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Bi-objective supply chain problem using MOPSO and NSGA-II  [PDF]
Hassan Javanshir,Sadoullah Ebrahimnejad,Samaneh Nouri
International Journal of Industrial Engineering Computations , 2012,
Abstract: The increase competition and decline economy has increased the relevant importance of having reliable supply chain. The primary objective of many supply chain problems is to reduce the cost of services and, at the same time, to increase the quality of services. In this paper, we present a multi-level supply chain network by considering multi products, single resource and deterministic cost and demand. The proposed model of this paper is formulated as a mixed integer programming and we present two metaheuristics namely MOPSO and NSGA-II to solve the resulted problems. The performance of the proposed models of this paper has been examined using some randomly generated numbers and the results are discussed. The preliminary results indicate that while MOPSO is able to generate more Pareto solutions in relatively less amount of time, NSGA-II is capable of providing better quality results.
Multi-Objective Optimization Problems with Arena Principle and NSGA-II  [PDF]
Wang Dong-Feng,Xu Feng
Information Technology Journal , 2010,
Abstract: Existing test problems for multi-objective optimization are mainly criticized for high computational complexity. In this study, we introduce a new non- dominated sorting algorithm based on Pareto optimal solutions which alleviates the problem of high computational complexity in NSGA-II. We use the Arena Principle in NSGA-II to retain the non-dominated solutions found during the evolutionary process. The main goal of this work is to keep the fast convergence exhibited by Arena Principle in global optimization when extending this heuristic to multi-objective optimization. The algorithm’s computational complexity is O(rmN). We adopt two standard test functions and simulation results show that the Arena Principle is able to find more useful and better spread of solutions.
Path Optimization Algorithm For Network Problems Using Job Sequencing Technique  [PDF]
Punit Kumar Singh,Rakesh Kumar
International Journal of Distributed and Parallel Systems , 2012,
Abstract: The job sequencing technique is used to determine an optimal sequence. It performs a series of jobs by a number of specific orders so that it calculates the optimal cost. In this paper, we propose a novel approach to find an optimal path from source to destination by taking advantage of job sequencing technique. Wehave used n jobs m machine sequencing technique and this is divided into n jobs 2 machine problems. Using Johnson’s sequencing rule, we solved the problem and obtained the (n-1) sub sequences of the route. Using the proposed algorithm, we calculated the optimal sequence, which leads to the shortest path of the network.
Simulation of Sequencing Rules Using Witness in a Milling Job Shop  [cached]
Liqi Ang,Kuan Yew Wong,Wai Peng Wong
Communications of the IBIMA , 2011,
Abstract: Simulation is essential when studying manufacturing processes or designing production systems. This project was a real case study which involved a job shop with five similar CNC milling machines. A total of six jobs were performed and each of them consisted of a different set of operations. The sequence of the six jobs to enter the system was determined by the sequencing rules including shortest setup time (SST), shortest processing time (SPT), shortest processing and setup time (SPST), earliest due date (EDD), least process (LP), and lowest volume (LV). The setup time was taken into consideration to make the results more realistic. Due to the complexity of the model, WITNESS was used to simulate all the sequencing rules. The best approach was then determined by comparing the results of each rule. By doing this, the case company would be able to make a better decision on which job should be processed first instead of selecting it randomly among the jobs.
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
Improved multi-objective genetic algorithm based on NSGA-II

CHEN Xiao-qing,HOU Zhong-xi,GUO Liang-min,LUO Wen-cai,

计算机应用 , 2006,
Abstract: Based on the study and analysis of NSGA-II algorithm, a new initial screening mechanism was designed, coefficient generating of crossover arithmetic operator was improved and more reasonable crowding mechanism was proposed. In this way, convergence was speeded up and its precision was improved. The testing results by representative applied functions show that with the improvements higher computational efficiency and more reasonable distributed solution can be obtained, and diversified distribution of the solutions can be maintained.
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]
- , 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

- , 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
Multi-Objective Flexible Job-Shop Scheduling Problem Based on  [PDF]
MO Jian-lin,WU Zhe
Journal of Chongqing Normal University , 2013,
Abstract: Aiming at the solving FJSP (Flexible job-shop scheduling problem), a scheduling algorism combined gene and tabu algorism were proposed. Firstly, the FJSP problem model was defined, then the improve gene algorism was used to obtain the solution, the chromosome was coded as double-stranded and the NEH algorism was used to get the initial solution. And the adaptive selection strategy, compound cross strategy and mutation strategy were introduced to protect the optimum chromosome and renew. When the gene algorism got the local optimum solution, the tabu algorism was used to get the global solution. The simulation experiment shows our method in this paper can resolve the FJSP effectively and get the optimal solution, compared with the other methods; the method has the rapid convergence and high solution efficiency.
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

- , 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
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