Chemical process dynamic optimization based on the differential evolution algorithm with an adaptive scheduling mutation strategy

To solve chemical process dynamic optimization problems, a differential evolution algorithm integrated with adaptive scheduling mutation strategy (ASDE) is proposed. According to the evolution feedback information, ASDE, with adaptive control parameters, adopts the round-robin scheduling algorithm to adaptively schedule different mutation strategies. By employing an adaptive mutation strategy and control parameters, the real-time optimal control parameters and mutation strategy are obtained to improve the optimization performance. The performance of ASDE is evaluated using a suite of 14 benchmark functions. The results demonstrate that ASDE performs better than four conventional differential evolution (DE) algorithm variants with different mutation strategies, and that the whole performance of ASDE is equivalent to a self-adaptive DE algorithm variant and better than five conventional DE algorithm variants. Furthermore, ASDE was applied to solve a typical dynamic optimization problem of a chemical process. The obtained results indicate that ASDE is a feasible and competitive optimizer for this kind of problem.     

A hybrid differential evolution and estimation of distribution algorithm based on neighbourhood search for job shop scheduling problems

Job shop scheduling problem (JSSP) is a typical NP-hard problem. In order to improve the solving efficiency for JSSP, a hybrid differential evolution and estimation of distribution algorithm based on neighbourhood search is proposed in this paper, which combines the merits of Estimation of distribution algorithm and Differential evolution (DE). Meanwhile, to strengthen the searching ability of the proposed algorithm, a chaotic strategy is introduced to update the parameters of DE. Two mutation operators are adopted. A neighbourhood search (NS) algorithm based on blocks on critical path is used to further improve the solution quality. Finally, the parametric sensitivity of the proposed algorithm has been analysed based on the Taguchi method of design of experiment. The proposed algorithm was tested through a set of typical benchmark problems of JSSP. The results demonstrated the effectiveness of the proposed algorithm for solving JSSP.     

Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison

This study presents a methodology which integrates single-objective evolutionary algorithms (EAs) and finite element (FE) model updating for damage inference in three-dimensional (3D) structures. First, original well-known EAs, namely the genetic algorithm, differential evolution (DE) and particle swarm optimization (PSO), are combined with FE model updating for detecting damage in a 3D four-storey modular structure and their performances are compared. Next, to obtain more accurate results, hybrid Lévy flights–DE and hybrid artificial bee colony–PSO are developed for enhancing damage identification. With each method, the objective function composed of modal strain energy and mode shape residuals, taken from the FE model of the intact structure and the simulated damage responses, is initially created. Then, the performance of each algorithm combined with FE model updating for damage detection is assessed in terms of three characteristics: consistency, computational cost and accuracy, and the best performing algorithm is recommended.     

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.     

A neuro-evolutive technique applied for predicting the liquid crystalline property of some organic compounds

A simple self-adaptive version of the differential evolution algorithm was applied for simultaneous architectural and parametric optimization of feed-forward neural networks, used to classify the crystalline liquid property of a series of organic compounds. The developed optimization methodology was called self-adaptive differential evolution neural network (SADE-NN) and has the following characteristics: the base vector used is chosen as the best individual in the current population, two differential terms participate in the mutation process, the crossover type is binomial, a simple self-adaptive mechanism is employed to determine the near-optimal control parameters of the algorithm, and the integration of the neural network into the differential evolution algorithm is performed using a direct encoding scheme. It was found that a network with one hidden layer is able to make accurate predictions, indicating that the proposed methodology is efficient and, owing to its flexibility, it can be applied to a large range of problems.     

A discrete artificial bee colony algorithm incorporating differential evolution for the flow-shop scheduling problem with blocking

A flow-shop scheduling problem with blocking has important applications in a variety of industrial systems but is underrepresented in the research literature. In this study, a novel discrete artificial bee colony (ABC) algorithm is presented to solve the above scheduling problem with a makespan criterion by incorporating the ABC with differential evolution (DE). The proposed algorithm (DE-ABC) contains three key operators. One is related to the employed bee operator (i.e. adopting mutation and crossover operators of discrete DE to generate solutions with good quality); the second is concerned with the onlooker bee operator, which modifies the selected solutions using insert or swap operators based on the self-adaptive strategy; and the last is for the local search, that is, the insert-neighbourhood-based local search with a small probability is adopted to improve the algorithm's capability in exploitation. The performance of the proposed DE-ABC algorithm is empirically evaluated by applying it to well-known benchmark problems. The experimental results show that the proposed algorithm is superior to the compared algorithms in minimizing the makespan criterion.     

