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.

Efficient AUV Path Planning in Time-Variant Underwater Environment Using Differential Evolution Algorithm

Robust and efficient AUV path planning is a key element for persistence AUV maneuvering in variable underwater environments. To develop such a path planning system, in this study, differential evolution(DE) algorithm is employed. The performance of the DE-based planner in generating time-efficient paths to direct the AUV from its initial conditions to the target of interest is investigated within a complexed 3D underwater environment incorporated with turbulent current vector fields, coastal area,islands, and static/dynamic obstacles. The results of simulations indicate the inherent efficiency of the DE-based path planner as it is capable of extracting feasible areas of a real map to determine the allowed spaces for the vehicle deployment while coping undesired current disturbances, exploiting desirable currents, and avoiding collision boundaries in directing the vehicle to its destination. The results are implementable for a realistic scenario and on-board real AUV as the DE planner satisfies all vehicular and environmental constraints while minimizing the travel time/distance, in a computationally efficient manner.

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.

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.

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.

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.

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.

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.

Hybrid Improved Self-adaptive Differential Evolution and Nelder-Mead Simplex Method for Solving Constrained Real-Parameters

In this paper, a new hybrid algorithm based on exploration power of a new improvement self-adaptive strategy for controlling parameters in DE （differential evolution） algorithm and exploitation capability of Nelder-Mead simplex method is presented （HISADE-NMS）. The DE has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters as number of particles （NP）, scaling factor （F） and crossover control （CR）, which are kept fixed throughout the entire evolutionary process. However, these control parameters are very sensitive to the setting of the control parameters based on their experiments. The value of control parameters depends on the characteristics of each objective function, therefore, we have to tune their value in each problem that mean it will take too long time to perform. In the new manner, we present a new version of the DE algorithm for obtaining self-adaptive control parameter settings. Some modifications are imposed on DE to improve its capability and efficiency while being hybridized with Nelder-Mead simplex method. To valid the robustness of new hybrid algorithm, we apply it to solve some examples of structural optimization constraints.

Biological Network Modeling Based on Hill Function and Hybrid Evolutionary Algorithm

Gene regulatory network inference helps understand the regulatory mechanism among genes, predict the functions of unknown genes, comprehend the pathogenesis of disease and speed up drug development. In this paper, a Hill function-based ordinary differential equation (ODE) model is proposed to infer gene regulatory network (GRN). A hybrid evolutionary algorithm based on binary grey wolf optimization (BGWO) and grey wolf optimization (GWO) is proposed to identify the structure and parameters of the Hill function-based model. In order to restrict the search space and eliminate the redundant regulatory relationships, L1 regularizer was added to the fitness function. SOS repair network was used to test the proposed method. The experimental results show that this method can infer gene regulatory network more accurately than state of the art methods.

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。

基于模糊需求和模糊运输时间的多式联运路径优化

考虑不确定性的模糊多式联运路径优化研究,可以在满足运输方案经济环保双重要求的同时,增强运输方案的鲁棒性,提高企业的抗风险能力.本文建立了模糊需求和模糊运输时间下低碳低成本多式联运路径优化模型,针对连续型元启发式算法无法直接求解离散型组合优化模型的问题,设计了基于优先级的通用编码方式.在此基础上,为进一步提高算法的求解质量,提出了带启发式因子的特殊解码方式,并且提出了一种带邻域搜索策略的自适应差分进化算法.结果表明,改进算法获得的最终方案在蒙特卡罗采样的大多数场景下满足约束,方案稳定性强,目标值最低.

基于SPADE算法的梯级水库群联合防洪优化调度

针对梯级水库群联合防洪优化调度问题,提出一种基于自适应成功历史策略的改进差分进化算法(strategy and parameter adaptive differential evolution,SPADE)。该算法通过自适应成功历史差分策略来提升随机搜索效率,通过精英种群保守策略提升局部收敛速度及全局探索能力。据此开展包含10个测试函数的数值实验和赣江中游梯级水库群联合防洪优化调度实例,用于检验所提出的算法应用效果。结果表明:在数值实验中,SPADE算法收敛结果的最优值、平均值、标准差和成功次数评价指标整体优于SHADE、自适应差分进化算法(self-adaptive differential evolution,SADE)、遗传算法(genetic algorithm,GA)、粒子群算法(particle swarm optimization,PSO)、人工蜂群算法(artificial bee colony,ABC);在梯级水库群联合防洪优化调度实例应用中,通过对1964单峰和1973多峰型历史洪水过程进行分析,发现SPADE算法结果在削峰率指标上明显优于SADE、GA、PSO算法,且相比SHADE在两次历史洪水条件下的削峰率指标结果分别提升0.9%、3.4%。实验结果充分验证所提SPADE算法的优越性,可作为梯级水库群联合优化调度问题的有效求解工具。

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。

基于鲁棒优化的冷热电联供型微网混合储能经济配置

为解决源荷双侧不确定性对冷热电联供CCHP(combined cooling,heating and power)型微网经济运行带来的电量实时平衡问题,提出一种基于鲁棒理论的CCHP微网电、热、冷混合储能容量配置模型。基于鲁棒理论,建立源荷双侧不确定性变量合集。考虑储能设备日折算成本,以微网运行成本最低为目标,采用自适应差分进化算法对模型进行求解,得到不同预测精度与置信概率下的微网储能最优容量合集。通过设置评价指标,选取最合适的储能配置方案,对微网配置储能前后的调度情况作对比。结果表明,基于鲁棒理论配置的电、热、冷这3类储能可有效提升微网在源荷双侧不确定下的电力电量实时平衡能力与运行经济性。

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。