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Multi-Objective Optimization of Two-Stage Helical Gear Train Using NSGA-II  [PDF]
R. C. Sanghvi,A. S. Vashi,H. P. Patolia,R. G. Jivani
Journal of Optimization , 2014, DOI: 10.1155/2014/670297
Abstract: Gears not only transmit the motion and power satisfactorily but also can do so with uniform motion. The design of gears requires an iterative approach to optimize the design parameters that take care of kinematics aspects as well as strength aspects. Moreover, the choice of materials available for gears is limited. Owing to the complex combinations of the above facts, manual design of gears is complicated and time consuming. In this paper, the volume and load carrying capacity are optimized. Three different methodologies (i) MATLAB optimization toolbox, (ii) genetic algorithm (GA), and (iii) multiobjective optimization (NSGA-II) technique are used to solve the problem. In the first two methods, volume is minimized in the first step and then the load carrying capacities of both shafts are calculated. In the third method, the problem is treated as a multiobjective problem. For the optimization purpose, face width, module, and number of teeth are taken as design variables. Constraints are imposed on bending strength, surface fatigue strength, and interference. It is apparent from the comparison of results that the result obtained by NSGA-II is more superior than the results obtained by other methods in terms of both objectives. 1. Introduction Designing a new product consists of several parameters and phases, which differ according to the depth of design, input data, design strategy, procedures, and results. Mechanical design includes an optimization process in which designers always consider certain objectives such as strength, deflection, weight, wear, and corrosion depending on the requirements. However, design optimization for a complete mechanical assembly leads to a complicated objective function with a large number of design variables. So it is a better practice to apply optimization techniques for individual components or intermediate assemblies than a complete assembly. For example, in an automobile power transmission system, optimization of gearbox is computationally and mathematically simpler than the optimization of complete system. The preliminary design optimization of two-stage helical gear train has been a subject of considerable interest, since many high-performance power transmission applications require high-performance gear train. A traditional gear design involves computations based on tooth bending strength, tooth surface durability, tooth surface fatigue, interference, efficiency, and so forth. Gear design involves empirical formulas, different graphs and tables, which lead to a complicated design. Manual design is very difficult
采用NSGA-II算法的混合动力能量管理控制 多目标优化方法
A Multi??Objective Optimization Method for Energy Management Control of Hybrid Electric Vehicles Using NSGA??II Algorithm
 [PDF]

邓涛,林椿松,李亚南,卢任之
- , 2015, DOI: 10.7652/xjtuxb201510023
Abstract: 综合考虑燃油经济性、排放性与驾驶性对混合动力能量管理控制优化的优点,以某款并联混合动力汽车为研究对象,选取能量管理控制参数与传动系参数作为待优化参数,以动力性作为约束条件,建立混合动力能量管理控制多目标优化评价方法,提出基于NSGA??II算法的混合动力系统多目标优化方法,并与优化前控制策略进行仿真对比分析。结果表明:在满足基本约束的前提下,优化后燃油经济性最多提高了7.8%,平均提高了6.38%;驾驶性性能指标最多提高了27??12%,平均提高了21.74%;排放性综合指标平均提高了41.51%。提出的多目标优化算法具有良好的收敛性与分布性,得到的Pareto最优解集能够给混合动力能量管理控制策略提供更多的权衡选择方案,体现了多目标优化的优势。
A multi??objective optimization evaluation method for hybrid electric vehicle (HEV) is proposed by comprehensively considering the influences of fuel economy, emission and drivability on the energy management control for HEV. The multi??objective optimization algorithm based on NSGA??II (non??dominated sorting genetic algorithm??II) is established by setting the parameters of the energy management control and the driveline system as the optimal parameters for the parallel hybrid electric vehicles, and the dynamic performance as the constraint condition. Then the proposed method is comparatively analyzed with the traditional control strategy that only considers the fuel economy. Simulation results show that the maximum fuel economy performance increases by 7.8% and the average value increases by 6.38%; the maximum drivability performance increases by 42.28% and the average value increases by 21??74%; the average synthetic emission performance increases by 41.51%. The proposed multi??objective optimization algorithm has good convergence and distribution. The obtained Pareto optimum solutions may provide more trade??off options for HEV energy management control strategy, which reflect the advantages of multi??objective optimization
基于Aspen Plus和NSGA-Ⅱ的隔壁塔多目标优化研究 Multi-Objective Optimization of Dividing Wall Columns with Aspen Plus and NSGA-Ⅱ  [PDF]
李军,王纯正,马占华,孙兰义
- , 2015,
Abstract: 以年总操作费用(TAC)和再沸器负荷为目标,提出了基于遗传算法NSGA-Ⅱ的优化方法,并将该方法应用于BTX分离隔壁塔的优化设计。首先应用Aspen Plus软件建立了BTX分离工艺的隔壁塔Radfrac两塔模型,并在Matlab平台上,通过MAP接口工具箱实现Matlab对Aspen Plus的操作与控制,同时Matlab调用NSGA-Ⅱ进行优化,完成种群大小为600、遗传代数为28的模拟过程,得到了10组Pareto解。研究表明,对于Pareto解分布,气相分配量βg、液相分配量βL、侧线抽出位置NS和液相分配位置NL基本不变,进料位置NF、预分馏塔板Nj和主塔板数Ni存在一定的线性关系。
采用NSGA-Ⅱ算法的面齿轮副小轮 拓扑修形多目标优化
NSGA-Ⅱ Based Multi??Objective Optimization on Topologically Modified Pinions for Face Gear Pairs
 [PDF]

