GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-ⅡFOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION

Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

An Optimization Approach for Convolutional Neural Network Using Non-Dominated Sorted Genetic Algorithm-Ⅱ

In computer vision,convolutional neural networks have a wide range of uses.Images representmost of today’s data,so it’s important to know how to handle these large amounts of data efficiently.Convolutional neural networks have been shown to solve image processing problems effectively.However,when designing the network structure for a particular problem,you need to adjust the hyperparameters for higher accuracy.This technique is time consuming and requires a lot of work and domain knowledge.Designing a convolutional neural network architecture is a classic NP-hard optimization challenge.On the other hand,different datasets require different combinations of models or hyperparameters,which can be time consuming and inconvenient.Various approaches have been proposed to overcome this problem,such as grid search limited to low-dimensional space and queuing by random selection.To address this issue,we propose an evolutionary algorithm-based approach that dynamically enhances the structure of Convolution Neural Networks(CNNs)using optimized hyperparameters.This study proposes a method using Non-dominated sorted genetic algorithms(NSGA)to improve the hyperparameters of the CNN model.In addition,different types and parameter ranges of existing genetic algorithms are used.Acomparative study was conducted with various state-of-the-art methodologies and algorithms.Experiments have shown that our proposed approach is superior to previous methods in terms of classification accuracy,and the results are published in modern computing literature.

Planning of DC Electric Spring with Particle Swarm Optimization and Elitist Non-dominated Sorting Genetic Algorithm

This paper addresses the planning problem of parallel DC electric springs (DCESs). DCES, a demand-side management method, realizes automatic matching of power consumption and power generation by adjusting non-critical load (NCL) and internal storage. It can offer higher power quality to critical load (CL), reduce power imbalance and relieve pressure on energy storage systems (RESs). In this paper, a planning method for parallel DCESs is proposed to maximize stability gain, economic benefits, and penetration of RESs. The planning model is a master optimization with sub-optimization to highlight the priority of objectives. Master optimization is used to improve stability of the network, and sub-optimization aims to improve economic benefit and allowable penetration of RESs. This issue is a multivariable nonlinear mixed integer problem, requiring huge calculations by using common solvers. Therefore, particle Swarm optimization (PSO) and Elitist non-dominated sorting genetic algorithm (NSGA-II) were used to solve this model. Considering uncertainty of RESs, this paper verifies effectiveness of the proposed planning method on IEEE 33-bus system based on deterministic scenarios obtained by scenario analysis.

Suspended sediment load prediction using non-dominated sorting genetic algorithm Ⅱ

Awareness of suspended sediment load (SSL) and its continuous monitoring plays an important role in soil erosion studies and watershed management.Despite the common use of the conventional model of the sediment rating curve (SRC) and the methods proposed to correct it,the results of this model are still not sufficiently accurate.In this study,in order to increase the efficiency of SRC model,a multi-objective optimization approach is proposed using the Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) algorithm.The instantaneous flow discharge and SSL data from the Ramian hydrometric station on the Ghorichay River,Iran are used as a case study.In the first part of the study,using self-organizing map (SOM),an unsupervised artificial neural network,the data were clustered and classified as two homogeneous groups as 70% and 30% for use in calibration and evaluation of SRC models,respectively.In the second part of the study,two different groups of SRC model comprised of conventional SRC models and optimized models (single and multi-objective optimization algorithms) were extracted from calibration data set and their performance was evaluated.The comparative analysis of the results revealed that the optimal SRC model achieved through NSGA-Ⅱ algorithm was superior to the SRC models in the daily SSL estimation for the data used in this study.Given that the use of the SRC model is common,the proposed model in this study can increase the efficiency of this regression model.

Optimization of dynamic aperture by using non-dominated sorting genetic algorithm-Ⅱ in a diffraction-limited storage ring with solenoids for generating round beam

Purpose Round beam,i.e.,with equal horizontal and vertical emittance,is preferable than a horizontally flat one for some beamline applications in Diffraction-limited storage rings(DLSRs),for the purposes of reducing the number of photons getting discarded and better phase space match between photon and electron beam.Conventional methods of obtaining round beam inescapably results in a reduction of dynamic aperture(DA).In order to recover the DA as much as possible for improving the injection efficiency,the DA optimization by using Non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ)to generate round beam,particularly to one of the designed lattice of the High Energy Photon Source(HEPS)storage ring,are presented.Method According to the general unconstrained model of NSGA-Ⅱ,we modified the standard model by using parallel computing to optimize round beam lattices with errors,especially for a strong coupling,such as solenoid scheme.Results and conclusion The results of numerical tracking verify the correction of the theory framework of solenoids with fringe fields and demonstrates the feasibility on the HEPS storage ring with errors to operate in round beam mode after optimizing DA.

