheduling Problem with the objective that minimizes the makespan. In a multiple colony ant algorithm, ants cooperate to find good solutions by exchanging information among colonies which are stored in a master pheromone matrix that serves the role of global memory. The exploration of the search space in each colony is guided by different heuristic information. Several specific features are introduced in the algorithm in order to improve the efficiency of the search. Among others is the local search method by which the ant can fine-tune their neighbourhood solutions. The proposed algorithm is tested over set of benchmark problems and the computational results demonstrate that the multiple colony ant algorithm performs well on the benchmark problems.     

Image reconstruction of buried multiple conductors by genetic algorithms

This paper presents an inverse scattering problem for recovering the shapes of multiple conducting cylinders with the immersed targets in a half‐space by genetic algorithm. Two separate perfectly conducting cylinders of unknown shapes are buried in one half‐space and illuminated by transverse magnetic (TM) plane wave from the other half‐space. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations are derived, and the electromagnetic imaging problem is reformulated into an optimization problem. The improved steady state genetic algorithm is used to find out the global extreme solution. Numerical results are given to demonstrate the performance of the inverse algorithm. Good reconstruction can be obtained even when the initial guesses are far different from the exact shapes, and then the multiple scattered fields between two conductors are serious. In addition, the effect of Gaussian noise on the reconstruction is investigated. We can find that the effect of noise is negligible for the normalized standard deviations below 0.01. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 276–281, 2008; Published online in Wiley InterScience (www.interscience.wiley.com).     

Material characterization and interfacial boundary identification by solving an inverse elasto statics boundary elements problem

An inverse geometry problem of identifying simultaneously two irregular interfacial boundaries along with the mechanical properties of the interface domain located between the components of multiple (three) connected regions is investigated. A discrete number of displacement measurements obtained from a uniaxial tension test are used as extra information to solve this inverse problem. A unique combination of global and local optimization method is used, that is, the imperialist competitive algorithm (ICA) to find the best initial guesses of the unknown parameters to be used by the local optimization methods, that is, the conjugate gradient method (CGM) and the simplex method (SM). The CGM and SM are used in series. The performance of these local optimization methods is dependents on the initial guesses of the unknown boundaries and the mechanical properties, that is, Poisson’s ratio and Young’s modulus, so ICA provides the best initial guesses. The boundary elements method is employed to solve the direct two-dimensional (2D) elastostatics problem. A fitness function, which is the summation of squared differences between measured and computed displacements at identical locations on the exterior boundary, is minimized. Several example problems are solved and the accuracy of the obtained results is discussed. The influence of the value of the material properties of the subregions and the effect of measurement errors on the estimation process are also addressed.     

An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method     

结构计算模型修正的区间反演方法

提出了结构计算模型修正的区间反演方法。该方法将计算模型修正问题归结为非线性全局优化问题，并采用一种遗传算法进行求解。方法考虑了作为修正参考值的试验模态参数具有一定误差，计算结果除可以给出修正后模型的估计值外还可以同时给出其不确定度，有利于对修正后计算模型的质量做出直观评价。算例表明本文提出的方法是可靠可行的，不仅可以判断采用的信息是否完备，而且可以对完备数据的稳定性情况进行判定。     

Application of the genetic algorithm for microwave imaging of a layered dielectric object via the regular shape expansion technique

A novel method combining the genetic algorithm (GA) and regular shape expansion technique is reported for electromagnetic imaging of a multilayer dielectric object of arbitrary shape. By measuring the scattered field, the shape, location, size, and permittivity of each layer of the object are retrieved quite successfully. The forward problem is solved based on the equivalent source current and the method of moments (MoM), while the inverse problem is reformulated as an optimization problem. The optimization problem is solved by the proposed method. Numerical simulation shows that good image reconstruction can be obtained for various multilayer dielectric objects as long as the noise level is ≤−20 dB. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol 10, 347–354, 1999     

Solving inverse electromagnetic problems using FDTD and gradient‐based minimization

We address time‐domain inverse electromagnetic scattering for determining unknown characteristics of an object from observations of the scattered field. Applications include non‐destructive characterization of media and optimization of material properties, for example, the design of radar absorbing materials. Another application is model reduction where a detailed model of a complex geometry is reduced to a simplified model. The inverse problem is formulated as an optimal control problem where the cost function to be minimized is the difference between the estimated and observed fields, and the control parameters are the unknown object characteristics. The problem is solved in a deterministic gradient‐based optimization algorithm using a parallel 2D FDTD scheme. Highly accurate analytical gradients are computed from the adjoint formulation. The inverse method is applied to the characterization of layered dispersive media and the determination of parameters in subcell models for thin sheets and narrow slots. Copyright © 2006 John Wiley & Sons, Ltd.     

