基于混合双种群差分进化的电力系统经济负荷分配

针对电力系统经济负荷分配本质上的非线性约束优化问题,提出一种双种群混合差分进化算法．采用两个种群且以较小的计算量实现目标函数的寻优并保持解的可行性,同时引入单纯型法来提高算法的局部搜索能力．基于典型算例对该算法的进化行为进行测试,并通过仿真和比较验证了所提出算法的有效性．

     

基于快速自适应差分进化算法的电力系统经济负荷分配

提出一种求解复杂电力系统经济负荷分配问题的快速自适应差分进化算法(FSADE).从矢量运算角度对变异算子进行分析,提出了一种改进的变异算子,大大提高了算法的收敛速率.根据个体的进化过程,引入自学习机制,对个体的变异和交叉概率常数进行自适应地调整,提高了算法的鲁棒性.3个不同规模的算例仿真结果表明,与其他4种典型智能优化算法相比, FSADE具有更好的计算精度和计算速度,是一种求解电力系统经济负荷分配问题的有效方法.     

基于差分蜂群算法的电力系统经济负荷分配

针对电力系统经济负荷分配问题,提出一种有效的差分蜂群算法．受差分进化算法的启发,该算法基于差分进化操作改进了雇佣蜂的搜索方式,提高了探索能力和收敛速度．此外,提出一种有效的修复机制以保证新个体的可行性．该算法在带有阀点效应和多燃料特征的典型电力系统经济负荷分配问题上进行了测试．仿真结果验证了所提算法的有效性．     

基于双种群的小生境差分进化算法

将非线性方程组的求解问题转化为函数优化问题,当方程组有多个解时,它的适应值函数就是具有多个最优解的多峰函数.为此,提出了基于双种群的小生境差分进化算法.在该算法中,进化在两个不同的子群间并行进行,通过使用不同的变异策略,实现种群在解空间具有尽可能分散的探索能力的同时在局部具有尽可能细致的搜索能力.通过子群重组实现子群间的信息交换,然后引入小生境淘汰机制.对典型测试函数的优化结果表明,该算法能找到全部解,而且精度好.     

基于改进差分进化鲸鱼算法的经济负荷分配

针对电力系统经济负荷分配这一典型的非凸、非线性、组合优化问题,提出一种将改进差分进化算法和鲸鱼算法相结合的优化算法。该算法首先在鲸鱼优化算法中引入了非线性的收敛变化策略,加速寻优算法的迭代;再利用差分进化算法的交叉和选择,丰富算法种群个体信息,增强优化算法的全局收敛性;同时引入一种淘汰机制,将适应度较好的个体信息更快地保留用于下一次鲸鱼优化算法的迭代,提高了求最优解的速度和精度;最后,对多个经济负荷分配问题进行了测试,将该算法与标准鲸鱼算法、标准差分进化算法进行对比,验证了差分进化鲸鱼算法可以更合理地配置电力系统的经济负荷,能够有效找到可行解,避免陷入局部最优,能实现经济负荷的合理分配。     

基于交叉变异策略的双种群差分进化算法

为加强差分进化算法的全局搜索能力,提出了一种基于交叉变异策略的双种群差分进化算法（CMDPDE）。CMDPDE中,两个种群分别采用大小不同的缩放因子和交叉因子,在每代进化完毕后,对其中缩放因子和交叉因子较小的种群执行交叉或变异策略来寻找更优的个体,同时两个种群之间每10代进行一次信息交流。这种方式与单种群差分进化算法相比,可以通过双种群和交叉变异策略来增加解的多样性,使算法能在更大的范围内寻优。6个Benchmark函数的实验结果证明CMDPDE具有较好的寻优能力。     