Satellite constellation design with genetic algorithms based on system performance

Satellite constellation design for space optical systems is essentially a multiple-objective optimization problem. In this work, to tackle this challenge, we first categorize the performance metrics of the space optical system by taking into account the system tasks（i.e., target detection and tracking）. We then propose a new non-dominated sorting genetic algorithm（NSGA） to maximize the system surveillance performance. Pareto optimal sets are employed to deal with the conflicts due to the presence of multiple cost functions. Simulation results verify the validity and the improved performance of the proposed technique over benchmark methods.

基于NSGA-Ⅱ的滑油泵叶轮结构优化设计

滑油泵常需要在高空、低压工况下稳定运转,常会出现供油不足、效率降低等问题。为了得到满足设计要求且具有最佳性能的滑油泵,以某直升机用滑油泵叶轮为研究对象,对其结构进行优化设计。选择高空两个典型工况的效率与扬程作为优化目标,利用NSGA-Ⅱ算法对滑油泵叶轮几何参数进行寻优,对优化前后的滑油泵效率、扬程进行对比分析。采用CFD流体仿真及实验方法对优化结果进行对比验证。结果表明:所选优化参数对滑油泵性能有较大影响,优化后的滑油泵叶片位置附近流动更加平稳,高低压区域过渡平缓,能量损失更小,且降低了汽蚀发生的可能性;优化后的滑油泵设计点扬程提高2.6 m,效率提高2.86%。

Models for Location Inventory Routing Problem of Cold Chain Logistics with NSGA-Ⅱ Algorithm

In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location,inventory and transportation.Due to the complex of LIR problem( LIRP), a multi-objective genetic algorithm(GA), non-dominated sorting in genetic algorithm Ⅱ( NSGA-Ⅱ) has been introduced. Its performance is tested over a real case for the proposed problems. Results indicate that NSGA-Ⅱ provides a competitive performance than GA,which demonstrates that the proposed model and multi-objective GA are considerably efficient to solve the problem.

Optimization of solar thermal power station LCOE based on NSGA-Ⅱ algorithm

In view of the high cost of solar thermal power generation in China,it is difficult to realize large-scale production in engineering and industrialization.Non-dominated sorting genetic algorithm II(NSGA-II)is applied to optimize the levelling cost of energy(LCOE)of the solar thermal power generation system in this paper.Firstly,the capacity and generation cost of the solar thermal power generation system are modeled according to the data of several sets of solar thermal power stations which have been put into production abroad.Secondly,the NSGA-II genetic algorithm and particle swarm algorithm are applied to the optimization of the solar thermal power station LCOE respectively.Finally,for the linear Fresnel solar thermal power system,the simulation experiments are conducted to analyze the effects of different solar energy generation capacities,different heat transfer mediums and loan interest rates on the generation price.The results show that due to the existence of scale effect,the greater the capacity of the power station,the lower the cost of leveling and electricity,and the influence of the types of heat storage medium and the loan on the cost of leveling electricity are relatively high.

基于代理模型和NSGA-Ⅱ的超高强钢电阻点焊工艺参数多目标优化

为寻求超高强钢电阻点焊时最佳的焊接工艺参数,开展正交试验法设计三因素五水平的平板搭接点焊试验,以焊接时间、焊接电流和电极压力为可调的工艺参数,将熔核直径、压痕深度、拉剪强度及飞溅情况作为焊接接头质量评价指标.基于高斯过程回归和BP神经网络建立起焊接工艺参数与焊接接头质量评价指标之间关系的代理模型,训练的结果显示模型精度很高.最后利用带精英策略的非支配排序的遗传算法NSGA-Ⅱ实现多目标优化,得到各评价指标之间的最优pareto解集.经验证,各评价模型的相对误差值都很小.结果表明,该优化方法有较好的预测效果和稳定性.通过使用较少的试验数据,建立优化模型的方法对电阻点焊及其它焊接领域最佳焊接工艺参数的选取具有重要的指导价值.

