Modified Differential Evolution Algorithm for Solving Dynamic Optimization with Existence of Infeasible Environments

Dynamic constrained optimization is a challenging research topic in which the objective function and/or constraints change over time.In such problems,it is commonly assumed that all problem instances are feasible.In reality some instances can be infeasible due to various practical issues,such as a sudden change in resource requirements or a big change in the availability of resources.Decision-makers have to determine whether a particular instance is feasible or not,as infeasible instances cannot be solved as there are no solutions to implement.In this case,locating the nearest feasible solution would be valuable information for the decision-makers.In this paper,a differential evolution algorithm is proposed for solving dynamic constrained problems that learns from past environments and transfers important knowledge from them to use in solving the current instance and includes a mechanism for suggesting a good feasible solution when an instance is infeasible.To judge the performance of the proposed algorithm,13 well-known dynamic test problems were solved.The results indicate that the proposed algorithm outperforms existing recent algorithms with a margin of 79.40%over all the environments and it can also find a good,but infeasible solution,when an instance is infeasible.

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.

Novel Control Vector Parameterization Method with Differential Evolution Algorithm and Its Application in Dynamic Optimization of Chemical Processes

Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution （DE） algorithm and control vector parameteri- zation （CVP） is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the oroposed methods.

Harmony search algorithm with differential evolution based control parameter co-evolution and its application in chemical process dynamic optimization

A modified harmony search algorithm with co-evolutional control parameters(DEHS), applied through differential evolution optimization, is proposed. In DEHS, two control parameters, i.e., harmony memory considering rate and pitch adjusting rate, are encoded as a symbiotic individual of an original individual(i.e., harmony vector). Harmony search operators are applied to evolving the original population. DE is applied to co-evolving the symbiotic population based on feedback information from the original population. Thus, with the evolution of the original population in DEHS, the symbiotic population is dynamically and self-adaptively adjusted, and real-time optimum control parameters are obtained. The proposed DEHS algorithm has been applied to various benchmark functions and two typical dynamic optimization problems. The experimental results show that the performance of the proposed algorithm is better than that of other HS variants. Satisfactory results are obtained in the application.

Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms

Dynamic optimization problems(DOPs) described by differential equations are often encountered in chemical engineering. Deterministic techniques based on mathematic programming become invalid when the models are non-differentiable or explicit mathematical descriptions do not exist. Recently, evolutionary algorithms are gaining popularity for DOPs as they can be used as robust alternatives when the deterministic techniques are invalid. In this article, a technology named ranking-based mutation operator(RMO) is presented to enhance the previous differential evolution(DE) algorithms to solve DOPs using control vector parameterization. In the RMO, better individuals have higher probabilities to produce offspring, which is helpful for the performance enhancement of DE algorithms. Three DE-RMO algorithms are designed by incorporating the RMO. The three DE-RMO algorithms and their three original DE algorithms are applied to solve four constrained DOPs from the literature. Our simulation results indicate that DE-RMO algorithms exhibit better performance than previous non-ranking DE algorithms and other four evolutionary algorithms.

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

An immune system based differential evolution algorithm using near-neighbor effect in dynamic environments

Many real-world problems are dynamic, requiring optimization algorithms being able to continuously track changing optima （optimum） over time. This paper proposes an improved differential evolutionary algorithm using the notion of the near-neighbor effect to determine one individuals neighborhoods, for tracking multiple optima in the dynamic environment. A new mutation strategy using the near-neighbor effect is also presented. It creates individuals by utilizing the stored memory point in its neighborhood, and utilizing the differential vector produced by the ＇near- neighbor-superior＇ and ＇near-neighbor-inferior＇. Taking inspirations from the biological immune system, an immune system based scheme is presented for rapidly detecting and responding to the environmental changes. In addition, a difference- related multidirectional amplification scheme is presented to integrate valuable information from different dimensions for effectively and rapidly finding the promising optimum in the search space. Experiments on dynamic scenarios created by the typical dynamic test instance--moving peak problem, have demonstrated that the near-neighbor and immune system based differential evolution algorithm （NIDE） is effective in dealing with dynamic optimization functions.

Dynamic Economic Dispatch for Wind Power System Considering System Security and Spinning Reserve

In this paper, dynamic economic dispatch model is proposed for power systems with bulk wind power integration. The wind turbine generators are assumed to partially undertake the spinning reserve for the thermal generator. A double-layer optimization model is proposed. The outer layer use the differential evolution to search for the power output of thermal generators, and the inner layer use the primal-dual interior point method to solve the OPF of the established output state. Finally, the impact of spinning reserve with wind power on power system operating is validated.

Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.