付学中,方宗德,关亚彬,李建华
- , 2017, DOI: 10.7652/xjtuxb201707015
Abstract: 为合理确定面齿轮副小轮的修形参数,设计了均由2段抛物线与1段直线组成的直齿小轮齿廓和齿向修形曲线,将由三次B样条拟合得到的修形曲面与理论齿面相叠加来构造拓扑修形齿面。采用带精英策略的快速非支配排序遗传算法(NSGA-Ⅱ),结合面齿轮副的几何接触分析(TCA)和承载接触分析(LTCA)技术,提出了以修形曲线参数为优化变量,使抛物线几何传动误差曲线两端对称、接触印痕限制在齿宽中部、承载传动误差波动幅值最小的小轮拓扑修形多目标优化设计方法,并编制了相应的Matlab程序。算例表明:优化修形参数后得到了对称的抛物线几何传动误差和位于大轮齿宽中部的接触印痕,并大幅度减小了承载传动误差波动,从而可有效降低安装误差敏感性和齿轮副的振动、噪声。
To reasonably determine the technical parameters in profile modification of face gear pairs, a tooth profile and an axial modification curve both composed of two sections of parabola and a straight line on a spur pinion are created. A topologically modified tooth surface can be represented as a superposition of theoretical tooth surface and the deviation surface obtained by cubic B??splines fitting on the tooth surface grid. Based on the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) of the face gear pairs, taking the parabolic transmission error curve being symmetrical in geometry, the contact path being limited in the central tooth width, and the minimum wave amplitude of loaded transmission errors as the three optimization objectives, a multi??objective optimization model is established, and the corresponding programs are developed by software Matlab. The fast elitist non??dominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ) is selected as the multi??objective optimization algorithm. An optimization example shows that the present method obtains symmetric parabola geometry transmission error and the contact path in the middle of gear tooth width, which greatly reduces the wave amplitude of loaded transmission errors, hence effectively reduces installation error sensitivity, vibration and noise
An Approach of Constructing Multi-Objective Pareto Optimal Solutions Using Arena''s Principle
用擂台赛法则构造多目标Pareto最优解集的方法

ZHENG Jin-Hua,JIANG Hao,KUANG Da,SHI Zhong-Zhi,
郑金华
,蒋浩,邝达,史忠植

软件学报 , 2007,
Abstract: 针对多目标进化的特点,提出了用擂台赛法则(arena's principle,简称AP)构造多目标Pareto最优解集的方法,论证了构造方法的正确性,分析了其时间复杂度为O(rmN)(0<m/N<1).理论上,当AP与Deb的算法以及Jensen的算法比较时(它们的时间复杂度分别为O(rN2)和O(Nlog(r-1)N)),AP优于Deb的算法;当目标数r较大时(如r≥5),AP优于Jensen的算法;此外,当m/N较小时(如m/N≤50%),AP的效率与其他两种算法比较具有优势.对比实验结果表明,AP具有比其他两种算法更好的CPU时间效率.在应用中,AP可以被集成到任何基于Pareto的MOEA中,并能在较大程度上提高MOEA的运行效率.
Improved non-dominated sorting genetic algorithm applied in multi-objective optimization of coal-fired boiler combustion
改进NSGA-Ⅱ算法在锅炉燃烧多目标优化中的应用