An enhanced chiller FDD strategy based on the combination of the LSSVR-DE model and EWMA control charts

Development of the fault detection and diagnosis (FDD) for chiller systems is very important for improving the equipment reliability and saving energy consumption. The results of FDD performance are strongly dependent on the accuracy of chiller models. Since the accuracy of the chiller models depends on the indefinite model parameters which are normally chosen by experiments or experiences, an accurate chiller model is difficult to build. Therefore, optimization of model parameters is very useful to increase the accuracy of chiller models. This paper presents a new FDD strategy for centrifugal chillers of building air-conditioning systems, which is the combination between the nonlinear least squares support vector regression (LSSVR) based on the differential evolution (DE) algorithm and the exponentially weighted moving average (EWMA) control charts. In this strategy, the nonlinear LSSVR, which is a reformulation of SVR model with better generalization performances, is adopted to develop the reference feature parameter models in a typical non-linear chiller system. The DE algorithm which is a real-coding optimal algorithm with powerful global searching capacity is employed to enhance the accuracy of LSSVR models. The exponentially weighted moving average (EWMA) control charts are introduced to improve the fault detection capability as well as to reduce the Type II errors in a t-statistics-based way. Six typical faults of the chiller from the real-time experimental data of ASHRAE RP-1043 project are chosen to validate proposed FDD methods. Comprehensive comparisons between the proposed method and two similarly previous studies are performed. The comparison results show that the proposed method has achieved significant improvement in accuracy and reliability, especially at low severity levels. The proposed DE-LSSVR-EWMA strategy is robust for fault detection and diagnosis in centrifugal chiller systems.     

一维EEP自适应技术新进展:从线性到非线性

有限元后处理中超收敛计算的EEP(单元能量投影)法以及基于该法的自适应分析方法对线性ODE(常微分方程)问题的求解已经获得了全面成功,也推动了非线性ODE问题自适应求解的研究。经过研究,已经实现了一维有限元自适应分析技术从线性到非线性的跨越,该文意在对这方面的进展作一简要综述与报道。该文提出一种基于EEP法的一维非线性有限元自适应求解方法,其基本思想是通过线性化,将现有的线性问题自适应求解方法直接引入非线性问题求解,而无需单独建立非线性问题的超收敛计算公式和自适应算法,从而构成一个统一的、通用的非线性问题自适应求解算法。该文给出的数值算例表明所提出的算法高效、稳定、通用、可靠,解答可逐点按最大模度量满足用户给定的误差限,可作为先进高效的非线性ODE求解器的核心理论和算法。     

An accelerated pseudo-genetic algorithm for dynamic finite element model updating

An effective accelerated pseudo-genetic algorithm (APGA), which combines an adaptive pseudo-genetic algorithm (P-GA) with an accelerated random search (ARS) method, is proposed to update finite element (FE) models in the presence of measured data. The algorithm explores the higher probability of converging to a global solution provided by genetic algorithms and the accelerated hill-climbing ability given by ARS. The objective of the optimization problem is to minimize the difference between measured and numerical FE vibration data. The effectiveness of the approach is first tested on mathematical benchmark functions. The best version of APGA is then applied to a simulated beam structure to test the applicability of the new approach for FE model updating. Finally, the algorithm is applied to update two real structures using measured modal data. The application of this new algorithm obtains results that correlate well with experiments in reduced time.     

利用试验模态参数修正有限元模型的再正交拉哥朗日乘子法

本文给出了一种利用试验模态参数来优化有限元动态模型的再正交拉哥朗日乘子法,即首先利用先验测试信息来优化初始分析模型,然后以优化模型得出的特征向量和测试频率再次作为先验模态信息来优化前次优化的模型。文末将此方法应用开工程结构的实际优化得到了满意的结果。     

Modified artificial bee colony optimization with block perturbation strategy

As a newly emerged swarm intelligence-based optimizer, the artificial bee colony (ABC) algorithm has attracted the interest of researchers in recent years owing to its ease of use and efficiency. In this article, a modified ABC algorithm with block perturbation strategy (BABC) is proposed. Unlike basic ABC, in the BABC algorithm, not one element but a block of elements from the parent solutions is changed while producing a new solution. The performance of the BABC algorithm is investigated and compared with that of the basic ABC, modified ABC, Brest's differential evolution, self-adaptive differential evolution and restart covariance matrix adaptation evolution strategy (IPOP-CMA-ES) over a set of widely used benchmark functions. The obtained results show that the performance of BABC is better than, or at least comparable to, that of the basic ABC, improved differential evolution variants and IPOP-CMA-ES in terms of convergence speed and final solution accuracy.     

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.     

Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy

An inverse analysis methodology to simultaneously identify the parameters of various anisotropic yield criteria together with isotropic work-hardening models of metal sheets is outlined. This identification makes use of results of the cruciform biaxial test, i.e., the evolution of the force during the test, for the two axes of the sample, and the major and minor strain distributions along both axes, at a given moment during the test. Based on a study of the sensitivity of the constitutive parameters to the biaxial tensile test results, the inverse identification consists on a procedure that sequentially minimises the gap between experimental and numerical results. Each step of the sequence uses a distinct cost function according to the type of results to be minimised, using a gradient-based optimisation algorithm, the Levenberg-Marquardt method. The inverse methodology allows for the identification of constitutive parameters of complex constitutive models. This sequential identification strategy is compared to a strategy based on a single cost function, involving all parameters and type of results, which has lower performance.     

