Solving Ordinary Differential Equations with Evolutionary Algorithms

In this paper, the authors show that the general linear second order ordinary Differential Equation can be formulated as an optimization problem and that evolutionary algorithms for solving optimization problems can also be adapted for solving the formulated problem. The authors propose a polynomial based scheme for achieving the above objectives. The coefficients of the proposed scheme are approximated by an evolutionary algorithm known as Differential Evolution (DE). Numerical examples with good results show the accuracy of the proposed method compared with some existing methods.

Parallel Evolutionary Modeling for Nonlinear Ordinary Differential Equations

We introduce a new parallel evolutionary algorithm in modeling dynamic systems by nonlinear higher-order ordinary differential equations (NHODEs). The NHODEs models are much more universal than the traditional linear models. In order to accelerate the modeling process, we propose and realize a parallel evolutionary algorithm using distributed CORBA object on the heterogeneous networking. Some numerical experiments show that the new algorithm is feasible and efficient.

An Immune Self-adaptive Differential Evolution Algorithm with Application to Estimate Kinetic Parameters for Homogeneous Mercury Oxidation

A new version of differential evolution(DE) algorithm,in which immune concepts and methods are applied to determine the parameter setting,named immune self-adaptive differential evolution(ISDE),is proposed to improve the performance of the DE algorithm.During the actual operation,ISDE seeks the optimal parameters arising from the evolutionary process,which enable ISDE to alter the algorithm for different optimization problems and improve the performance of ISDE by the control parameters' self-adaptation.The performance of the proposed method is studied with the use of nine benchmark problems and compared with original DE algorithm and other well-known self-adaptive DE algorithms.The experiments conducted show that the ISDE clearly outperforms the other DE algorithms in all benchmark functions.Furthermore,ISDE is applied to develop the kinetic model for homogeneous mercury(Hg) oxidation in flue gas,and satisfactory results are obtained.

Investigation of the optimum differential gear ratio for real driving cycles by experiment design and genetic algorithm

Experiment statistical method and genetic algorithms based optimization method are used to obtain the optimum differential gear ratio for heavy truck that provides best fuel consumption when changing the working condition that affects its torque and speed range. The aim of the study is to obtain the optimum differential gear ratio with fast and accurate optimization calculation without affecting drivability characteristics of the vehicle according to certain driving cycles that represent the new working conditions of the truck. The study is carried on a mining dump truck YT3621 with 9 for- ward shift manual transmission. Two loading conditions, no load and 40 t, and four on road real driving cycles have been discussed. The truck powertrain is modeled using GT-drive, and DOE -post processing tool of the GT-suite is used for DOE analysis and genetic algorithm optimization.

An Adaptive Differential Evolution Algorithm to Solve Constrained Optimization Problems in Engineering Design

Differential evolution (DE) algorithm has been shown to be a simple and efficient evolutionary algorithm for global optimization over continuous spaces, and has been widely used in both benchmark test functions and real-world applications. This paper introduces a novel mutation operator, without using the scaling factor F, a conventional control parameter, and this mutation can generate multiple trial vectors by incorporating different weighted values at each generation, which can make the best of the selected multiple parents to improve the probability of generating a better offspring. In addition, in order to enhance the capacity of adaptation, a new and adaptive control parameter, i.e. the crossover rate CR, is presented and when one variable is beyond its boundary, a repair rule is also applied in this paper. The proposed algorithm ADE is validated on several constrained engineering design optimization problems reported in the specialized literature. Compared with respect to algorithms representative of the state-of-the-art in the area, the experimental results show that ADE can obtain good solutions on a test set of constrained optimization problems in engineering design.

Chemical process dynamic optimization based on hybrid differential evolution algorithm integrated with Alopex

To solve dynamic optimization problem of chemical process (CPDOP), a hybrid differential evolution algorithm, which is integrated with Alopex and named as Alopex-DE, was proposed. In Alopex-DE, each original individual has its own symbiotic individual, which consists of control parameters. Differential evolution operator is applied for the original individuals to search the global optimization solution. Alopex algorithm is used to co-evolve the symbiotic individuals during the original individual evolution and enhance the fitness of the original individuals. Thus, control parameters are self-adaptively adjusted by Alopex to obtain the real-time optimum values for the original population. To illustrate the whole performance of Alopex-DE, several varietal DEs were applied to optimize 13 benchmark functions. The results show that the whole performance of Alopex-DE is the best. Further, Alopex-DE was applied to solve 4 typical CPDOPs, and the effect of the discrete time degree on the optimization solution was analyzed. The satisfactory result is obtained.

Differential evolution with controlled search direction

A novel and simple technique to control the search direction of the differential mutation was proposed.In order to verify the performance of this method,ten widely used benchmark functions were chosen and the results were compared with the original differential evolution(DE)algorithm.Experimental results indicate that the search direction controlled DE algorithm obtains better results than the original DE algorithm in term of the solution quality and convergence rate.