双种群差分进化规划算法

标准差分进化算法（SDE）具有算法简单,控制参数少,易于实现等优点。但在难优化问题中,算法存在收敛速度较慢和容易早熟等缺陷。为克服此缺点,提出一种改进算法--双种群差分进化规划算法（BGDEP）。该算法将种群划分为两个子群独立进化,分别采用DE/rand/1/bin和DE/best/2/bin版本生成变异个体。每隔δt（取5~10）代,将两个子群合并为一个种群,再应用混沌重组算子将之划分为两个子群,以实现子群间的信息交流。在双种群协同差分进化的同时,应用非均匀变异算子对其最优个体执行进化规划操作,使得算法具有较快的收敛速度和较强的全局寻优能力。为测试BGDEP的性能,给出了4个30维benchmark函数优化问题的对比数值实验。结果表明,BGDEP的求解精度、收敛速度、鲁棒性等性能优于SDE、双种群差分进化（BGDE）和非均匀变异进化规划（NUMEP）等4种算法。     

双种群进化模型的电力负荷预测

传统灰色预测模型GM（1,1）在预测增长较快的电力负荷时效果会变差。针对这一缺陷,提出了一种改进的双种群ESOGM模型,将进化策略对参数优化处理的优点与GM（1,1）模型相结合,利用进化策略算法优化模型中的参数。电力负荷预测实例表明该模型具有较高的预测精度和较广的应用范围。     

基于双种群两阶段变异策略的差分进化算法

针对差分进化算法差分策略优化问题上的不足, 解决DE/best/1策略全局探测能力差, DE/rand/1局部搜索能力弱而带来的鲁棒性降低及陷入局部最优等问题, 本文在差分策略上进行改进, 并且加入邻域分治思想提高进化效率, 提出一种基于双种群两阶段变异策略的差分进化算法(TPSDE). 第一个阶段利用DE/best/1的优势对邻域向量划分完成的子种群区域进行局部优化, 第二个阶段借鉴DE/rand/1的思想实现全局优化, 最终两阶段向量加权得到最终变异个体使得算法避免了过早收敛和搜索停滞等问题的出现. 6个测试函数的仿真实验结果表明TPSDE在收敛速度、优化精度和鲁棒性方面都得到了明显改善.     

多目标差分进化在热连轧负荷分配中的应用

提出一种基于差分进化算法的多目标进化算法, 该算法个体的选择是通过非支配排序和拥挤度距离进行综合考虑. 保证了算法收敛到Pareto最优解集的同时, 提高了最优解个体分布的多样性. 通过与非支配排序遗传算法Ⅱ(NSGA Ⅱ)算法进行仿真对比, 结果显示基于拥挤度排序的多目标差分进化算法在收敛性和Pareto最优解集分布的多样性上均优于NSGA Ⅱ算法. 最后将其引入到热连轧负荷分配优化计算中, 给出了目标函数的表达方式, 对多目标进化算法在热连轧负荷分配计算中的应用进行了研究.     

Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems

Economic Load Dispatch (ELD) is an important and difficult optimization problem in power system planning. This article aims at addressing two practically important issues related to ELD optimization: (1) analyzing the ELD problem from the perspective of evolutionary optimization; (2) developing effective algorithms for ELD problems of large scale. The first issue is addressed by investigating the fitness landscape of ELD problems with the purpose of estimating the expected performance of different approaches. To address the second issue, a new algorithm named “Estimation of Distribution and Differential Evolution Cooperation” (ED-DE) is proposed, which is a serial hybrid of two effective evolutionary computation (EC) techniques: estimation of distribution and differential evolution. The advantages of ED-DE over the previous ELD optimization algorithms are experimentally testified on ELD problems with the number of generators scaling from 10 to 160. The best solution records of classical 13 and 40-generator ELD problems with valve points, and the best solution records of 10, 20, 40, 80 and 160-generator ELD problems with both valve points and multiple fuels are updated in this work. To further evaluate the efficiency and effectiveness of ED-DE, we also compare it with other state-of-the-art evolutionary algorithms (EAs) on typical function optimization tasks.     

Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems

Evolutionary algorithms (EAs) are general-purpose stochastic search methods that use the metaphor of evolution as the key element in the design and implementation of computer-based problems solving systems. During the past two decades, EAs have attracted much attention and wide applications in a variety of fields, especially for optimization and design. EAs offer a number of advantages: robust and reliable performance, global search capability, little or no information requirement, and others. Among various EAs, differential evolution (DE), which characterized by the different mutation operator and competition strategy from the other EAs, has shown great promise in many numerical benchmark problems and real-world optimization applications. The potentialities of DE are its simple structure, easy use, convergence speed and robustness. To improve the global optimization property of DE, in this paper, a DE approach based on measure of population's diversity and cultural algorithm technique using normative and situational knowledge sources is proposed as alternative method to solving the economic load dispatch problems of thermal generators. The traditional and cultural DE approaches are validated for two test systems consisting of 13 and 40 thermal generators whose nonsmooth fuel cost function takes into account the valve-point loading effects. Simulation results indicate that performance of the cultural DE present best results when compared with previous optimization approaches in solving economic load dispatch problems.     

Chaotic differential evolution methods for dynamic economic dispatch with valve-point effects

The dynamic economic dispatch (DED), with the consideration of valve-point effects, is a complicated non-linear constrained optimization problem with non-smooth and non-convex characteristics. In this paper, three chaotic differential evolution (CDE) methods are proposed based on the Tent equation to solve DED problem with valve-point effects. In the proposed methods, chaotic sequences are applied to obtain the dynamic parameter settings in DE. Meanwhile, a chaotic local search (CLS) operation for solving DED problem is designed to help DE avoiding premature convergence effectively. Finally, in order to handle the complicated constraints with efficiency, new heuristic constraints handling methods and feasibility based selection strategy are embedded into the proposed CDE methods. The feasibility and effectiveness of the proposed CDE methods are demonstrated for two test systems. The simulation results reveal that, compared with DE and those other methods reported in literatures recently, the proposed CDE methods are capable of obtaining better quality solutions with higher efficiency.     

基于改进遗传算法的电力系统经济负荷分配

针对电力系统经济负荷分配问题,分析了遗传算法与传统数学优化方法的不同优势与特性,提出一种求解电力系统经济负荷分配问题的改进遗传算法.利用极大熵理论将经济负荷分配问题转化为可微问题,将BFGS法引入遗传算法,提出了BFGS算子,以提高遗传算法的寻优速度与局部搜索能力.同时,应用单纯形交叉算子将种群逐步向最优点进行引导,实现算法的快速寻优.实例研究结果验证了所提出方法的有效性.     

基于协同差分进化的多出救点应急物资调度

主要利用差分进化算法来研究时间约束下的多出救点应急物资调度优化问题。针对传统差分进化算法搜索速度慢、易陷入局部最优解的缺点,提出一个并行协同差分进化算法,将该算法应用于时间约束下的多出救点应急物资调度优化,建立相应的数学模型,在此基础上设计相应的算法。实例验证表明,同遗传算法、标准差分进化算法相比,该算法在解决具有时间约束的多出救点应急物资调度优化问题方面具有较快的搜索速度和较好的寻优能力。     

Multiagent based differential evolution approach to optimal power flow

This paper proposes a new differential evolution approach named as multiagent based differential evolution (MADE) based on multiagent systems, for solving optimal power flow problem with non-smooth and non-convex generator fuel cost curves. This method integrates multiagent systems (MAS) and differential evolution (DE) algorithm. An agent in MADE represents an individual to DE and a candidate solution to the optimization problem. All agents live in a lattice like environment, with each agent fixed on a lattice point. In order to obtain optimal solution quickly, each agent competes and cooperates with its neighbors and it can also use knowledge. Making use of these agent-agent interaction and DE mechanism, MADE realizes the purpose of minimizing the value of objective function. MADE applied to optimal power flow is evaluated on 6 bus system and IEEE 30 bus system with different generator characteristics. Simulation results show that the proposed method converges to better solutions much faster than earlier reported approaches.     

Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch

This paper proposes an improved multi-objective differential evolutionary algorithm named multi-objective hybrid differential evolution with simulated annealing technique (MOHDE-SAT) to solve dynamic economic emission dispatch (DEED) problem. The proposed MOHDE-SAT integrates the orthogonal initialization method into the differential evolution, which enlarges the population diversity at the beginning of population evolution. In addition, modified mutation operator and archive retention mechanisms are used to control convergence rate, and simulated annealing technique and entropy diversity method are utilized to adaptively monitor the population diversity as the evolution proceeds, which can properly avoid the premature convergence problem. Furthermore, the MOHDE-SAT is applied on the thermal system with a heuristic constraint handling method, and obtains more desirable results in comparison to those alternatives established recently. The obtained results also reveal that the proposed MOHDE-SAT can provide a viable way for solving DEED problems.     

A hybrid differential evolution approach based on surrogate modelling for scheduling bottleneck stages

Surrogate modelling based optimization has attracted much attention due to its ability of solving expensive-to-evaluate optimization problems, and a large majority of successful applications from various fields have been reported in literature. However, little effort has been devoted to solve scheduling problems through surrogate modelling, since evaluation for a given complete schedule of these complex problems is computationally cheap in most cases. In this paper, we develop a hybrid approach for solving the bottleneck stage scheduling problem (BSP) using the surrogate modelling technique. In our approach, we firstly transform the original problem into an expensive-to-evaluate optimization problem by cutting the original schedule into two partial schedules using decomposition, then a surrogate model is introduced to, quickly but crudely, evaluate a given partial schedule. Based on the surrogate model, we propose a differential evolution (DE) algorithm for solving BSPs in which a novel mechanism is developed to efficiently utilize the advantage of the surrogate model to enhance the performance of DE. Also, an improved adaptive proximity-based method is introduced to balance the exploration and exploitation during the evolutionary process of DE. Considering that data for training the surrogate model is generated at different iteration of DE, we adopt an incremental extreme learning machine as the surrogate model to reduce the computational cost while preserving good generalization performance. Extensive computational experiments demonstrate that significant improvements have been obtained by the proposed surrogate-modelling based approach.     

基于两种进化模式的双种群协作差分演化算法

提出了一种基于两种进化模式的双种群协作差分演化算法（DPDE）。在DPDE中,两个种群通过协作共同进化。首先,各种群以不同的进化模式,通过个体竞争实现自身进化;其次,种群之间基于局部信息传递和共享机制,通过随机交换个体方式相互协作、共同进化,既实现了不同进化模式间的优势互补,又可以改善种群的多样性。对于5个典型Benchmark测试函数,通过与DE和DEfirDE算法的比较表明：DPDE具有更好的全局收敛性和鲁棒性,特别适合求解高维多模态函数的最优化问题。     

Colonial competitive differential evolution: An experimental study for optimal economic load dispatch

Differential evolution (DE) algorithm is a population-based algorithm designed for global optimization of the optimization problems. This paper proposes a different DE algorithm based on mathematical modeling of socio-political evolution which is called Colonial Competitive Differential Evolution (CCDE). The two typical CCDE algorithms are benchmarked on three well-known test functions, and the results are verified by a comparative study with two original DE algorithms which include DE/best/1 and DE/rand/2. Also, the effectiveness of CCDE algorithms is tested on Economic Load Dispatch (ELD) problem including 10, 15, 40, and 140-unit test systems. In this study, the constraints and operational limitations, such as valve-point loading, transmission losses, ramp rate limits, and prohibited operating zones are considered. The comparative results show that the CCDE algorithms have good performance and are reliable tools in solving ELD problem.