YU Ting-fang,WANG Lin,PENG Chun-hua,
余廷芳
,王 林,彭春华

计算机应用研究 , 2013,
Abstract: 提出改进非劣分类遗传算法NSGA-Ⅱ在燃煤锅炉多目标燃烧优化中的应用, 优化的目标是锅炉热损失及NOx排放最小化。首先, 采用BP神经网络模型分别建立了300MW燃煤锅炉的NOx排放特性模型和锅炉热损失模型, 同时利用锅炉热态实验数据对模型进行了训练和验证, 结果表明, BP神经网络模型可以很好地预测锅炉的排放特性和锅炉的热损失特性。在建立的锅炉排放特性和热损失BP神经网络模型基础上, 采用非劣分类遗传算法对锅炉进行多目标优化, 针对NSGA-Ⅱ在燃煤锅炉燃烧多目标优化问题应用中Pareto解集分布不理想、易早熟收敛的问题, 在拥挤算子及交叉算子上进行了相应改进。优化结果表明, 改进NSGA-Ⅱ方法与BP神经网络模型结合可以对锅炉燃烧实现有效的多目标寻优、得到理想的Pareto解, 是对锅炉燃烧进行多目标优化的有效工具, 同改进前的NSGA-Ⅱ优化结果比较, 其Pareto优化结果集分布更好、解的质量更优。
Optimization and Design of PV-Wind Hybrid System for DC Micro Grid Using NSGA II  [PDF]
R. Sathishkumar, V. Malathi, V. Premka
Circuits and Systems (CS) , 2016, DOI: 10.4236/cs.2016.77094
Abstract: The world is heading towards renewable energy, but the two key disputes that stop its well-known adoption are the power production level and the price of the production. Distributed generation (DG), and hybrid systems with battery backup are the solution for uninterrupted power supply. It is obtained using the Multi-Objective Genetic Algorithm (NSGA II). Techno-economic methodology is used in this proposed system for the size optimization. The result is based on the system cost, in order to meet the load requirements. The effect of temporal sampling is optimized using low-rate temporal data. It is compared with hybrid DC microgrid, which has been optimized using high temporal resolution data.
Modified NSGA-II for a Bi-Objective Job Sequencing Problem  [PDF]
Susmita Bandyopadhyay
Intelligent Information Management (IIM) , 2012, DOI: 10.4236/iim.2012.46036
Abstract: This paper proposes a better modified version of a well-known Multi-Objective Evolutionary Algorithm (MOEA) known as Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The proposed algorithm contains a new mutation algorithm and has been applied on a bi-objective job sequencing problem. The objectives are the minimization of total weighted tardiness and the minimization of the deterioration cost. The results of the proposed algorithm have been compared with those of original NSGA-II. The comparison of the results shows that the modified NSGA-II performs better than the original NSGA-II.
翅片式热管散热器自然对流换热特性分析与多目标结构优化
Analysis of natural convection heat transfer characteristics and multi-objective optimization of structure-parameters for finned heat pipe radiator
 [PDF]

黄晓明,师春雨,孙佳伟,杜阳,朱一萍,许国良
- , 2018, DOI: 10.13738/j.issn.1671-8097.018048
Abstract: 采用数值计算方法对一种应用于半导体制冷片热端散热的翅片式热管散热器进行模拟,探究自然对流条件下不同翅片参数对散热器换热特性的影响。结合多目标遗传算法(NSGA-II),以影响散热器散热的两个主要参数――翅片换热系数和肋面效率为优化目标,对散热器整体做出综合优化,并对优化结果进行K均值聚类分析,提出了翅片端优化原则。结果表明,肋面效率对散热器性能的影响有限,提高换热系数可显著降低散热器总热阻;与未优化方案相比,所选优化方案可使基板热端面温度下降3.5K,散热器热阻降低18.22%。
A finned heat pipe radiator for heat dissipation of the thermoelectric refrigerator was analyzed by numerical simulation to investigate the effects of different structure parameters on the heat transfer characteristics under natural convection. Combined with multi-objective genetic algorithm (NSGA-II), two main parameters affecting the heat dissipation of radiators, heat transfer coefficient and fin synthesis efficiency, were taken as optimization objective, then the radiator was comprehensively optimized. Using k-means clustering method to analyze the optimized solutions, the optimization principle was proposed. The results show that the influence of fin synthesis efficiency on the radiator performance is limited, and the total heat resistance of the radiator can be significantly reduced by increasing the heat transfer coefficient. Compared with the non-optimized situation, the optimization results can reduce the base temperature by 3.5 K and reduce the total heat resistance of the radiator by 18.22%.
Multi-Objective Optimization Using Multi Parent Crossover Operators  [cached]
Rahila Patel,M.M.Raghuwanshi
Journal of Emerging Trends in Computing and Information Sciences , 2011,
Abstract: The crossover operator has always been regarded as the primary search operator in genetic algorithm (GA) be-cause it exploits the available information from the population about the search space. Moreover, it is one of the components to consider for improving the behavior of the GA. To improve performance of GA multi parent crossover operators have been used. Multi parent crossover operators involve sampling of features of more than two parent solution into the offspring that accelerated speed of convergence to global optima. These operators are based on some probability distribution and are gene-level parent centric crossover operators. In this work, we have used MPX (multi-parent crossover with polynomial distribution) and MLX (multi-parent cross-over with lognormal distribution) operators for multi-objective optimization. The performance of these operators is investigated on commonly used multi-objective functions. GA used for experimentation is Non-dominated Sort Genetic Algorithm-II (NSGA-II). It is observed that these operators work well with NSGA-II and have given encouraging results.
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