Dynamic reactive power planning method for CSP-PV hybrid power generation system

Aiming at the faults of some weak nodes in the concentrated solar power-photovoltaic(CSP-PV)hybrid power generation system,it is impossible to restore the transient voltage only relying on the reactive power regulation capability of the system itself.We propose a dynamic reactive power planning method suitable for CSP-PV hybrid power generation system.The method determines the installation node of the dynamic reactive power compensation device and its compensation capacity based on the reactive power adjustment capability of the system itself.The critical fault node is determined by the transient voltage stability recovery index,and the weak node of the system is initially determined.Based on this,the sensitivity index is used to determine the installation node of the dynamic reactive power compensation device.Dynamic reactive power planning optimization model is established with the lowest investment cost of dynamic reactive power compensation device and the improvement of system transient voltage stability.Furthermore,the component of the reactive power compensation node is optimized by particle swarm optimization based on differential evolution(DE-PSO).The simulation results of the example system show that compared with the dynamic position compensation device installation location optimization method,the proposed method can improve the transient voltage stability of the system under the same reactive power compensation cost.

Temporal Prediction of Aircraft Loss-of-Control: A Dynamic Optimization Approach

Loss of Control (LOC) is the primary factor responsible for the majority of fatal air accidents during past decade. LOC is characterized by the pilot’s inability to control the aircraft and is typically associated with unpredictable behavior, potentially leading to loss of the aircraft and life. In this work, the minimum time dynamic optimization problem to LOC is treated using Pontryagin’s Maximum Principle (PMP). The resulting two point boundary value problem is solved using stochastic shooting point methods via a differential evolution scheme (DE). The minimum time until LOC metric is computed for corresponding spatial control limits. Simulations are performed using a linearized longitudinal aircraft model to illustrate the concept.

应用差分进化-神经网络模型的杀爆弹瞄准点分配方法

为在不增加计算时耗的前提下提升多枚杀爆弹对面目标打击毁伤效能,建立融入动爆威力计算的多瞄准点规划方法.对面目标采用结构化网格划分方法实现多枚杀爆弹对目标毁伤区域的精确计算,并进行计算结果验证,基于多次计算结果采用神经网络方法建立单枚弹药对面目标毁伤区域的计算代理模型,在同样计算条件下,比非代理模型计算时间缩短1000倍;据此,通过差分进化算法实现多枚杀爆弹对面目标打击瞄准点及末端弹道参数的规划.通过实例对比分析表明:该瞄准点规划方法形成的打击方案比传统以毁伤半径为输入的方法毁伤效果大幅提升,最低提升25.5%,且单次规划时间不超过3 s,解决了瞄准点规划中毁伤效能模型复杂度与计算耗时之间的矛盾.

动态上下料路径下柔性产品族生产调度研究

针对汽车零部件柔性产品族制造单元考虑工序间动态上下料路径与时间的生产调度求解问题,文中提出一种用于动态上下料路径柔性作业调度问题优化的自适应离散差分进化算法。通过自适应缩放参数实现收敛速度提升,构建基于矩阵映射的离散编码规则实现变异操作离散化及基于机器人实际运动路径的动态调度解码。通过对某平台化车型架构的转向器壳体加工单元实例分析并验证了算法有效性及优越性。

基于生物入侵的特征选择算法

在自然界中,生物入侵以其发展的迅速和巨大的生态影响而受到关注,所引入种群对合适栖息地的寻找过程往往有其内在的逻辑,种群之间的交流和种群的扩张也在这个过程中起到了重要作用。通过探究种群对适宜栖息地的寻找原理,提出一种基于生物入侵的特征选择(BIAFS)算法。在BIAFS算法中,生物入侵过程分为种群建立、种群迁移、种群交流和扩张、种群发展4个阶段。在实验验证过程中,在9个数据集上将BIAFS算法与8种高性能算法进行实验比较。实验结果显示,BIAFS算法在7个数据集上的分类准确率(CA)和降维(DR)率均超过了对比算法。此外,适应度标准偏差的比较实验也证实了BIAFS算法的高稳定性,表明其在多个数据集上能更加稳健地寻找最优解。上述实验结果证明了BIAFS算法在特征选择任务中的有效性和优越性。

基于改进差分进化算法的动态防空资源分配优化

面对动态防空资源分配问题中存在的空袭目标突现和雷达、发射车等资源受干扰现象,在综合考虑雷达、发射车和导弹等武器装备性能的基础上,基于目标集、资源集建立了最小化目标总拦截价值与生存概率的混合整数决策模型。提出了一种新的改进差分进化算法进行求解,采用反向学习策略生成初始解,确保初始种群的质量,设计了一种快速修复与重构的启发式规则作用于多阶段,以提升算法的搜索能力。仿真实验验证了该算法具有求解时间和求解精度上的优越性。该研究能使武器系统在动态事件的随机影响下,保持高效的作战能力和决策效果。

基于DDE改进蝙蝠算法的动态火力分配方法

针对动态火力分配算法耗时长,而传统的蝙蝠算法寻优精度不高等问题,提出了一种基于动态差分改进的蝙蝠算法。该算法首先通过放宽部分约束条件加快生成初始解,然后将动态差分进化算法中的差分变异机制融入到蝙蝠算法中,再利用惩罚函数确保生成的解满足约束条件,最后利用蝙蝠种群进行解的迭代寻优。仿真结果表明,与蝙蝠算法、遗传算法、粒子群算法相比,改进的算法有较高的收敛精度和较快的收敛速率,且更适合应用在较大规模的火力分配问题中。