Parallel Implementations of Modeling Dynamical Systems by Using System of Ordinary Differential Equations

First, an asynchronous distributed parallel evolutionary modeling algorithm (PEMA) for building the model of system of ordinary differential equations for dynamical systems is proposed in this paper. Then a series of parallel experiments have been conducted to systematically test the influence of some important parallel control parameters on the performance of the algorithm. A lot of experimental results are obtained and we make some analysis and explanations to them.

An Improved Differential Evolution and Its Industrial Application

In this paper, an improved Differential Evolution (DE) that incorporates double wavelet-based operations is proposed to solve the Economic Load Dispatch (ELD) problem. The double wavelet mutations are applied in order to enhance DE in exploring the solution space more effectively for better solution quality and stability. The first stage of wavelet operation is embedded in the DE mutation operation, in which the scaling factor is governed by a wavelet function. In the second stage, a wavelet-based mutation operation is embedded in the DE crossover operation. The trial population vectors are modified by the wavelet function. A suite of benchmark test functions is employed to evaluate the performance of the proposed DE in different problems. The result shows empirically that the proposed method out-performs signifycantly the conventional methods in terms of convergence speed, solution quality and solution stability. Then the proposed method is applied to the Economic Load Dispatch with Valve-Point Loading (ELD-VPL) problem, which is a process to share the power demand among the online generators in a power system for minimum fuel cost. Two different conditions of the ELD problem have been tested in this paper. It is observed that the proposed method gives satisfactory optimal costs when compared with the other techniques in the literature.

Differential Evolution Using Opposite Point for Global Numerical Optimization

The Differential Evolution (DE) algorithm is arguably one of the most powerful stochastic optimization algorithms, which has been widely applied in various fields. Global numerical optimization is a very important and extremely dif-ficult task in optimization domain, and it is also a great need for many practical applications. This paper proposes an opposition-based DE algorithm for global numerical optimization, which is called GNO2DE. In GNO2DE, firstly, the opposite point method is employed to utilize the existing search space to improve the convergence speed. Secondly, two candidate DE strategies “DE/rand/1/bin” and “DE/current to best/2/bin” are randomly chosen to make the most of their respective advantages to enhance the search ability. In order to reduce the number of control parameters, this algorithm uses an adaptive crossover rate dynamically tuned during the evolutionary process. Finally, it is validated on a set of benchmark test functions for global numerical optimization. Compared with several existing algorithms, the performance of GNO2DE is superior to or not worse than that of these algorithms in terms of final accuracy, convergence speed, and robustness. In addition, we also especially compare the opposition-based DE algorithm with the DE algorithm without using the opposite point method, and the DE algorithm using “DE/rand/1/bin” or “DE/current to best/2/bin”, respectively.

Evolution Performance of Symbolic Radial Basis Function Neural Network by Using Evolutionary Algorithms

Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.

烘丝筒出口叶丝含水率预测模型研究

烘丝的最佳工艺参数难以确认,且叶丝含水率预测误差较大。为了在信息技术方面辅助提升烟草成品质量,研究基于极限学习机(ELM)的烘丝筒出口叶丝含水率预测模型。选取叶丝烘丝过程中松散回潮、预混柜、润叶加料等工艺阶段环境温度、湿度、加水比例等工艺参数。通过随机森林方法,将处理后有效数据中的各烘丝工艺参数以平均精准度逐渐减少顺序进行重新排序,筛选出对烘丝筒叶丝含水率预测作用较大的烘丝工艺参数。将筛选后的烘丝工艺参数作为ELM的输入数据,获取叶丝含水率预测结果。以含水率预测平均绝对误差最小为差分进化算法的适应度函数,优化ELM的隐含层神经元数量,提升烘丝筒出口叶丝含水率预测精度。试验结果表明,该模型可实现烘丝筒出口叶丝含水率预测,且预测误差小于0.3%,预测精度高。该研究有助于提升烟草质量。

混合整数优化问题的差分进化算法研究

为求解混合整数优化问题,提出了混合整数差分进化算法(Mixed Integer Differential Evolution,MIDE)。该算法结合整数变量的特点,为整数类型变量设计了专用的变异算子,使整数变量可以在差分进化算法中直接进化;为了维持种群多样性,采用了灾变策略;采用双编码方式,使整数变量与连续变量并行进化,进而提出了混合整数差分进化算法。通过与其它混合整数优化算法的比较,证明该算法具有较好的收敛速度、全局收敛性及算法稳定性等优点。