面向批量订单包装的物流箱规格优化问题研究

目的 针对面向仓储物流环境下多型号多批量产品的订单包装问题,提出一种预制物流箱规格优化模型及算法。方法 对产品订单建立订单分包规则,确定分包方案,以订单包装材料总成本最小为优化目标建立物流箱规格优化模型。针对该模型提出一种改进模拟退火算法,通过贪婪策略求解最优分包方案,降低模型计算复杂度,设计一种新型解更新算子,以提高算法寻优能力,设计一种自适应步长策略,以平衡算法前期全局搜索与后期局部搜索的能力。结果 通过实例证明,文中提出的算法相较于其他算法,具有更强的求解能力,与实例企业仓储包装现状相比,同批订单降低了17%的包装材料成本。结论 该方法可用于解决产品种类多、尺寸差异大、动态更新等应用场景下的系列运输包装纸箱规格优化问题,为企业物流运输管理提供了一种有效的包装优化思路和解决方法。     

A two-stage approach for multi-objective decision making with applications to system reliability optimization

This paper proposes a two-stage approach for solving multi-objective system reliability optimization problems. In this approach, a Pareto optimal solution set is initially identified at the first stage by applying a multiple objective evolutionary algorithm (MOEA). Quite often there are a large number of Pareto optimal solutions, and it is difficult, if not impossible, to effectively choose the representative solutions for the overall problem. To overcome this challenge, an integrated multiple objective selection optimization (MOSO) method is utilized at the second stage. Specifically, a self-organizing map (SOM), with the capability of preserving the topology of the data, is applied first to classify those Pareto optimal solutions into several clusters with similar properties. Then, within each cluster, the data envelopment analysis (DEA) is performed, by comparing the relative efficiency of those solutions, to determine the final representative solutions for the overall problem. Through this sequential solution identification and pruning process, the final recommended solutions to the multi-objective system reliability optimization problem can be easily determined in a more systematic and meaningful way.     

Application of the inverse elasticity problem to identify irregular interfacial configurations

An inverse elasticity problem is solved to identify the irregular boundary between the components of a multiple connected domain using displacement measurements obtained from an uniaxial tension test. The boundary elements method (BEM) coupled with the particle swarm optimization (PSO) and conjugate gradient method (CGM) are employed. Due to the ill-posed nature of this inverse elasticity problem, and the need for an initial guess of the unknown interfacial boundary when local optimization methods are implemented, a Meta heuristic procedure based on the PSO algorithm is presented. The CGM is then employed using the best initial guess obtained by the PSO to reach convergence. This procedure is highly effective, since the computational time reduces considerably and accuracy of the results is reasonable. Several example problems are solved and the accuracy of obtained results is discussed. The influence of material properties and the effect of measurement errors on the estimation process are also addressed.     

Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems

This article presents an algorithm based on the Bernstein form of polynomials for solving the optimal power flow (OPF) problem in electrical power networks. The proposed algorithm combines local and global optimization methods and is therefore referred to as a ‘hybrid’ Bernstein algorithm in the context of this work. The proposed algorithm is a branch-and-bound procedure wherein a local search method is used to obtain a good upper bound on the global minimum at each branching node. Subsequently, the Bernstein form of polynomials is used to obtain a lower bound on the global minimum. The performance of the proposed algorithm is compared with the previously reported Bernstein algorithm to demonstrate its efficacy in terms of the chosen performance metrics. Furthermore, the proposed algorithm is tested on the OPF problem for several benchmark IEEE power system examples and its performance is compared with generic global optimization solvers such as BARON and COUENNE. The test results demonstrate that the hybrid Bernstein global optimization algorithm delivers satisfactory performance in terms of solution optimality.     

Gaining-Sharing Knowledge Based Algorithm for Solving Stochastic Programming Problems

This paper presents a novel application of metaheuristic algorithms for solving stochastic programming problems using a recently developed gaining sharing knowledge based optimization (GSK) algorithm. The algorithm is based on human behavior in which people gain and share their knowledge with others. Different types of stochastic fractional programming problems are considered in this study. The augmented Lagrangian method (ALM) is used to handle these constrained optimization problems by converting them into unconstrained optimization problems. Three examples from the literature are considered and transformed into their deterministic form using the chance-constrained technique. The transformed problems are solved using GSK algorithm and the results are compared with eight other state-of-the-art metaheuristic algorithms. The obtained results are also compared with the optimal global solution and the results quoted in the literature. To investigate the performance of the GSK algorithm on a real-world problem, a solid stochastic fixed charge transportation problem is examined, in which the parameters of the problem are considered as random variables. The obtained results show that the GSK algorithm outperforms other algorithms in terms of convergence, robustness, computational time, and quality of obtained solutions.     