Q学习差分进化算法求解热电动态经济排放调度

热电联产动态经济排放调度同时考虑了燃料成本花费和污染气体排放两个目标值,且下一时间段的热电产量受当前时间段热电产量的影响,这是近年来电力系统运行中的一个重要问题。文中提出一种基于Q学习强化多目标差分进化(Q Learning Multi-Objective Differential Evolution,QLMODE)算法,以此求解热电联产动态经济排放调度(Combined Heat and Power Dynamic Economic Emission Dispatch,CHPDEED)问题。在QLMODE中,采用Q学习技术调整算法的比例因子参数,即在迭代过程中利用子代解和父代解之间的支配关系确定动作奖励和惩罚,并通过Q学习调整参数值,以获得最适合环境模型的算法参数。文中将所提QLMODE用于求解11机组和33机组的热电联产动态经济排放调度问题。仿真结果表明,与4种成熟的多目标优化算法相比,QLMODE算法燃料成本最小,污染气体排放最少,收敛性和多样性指标优于其他4种算法,且QLMODE在两组问题上都获得了更好的Pareto最优前沿。

中国农业农村碳中和效应时空分异与动态演进特征

[目的]分析中国2000—2020年中国30个省(市、区)碳中和效应的变化特征和动态演进趋势,定量揭示农业农村生态环境特征和内在动因机理,为进一步推动中国农业农村“碳中和”进程提供理论依据。[方法]基于大农业视角,运用排放系数法选取37类碳源和28类碳汇指标,测算了中国2000—2020年21期30个省(市、区)农业农村碳中和效应,揭示其时空分布特征,并采用Kernel-Density方法观测其动态演进特征。[结果]①中国农业农村碳中和效应呈平稳上升趋势,年均递增2.79%,环比增速总体处于波动上升态势,其中碳汇增速明显快于碳排放增速。②中国农业农村碳中和效应空间分布不均衡程度明显增加,呈“中间低四周高”的分布格局,省域差异明显:排在前10位的省(市、区)占全国碳中和效应的66.42%,而排在后10位的省(市、区)仅占全国的4.72%。③碳中和效应水平呈现:中部地区>东部地区>西部地区的态势,各地区间存在较大差异,种植业是减排增汇的最大源头。④中国农业农村碳中和效应密度函数曲线中心整体向右偏移,各省(市、区)空间差距逐步扩大,存在区域发展不均衡的现象。[结论]低碳经济与现代农业相互交织,各地区应当因地制宜地制定农业农村领域碳中和发展规划,实现区域间碳中和协同机制,加速农业农村碳中和进程。

基于改进布谷鸟算法结合电导增量法的最大功率点追踪

动态遮阴下,光伏阵列的输出P-U曲线会出现多个功率极值点,传统最大功率点追踪会陷入局部最优。为此,提出基于自适应差分进化的改进布谷鸟搜索(improved cuckoo search,ICS)算法与电导增量法(incremental conductance,INC)相结合的复合算法(ICS-INC)。该算法在前期提出自适应的抛弃概率和随机步长因子,结合差分变异进行随机偏好游走,使算法的搜索开发能力得到提升,有效跳出局部最优。通过改进Lévy飞行公式减小其随机性,减小算法的迭代次数来缩短跟踪时间,实现快速高效定位最大功率点区域,在后期由INC实现局部快速搜索,稳定输出最大功率。在MATLAB/Simulink中建立了仿真模型,对多种算法进行实验,仿真结果表明该算法的追踪速度、全局搜索性以及环境变化的适应能力均得到提升。

改进猎人猎物优化算法在WSN覆盖中的应用

针对传统无线传感器网络(WSN)节点部署覆盖盲区大、分布不均等问题,提出一种改进的猎人猎物优化(IHPO)算法优化网络覆盖。首先,在猎物位置更新阶段,引入差分进化(DE)思想并借助动态比例因子进行交叉变异,从而增强种群信息交流;其次,在全局最优位置更新阶段,由α稳定分布提出自适应α变异对全局最优位置进行扰动,从而平衡不同时期算法的性能需求;最后,利用自适应α变异扰动的全局最优位置引导种群完成动态反向学习,从而增加种群的全局搜索能力和多样性。在WSN覆盖问题中,使用IHPO优化的网络节点分布更均匀、覆盖率更高,在传感器感知能力不足时能达到92.56%的覆盖率,对比原始HPO算法优化的节点提高了25.74%,对比改进粒子群优化(IPSO)算法、改进灰狼优化算法(IGWO)优化的节点分别提高了13.98%、16.41%。同时,IHPO算法优化的节点能耗更均衡,在路由测试中的网络工作时间可以延长至2500轮次。