Comparison of Dynamic Differential Evolution and Self-Adaptive Dynamic Differential Evolution for Buried Metallic Cylinder

The application of two techniques for the reconstruction of shape reconstruction of a metallic cylinder from scattered field measurements is studied in this paper. These techniques are applied to two-dimensional configurations, for which the method of moment (MoM) is applied to solve the integral equations. Considering that the microwave imaging is recast as a nonlinear optimization problem, an objective function is defined by the norm of the difference between the measured scattered electric fields and those calculated for each estimated metallic cylinder. Thus, the shape of a metallic cylinder can be obtained by minimizing the objective function. In order to solve this inverse scattering problem, two techniques are employed. The first one is based on dynamic differential evolution (DDE) algorithm, while the second one is an improved version of the DDE algorithm with self-adaptive control parameters, called SADDE. Both techniques are tested for the simulated data contaminated by additive white Gaussian noise. Numerical results indicate that SADDE algorithm outperforms DDE algorithm in terms of reconstruction accuracy and convergence speed.     

一种改进的利用频响函数进行有限元模型修正的方法

在对机械结构的动态特性进行准确而可靠的预测时，有限元模型的设计参数的修正是很重要的。利用试验测试和预测的有限元模型计算得到的频响函数（FRF），在结构动力缩聚技术的基础上，推导出了一种改进的基于频响函数的灵敏度分析的修正方程。数值实例研究结果表明该方法利用不完备的测量数据，也可在很宽的频率范围内，同时对多个参数进行修正，有限元模型修正解与真实结构参数完全吻合。本文的方法可适用于大型复杂结构的模型修正。     

A new modified differential evolution algorithm scheme-based linear frequency modulation radar signal de-noising

The main intention of this study was to investigate the development of a new optimization technique based on the differential evolution (DE) algorithm, for the purpose of linear frequency modulation radar signal de-noising. As the standard DE algorithm is a fixed length optimizer, it is not suitable for solving signal de-noising problems that call for variability. A modified crossover scheme called rand-length crossover was designed to fit the proposed variable-length DE, and the new DE algorithm is referred to as the random variable-length crossover differential evolution (rvlx-DE) algorithm. The measurement results demonstrate a highly efficient capability for target detection in terms of frequency response and peak forming that was isolated from noise distortion. The modified method showed significant improvements in performance over traditional de-noising techniques.     

基于逆响应面法的有限元模型修正

基于响应面法（RSM）的有限元模型修正是以若干设计参数（如密度、弹性模量等）为自变量,以若干特征参数（如固有频率、振型等）为因变量,通过回归分析方法来拟合特征参数关于修正参数的显式表达式。提出的逆响应面法（IRSM）则是以特征参数作为自变量,设计参数作为因变量。利用此法的有限元模型修正可直接根据特征参数的目标值得到设计参数的修正量,而不需要经过迭代计算,有效地提高计算速度和精度。介绍逆响应面法及其应用,讨论使用响应面法和逆响应面法进行有限元模型修正的优缺点和适用范围,分析适合于逆响应面法的逆响应面函数、实验设计方案和回归精度检验的方法。利用逆响应面法对一简支梁进行有限元模型修正的结果表明,逆响应面法能高效准确地修正设计参数,对于输出变量少于输入变量的情况更能显著减少有限元计算次数,适用于复杂的工程结构。     

增强差异演化算法及其应用

针对约束优化问题,提出一种适于约束优化的增强差异演化算法(enhanced differential evolution algorithm for constrained optimization, ECDE).在约束处理上采用不可行域与可行域更新规则的方法,避免了传统的惩罚函数方法中对惩罚因子的设置,使算法的实现变得简单.改进了DE算法的变异操作,对选择的3个父代个体进行操作遍历,产生6个候选解,取适应值最优的为变异操作的解,大大改善了算法的稳定性、鲁棒性和搜索性能.通过4个测试函数和1个设计实例仿真,表明所提出的算法具有较快的收敛速度和较好的稳定性和鲁棒性.     

基于离散差分进化算法的随机车辆路径问题

针对差分进化算法求解组合优化问题存在的局限性,引入计算机语言中的2种按位运算符,对差分进化算法的变异算子进行重新设计,用来求解不确定需求和旅行时间下同时取货和送货的随机车辆路径问题（SVRPSPD）。通过对车辆路径问题的benchmark问题和SVRPSPD问题进行路径优化,并同差分进化算法和遗传算法的计算结果进行比较,验证了离散差分进化算法的性能。结果表明,离散差分进化算法在解决复杂的SVRPSPD问题时,具有较好的优化性能,不仅能得到更好的优化结果,而且具有更快的收敛速度。     

微分进化算法在圆度误差评定中的应用

为了精确快速计算圆度误差,提出了基于微分进化智能优化算法的最小区域圆度误差评定方法。介绍了微分进化算法的基本原理及种群初始化、变异、交叉、选择实现步骤,建立了该算法求解最小区域圆度误差的数学模型。为验证算法的有效性,进行了大量实验并与多种算法进行对比,证实了方法的评定结果不仅小于最小二乘法及标准遗传算法评定结果,精度高,而且计算结果稳定,运算速度快。实验表明:微分进化算法用于最小区域圆度误差评定有较强的自适应能力、快速全局收敛性和高稳定性,适于对高精度圆度误差的快速评定。