基于改进NSGA-Ⅱ算法的RV减速器参数多目标优化研究

旋转矢量(RV)减速器是工业机器人核心部件,对于机器人的性能起到关键作用。针对提升RV减速器综合性能的问题,从优化传动压力角的相关参数出发,对其结构参数(摆线轮齿数、短幅系数、针径系数、摆线轮宽度等)的多目标优化设计进行了研究。首先,研究了摆线轮平均压力角、传动效率和传动机构体积三者的相关参数之间的关系;然后,以此为优化目标,在摆线轮标准齿廓方程的基础上建立了多目标优化数学模型(该模型采用了基于非支配占优排序遗传学算法(NSGA-Ⅱ)改进了交叉算子系数生成的改进NSGA-Ⅱ算法);通过模型求解得到了帕累托最优解集,根据模糊集合理论的相关方法选取了最优解;最后,以某公司220-BX型RV减速器为例,进行了优化设计,建立了3D模型后进行了有限元分析,并加工出实验样机,进行了传动效率对比实验。实验结果表明:摆线轮平均压力角减小了7.19%,体积减小了11.1%,传动效率提高了4.9%。研究结果表明:该模型交互性强,能提高设计效率并节省设计开销,可为实际RV减速器工程优化设计提供参考。

Strengthened Dominance Relation NSGA-Ⅲ Algorithm Based on Differential Evolution to Solve Job Shop Scheduling Problem

The job shop scheduling problem is a classical combinatorial optimization challenge frequently encountered in manufacturing systems.It involves determining the optimal execution sequences for a set of jobs on various machines to maximize production efficiency and meet multiple objectives.The Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ)is an effective approach for solving the multi-objective job shop scheduling problem.Nevertheless,it has some limitations in solving scheduling problems,including inadequate global search capability,susceptibility to premature convergence,and challenges in balancing convergence and diversity.To enhance its performance,this paper introduces a strengthened dominance relation NSGA-Ⅲ algorithm based on differential evolution(NSGA-Ⅲ-SD).By incorporating constrained differential evolution and simulated binary crossover genetic operators,this algorithm effectively improves NSGA-Ⅲ’s global search capability while mitigating pre-mature convergence issues.Furthermore,it introduces a reinforced dominance relation to address the trade-off between convergence and diversity in NSGA-Ⅲ.Additionally,effective encoding and decoding methods for discrete job shop scheduling are proposed,which can improve the overall performance of the algorithm without complex computation.To validate the algorithm’s effectiveness,NSGA-Ⅲ-SD is extensively compared with other advanced multi-objective optimization algorithms using 20 job shop scheduling test instances.The experimental results demonstrate that NSGA-Ⅲ-SD achieves better solution quality and diversity,proving its effectiveness in solving the multi-objective job shop scheduling problem.

基于NSGA-Ⅱ的智能化电铲多目标最优挖掘轨迹规划

为实现智能化电铲实时节能的挖掘,提出了一种基于非支配排序遗传算法(Non-dominated Sorting Genetic Algorithm-II,NSGA-Ⅱ)的智能化电铲多目标最优挖掘轨迹规划方法。首先,通过拉格朗日方程建立智能化电铲工作装置动力学模型;然后,使用高次多项式对挖掘轨迹进行插值,将挖掘轨迹寻优问题转化为多项式系数寻优问题,最后,以挖掘时间最短及单位体积物料的挖掘能耗最小作为优化目标,以电机性能与挖掘过程中几何条件等作为约束,利用多目标优化平台PlatEMO,将NSGA-Ⅱ作为多目标优化算法,指定待优化问题的目标函数及约束函数,获取到多目标优化Pareto最优解集,基于决策偏好设置权重并根据TOPSIS法获取最优解,得到多目标最优挖掘轨迹规划结果。结果表明,优化后挖掘轨迹满足实时节能的挖掘要求。

基于非支配排序遗传算法-Ⅱ的静态换相开关优化配置方法

为应对低压配电网中光伏系统带来的电压三相不平衡问题,本文提出了一种基于非支配排序遗传算法-II的静态换相开关优化配置方法。通过考虑静态换相开关的最佳部署位置,采用NSGA-II算法优化静态换相开关的数量和位置,从而实现成本效益最大化。并在IEEE 123节点测试馈线上进行了仿真实验,以验证方法的有效性。仿真结果表明,该方法在IEEE 123节点测试馈线中能够显著减少电压不平衡和网络损耗。在不同渗透水平下,沿馈线的最大电压不平衡度分别降低了80%和60%,总能量损失减少了(69.2~75.7)kWh。本文提出的方法在提高配电系统运行效率和稳定性方面展现了良好的应用前景,为智能电网和可再生能源的可持续发展提供了有力支持。

NSGA-Ⅱ算法的改进策略研究

带精英策略的非支配排序遗传算法(NSGA-Ⅱ)在多目标优化领域具有广泛的应用,但该算法种群收敛分布不均匀,全局搜索能力较弱,算法运行速度较慢。针对这些局限性提出了改进的排序适应度策略、算术交叉算子策略、按需分层策略和设定阈值选择策略。在典型的测试函数集上的数值实验结果表明,根据这些策略改进的算法得到的非劣解集具有较好的分布性,同时收敛速度更快。