平面并联机器人离线PID控制优化研究

为了使平面并联机器人在闭环控制系统中具有更稳定的控制性能。对此,这里构建了平面五杆并联机器人动力学模型及其控制系统模型,给出了控制系统的增益矢量p。对机器人系统模型进行离线PID控制优化,通过控制增益来设计控制系统中的增益矢量p,从而实现非线性单目标动态优化(NLMODOP)。在NLMODOP中加入动态约束,采用带约束处理机制的差分进化(DE)算法求解平面并联机器人的非线性规划问题,进而处理不稳定的动态优化。对机器人模型中的五个连杆进行仿真实验,并对有无DE算法控制的仿真结果进行了比较。结果表明:相比于无DE算法,采用DE算法下的机器人系统模型的连杆跟踪位移基本无跟踪误差。说明基于差分进化算法的平面并联机器人离线PID控制优化具有较好的控制精度和跟踪性能。

基于无人机遥感影像的滑坡形态变形特征:以陇南白龙江流域泻流坡滑坡为例

2020年8—9月陇南白龙江流域泻流坡滑坡持续发生变形,严重威胁坡脚居民生命财产安全。以泻流坡滑坡为研究对象,基于高分辨率无人机影像提取了泻流坡滑坡滑动前后的正射影像和数字地表模型,利用COSI-Corr软件对滑动前后的两期影像进行相关性分析,计算得到滑坡表面特征点的偏移量信息,并通过DSM(digital surface model)的方法获取垂直向的变化量,最后对泻流坡滑坡的运动和物质变化进行了解译和分析,探讨了中高山峡谷区堆积层滑坡形成演化过程及破坏机制。研究结果表明:泻流坡滑坡变形区主要为滑源区左侧中下部和右侧次级滑坡,垂向最下滑移量5.89 m,平均水平位移6.24 m,滑源区近42%区域发生了形变;2020年6—9月,泻流坡滑坡滑动体积33 871 m3,堆积体积10 215 m3,降雨侵蚀体积23 656 m3;破坏模式为倾倒拉裂-蠕滑复合型滑坡。无人机高精度数据不仅可以清楚直观地识别滑坡形变破坏迹象,还可以进行地表垂直位移、水平位移、体积变化及滑动前后剖面的计算,为抢险救灾、科学决策提供了重要依据,具有广阔的应用前景。

基于进化集成学习的用户购买意向预测

在电子商务时代背景下,精准预测用户的购买意向已经成为提高销售效率和优化客户体验的关键因素。针对传统集成策略在模型设计阶段往往受人为因素限制的问题,构建了一种自适应进化集成学习模型用于预测用户的购买意向。该模型能够自适应地选择最优基学习器和元学习器,并融合基学习器的预测信息和特征间的差异性扩展特征维度,从而提高预测的准确性。此外,为进一步优化模型的预测效果,设计了一种二元自适应差分进化算法进行特征选择,旨在筛选出对预测结果有显著影响的特征。研究结果表明,与传统优化算法相比,二元自适应差分进化算法在全局搜索和特征选择方面表现优异。相较于六种常见的集成模型和DeepForest模型,所构建的进化集成模型在AUC值上分别提高了2.76%和2.72%,并且能够缓解数据不平衡所带来的影响。

基于差分进化粒子群混合算法的多无人机协同区域搜索策略

为提高无人机群在未知环境中的区域搜索效率,提出一种多无人机协同区域搜索策略。首先,根据区域搜索任务需求,建立包含区域覆盖率、区域不确定度、目标存在概率三种属性的区域信息地图;其次,以最大化搜索效率、同时最小化无人机搜索过程中的能耗为目标,建立无人机区域搜索滚动时域优化目标函数,指导无人机在线决策搜索路线;然后针对传统群智能优化算法易陷入局部最优的缺陷,设计差分进化粒子群混合算法在线求解该多目标优化问题,提高算法的寻优性能,从而提高无人机的搜索效率。最后,通过数值仿真实验,对所提算法进行验证,仿真结果表明,文中设计的基于差分进化粒子群混合算法的多无人机协同区域搜索策略与传统的群智能优化算法相比具有更高的区域搜索效率。

分布式数据驱动的多约束进化优化算法

泛在计算模式下,数据分布式获取和处理带来了分布式数据驱动优化的需求。针对数据分布获取、约束异步评估且信息缺失的挑战,构建分布式数据驱动的多约束进化优化算法(DDDEA)框架,由一系列终端节点负责数据提供和分布式评估,服务器节点负责全局进化优化。基于该框架具体实现了一个算法实例,终端节点利用局部数据构建径向基函数(RBF)模型,辅助驱动服务器节点差分进化(DE)算法对问题进行寻优。通过与3个集中式数据驱动的多约束进化优化算法在两个标准测试集的实验对比,DDDEA在68.4%的测试用例中取得显著最优结果,在84.2%的测试用例中找到可行解的成功率为1.00,表明该算法具有良好的全局搜索能力和收敛能力。