Solution of convergence problem in ultrasound inverse scattering tomography

When the product of contrast and size of an object, which is to be reconstructed by using the ultrasound inverse scattering tomography algorithm, is large, it is well known that those algorithms fail to converge to a unique global minimum. In order to solve this well known and difficult convergence problem, in this paper we present a new method, which converges to the true solution, for obtaining the scattering potential without using the Born or Rytov approximation. This method converts the nonlinear nature of the problem into a linear one. Through computer simulations we will show the validity of the new approach for high contrast two-dimensional scattering objects which are insonified by an incident ultrasound plane wave. Numerical results show that the reconstruction error is very small for circularly symmetric two-dimensional cylindrical objects whose refractive indices range from small to even sufficiently large values for which the previous inverse scattering algorithms fail to converge.     

Application of the sinc basis moment method to the reconstruction of infinite circular cylinders

A solution of the ultrasonic scattering and inverse scattering problem has been obtained by solving the inhomogeneous Helmholtz wave equation by the sinc basis moment method. In this numerical study, the algorithm of S.A. Johnson and M.L. Tracy (1983) has been applied to the reconstruction of an infinite circular cylinder that is subject to an incident cylindrical wave of ultrasound and is surrounded by a homogeneous coupling medium. For weak scattering cylinders, successful reconstructions have been obtained using the known exact solution for the scattered field as the input data for the algorithm. A detailed discussion of sampling requirements for this algorithm is presented, and the threshold derived correlates well with results of a numerical study of variation of the sampling density. Effects of varying object contrast, object size, grid size, sampling density, and method of iteration are investigated. Because the algorithm is slow, optimization of computation is described.     

An efficient global optimization algorithm for multifactor dynamic systems

Abstract

In this study we present an efficient global optimization method, DIviding RECTangle (DIRECT) algorithm, for parametric analysis of dynamic systems. In a bounded constrained problem the DIRECT algorithm explores multiple potentially optimal subspaces in one search. The algorithm also eliminates the need for derivative calculations which are required in some efficient gradient‐based methods. In this study the first optimization example is to find the dynamic parameters of a tennis racket. The second example is a biomechanical parametric study of a heel‐toe running model governed by six factors. The effectiveness of the DIRECT algorithm is compared with a genetic algorithm in an analysis of heel‐toe running. The result shows that the DIRECT algorithm obtains an improved result in 83% less execution time. It is demonstrated that the straightforward DIRECT algorithm provides a general procedure for solving global optimization problems efficiently and confidently.     

A new multi-objective evolutionary algorithm: neighbourhood exploring evolution strategy

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+λ)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful.     

基于同伦延拓的冗余机械臂逆运动学优化算法研究

目的 针对偏置冗余机械臂的逆运动学,采用传统数值法存在依赖初始值、奇异位姿收敛性差等问题,提出一种改进数值法。方法 首先将非线性方程组转化为同伦方程组,引入同伦延拓算法能够有效避免依赖初始值的问题,同时能够获取逆运动学解空间。然后考虑奇异位姿,将同伦方程组转化为最小二乘问题,采用Levenberg Marquardt算法对同伦方程组进行路径追踪,以获取逆运动学解空间。最后将关节极限避免问题映射为解空间优化问题,引入二进制改进粒子群优化算法,获得最优逆运动学解。结果 实验结果表明,相较于传统数值法,文中所提数值法针对逆运动学求解具有更高的收敛率、更快的收敛速度,同时二进制改进粒子群算法能够有效避免关节极限问题。结论 采用文中所提数值法求解逆运动学的精度较高,能够满足实时性要求,对于机械臂用于包装作业具有一定的理论意义和工程应用价值。     

Inverse scattering of a buried imperfect conductor by the genetic algorithm

Inverse scattering of an imperfectly conducting cylinder buried in a half‐space is presented. A conducting cylinder of unknown shape and conductivity is buried in one half‐space and scatters the incident field from another half‐space. Based on the measured scattered field and the boundary condition, a set of nonlinear integral equations is derived and the inverse problem is reformulated into an optimization problem. The genetic algorithm is then employed to find the global extreme solution of the object function. As a result, the shape and the conductivity of the scatterer can be reconstructed. Even when the initial guess is far away from the exact one, the genetic algorithm can avoid the local extreme and converge to a global extreme solution. In such a case, the gradient‐based method often gets stuck in a local extreme. Numerical results are given to show the effectiveness of the genetic algorithm. Multiple incident directions permit good reconstruction of shape and, to a lesser extent, conductivity in the presence of noise in measured data. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 355–360, 2000     

流体饱和孔隙介质参数反演的模拟退火算法

本文研究了模拟退火算法在流体饱和孔隙介质参数反演中的应用。通过计算响应数据与实测响应数据的拟合将参数反问题归结为最优化问题。由于流体饱和孔隙介质运动方程的复杂性，动力响应与材料参数之间呈复杂的非线性关系，优化目标函数是非凸多峰函数。传统的梯度类优化方法一方面受局部极值的困扰难以搜索到全局最优解； 另一方面确定搜索方向须进行复杂的参数敏度分析。为克服这些困难，本文应用模拟退火算法进行了多参数反演数值模拟，模拟结果表明了模拟退火算法的可行性和稳健性。