采用NSGA-Ⅱ混合智能算法的风电场多目标电网规划

风电并网在实现节约化石能源和减少有害气体排放等效益的同时,也将对电力系统的可靠性造成一定的负面影响。为达到投资经济性、系统可靠性、环保效果的整体最优,构建了多目标风电场接入的输电线路与电网的联合优化规划模型;针对目标权重未知、人工神经网络(artificial neuralnetwork,ANN)收敛困难、无法合理决策等问题,采用方差最大化决策和分类逼近理想解的排序方法(technique fororder preference by similarity to an ideal solution,TOPSIS)缩小最优解的范围,并在此基础上提出了随机模拟、神经元网络和非劣排序遗传算法II(non-dominated sorting geneticalgorithm II,NSGA-Ⅱ)相结合的混合智能算法;对增加风电场的改进IEEE Garver-6系统进行计算分析,结果表明该方法具有较高的决策效率和计算精度,从而验证了所提出模型和方法的合理性和有效性。

基于NSGA-Ⅱ算法的白洋淀上游种植结构优化

合理的种植结构是实现区域水资源及土地资源优化配置的基础。针对白洋淀上游水资源紧缺、种植结构不合理等问题,结合当前主要作物种植结构现状,本研究以作物种植面积为优化变量,以水资源、土地资源、社会需求等为约束条件,以经济效益、生态效益最大及总灌溉耗水量最小为目标,构建基于非支配排序遗传算法(NSGA-Ⅱ)的作物种植结构多目标调整模型,并提出了针对白洋淀上游平原区、山区等不同水资源限制和农业机械化程度情景下的种植结构调整优化方案。研究结果表明,在平原区现状机械化水平下,在不限制用水的情景下,可以通过调减一年两作的种植面积,增加蔬菜和绿豆-鲜食玉米等的种植面积,达到提高经济效益12.6%的目的,而生态效益和节水效益都有所降低。在限水情景下,小麦-玉米调减比例增加,调增绿豆-鲜食玉米、春季甘薯、蔬菜和果蔬的面积,实现经济效益和节水效益的提高;而要达到节水20%的目标,所有作物的种植面积都要缩减,高耗水种植制度小麦-玉米种植面积缩减比例达21.5%,同时经济效益和生态效益都下降。在未来提高机械化水平的情景下,调整优化后的经济效益相比现状机械化水平提高或下降减少。在山区所有情景下,小麦-玉米种植面积随着对水分限制水平(不限水—小于现状水资源—节水20%)的增加调减比例增加,同时增加果树的种植面积。在山区可以通过种植结构的调整达到既节水20%,同时经济效益提高的目标,这是平原区所不能达到的。总之,无论是平原区还是山区,均是在不限水情景下优化后的经济效益、生态效益相对较高,而节水越多,优化后的经济效益、生态效益增幅越小、降幅越大。并且在平原区如果在节水要求不高的情景下应适当增加蔬菜面积,减少粮食种植面积;在节水要求高的情景下应削减所有作物包括水果、蔬菜的种植面积,在山区应该适当削减粮食种植面积,扩大果树的种植面积。该研究不仅可为研究区未来作物种植结构调整提供决策依据,也为在类似地区种植结构调整和水资源优化管理提供了新的情景参考。

基于NSGA-Ⅱ的水文模型参数多目标优化研究

为了对水文模型中难以直接测算的参数进行调试和优化,将带精英策略的非支配排序遗传算法(NSGA-Ⅱ)应用于水文模型(HYMOD)参数多目标优化计算中,得到最优解Pareto集合。通过多目标距离函数法从Pareto集中求出一组协调集。采用非支配解集覆盖度和非支配解的空间分布两个性能度量指标,对NSGA-Ⅱ算法与多目标粒子群算法(MOPSO)的优化结果进行比较分析。结果表明,NSGA-Ⅱ优化得到的非支配集比MOPSO算法得到的支配比例高;但前者的非支配解的空间分布较MOPSO算法相对均匀。

基于NSGA-Ⅱ的化工园区无约束双目标安全规划

化工园区安全规划是一个复杂的多目标决策问题,降低潜在事故风险、保证较高经济收益是化工园区安全规划的两个主要目标。应用多目标决策的理论方法,以潜在死亡人数最小化、工业总产值最大化为优化目标,建立了化工园区安全规划无约束双目标优化模型。选用非劣排序遗传算法-Ⅱ(NSGA-II)求解该模型,得出如下结论:(1)建立的化工园区安全规划无约束双目标优化模型是可行的。(2)采用的NSGA-Ⅱ算法是有效的优化方法。(3)无约束情况下,示例中的化工园区只布置甲类、乙类易燃液体存储地块,优先布置乙类易燃液体存储地块,不布置其他类型工业用地。