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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.
计算机应用 , 2007,
Abstract: 用多目标粒子群优化(MOPSO)算法的粒子位置更新模式替代NSGAⅡ的交叉操作,获得一个新的算法(NSGAⅡMOPSO)。为使这两种差异较大的算法实现无缝融合,在NSGAⅡ算法范围内对MOPSO中特有的概念粒子及其速度、Pbest、引导者进行处理: 1)粒子对应于NSGAⅡ中子代群体的个体; 2)不再使用粒子速度概念; 3)不再使用粒子Pbest概念,代之以从父代群体中为每个粒子的每一维寻找一个最近的该粒子非支配个体; 4)每一个粒子的引导者可以是父代群体中稀疏程度最大的个体或者是按照二进制随机竞赛选择方法从父代群体中选择的一个个体,具体哪一种方式发挥作用依赖于预先设定的概率。另外,引入稀疏程度概念来评价粒子在目标函数空间的分布。6个算例的结果表明,与NSGAⅡ及最新的两种MOPSO算法(CLMOPSO 和 EMMOPSO)相比,新算法是一个有效、稳定的算法。
A multi-objective particle swarm optimization for production-distribution planning in supply chain network  [PDF]
Alireza Pourrousta,Saleh dehbari,Reza Tavakkoli-Moghaddam,Mohsen sadegh amalnik
Management Science Letters , 2012,
Abstract: Integrated supply chain includes different components of order, production and distribution and it plays an important role on reducing the cost of manufacturing system. In this paper, an integrated supply chain in a form of multi-objective decision-making problem is presented. The proposed model of this paper considers different parameters with uncertainty using trapezoid numbers. We first implement a ranking method to covert the fuzzy model into a crisp one and using multi-objective particle swarm optimization, we solve the resulted model. The results are compared with the performance of NSGA-II for some randomly generated problems and the preliminary results indicate that the proposed model of the paper performs better than the alternative method.
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.
Methodology of Fuzzy Linear Symmetrical Bi-level Programming and its Application in Supply Chain Management  [cached]
Wei Deng,Qizong Wu,Jibin Li
Journal of Software , 2011, DOI: 10.4304/jsw.6.1.83-90
Abstract: Fuzzy linear symmetrical bi-level programming is the most extensive problem in multi-level programming. A new method based on tolerance degree has been introduced in this paper. The method mainly concerns the modeling of complicated Supply Chain with bi-level Stackelberg structure. We analyze the reason lead to uncertainties in supply chain, summarize methods of dealing with uncertainties, and present a fuzzy bi-level programming modeling method which could not only describe the layered structure but also construct the uncertainties. An actual mathematical model based on fuzzy bi-level programming is applied in supply chain management. At last, a numerical example is given to prove the validity of the new method.
Hybrid Optimized Algorithm Based on Improved MOPSO and Local Search and its Application

计算机科学 , 2012,
Abstract: In order to improve the weaknesses of the particle swarm's easily premature and slow convergence in late stage, the H-MOPSO, based on the integration of improved MOPSO and local search, was proposed. First of all, the non-uniform mutation operator and self-adaptive inertia weight were adopted to enhance its ability of global search. I}hen, the model of MOPSO hybrid with local search was established. According to the model, the local search algorithm based on hill climbing strategy with sidesteps was periodically used to optimize the swarm, making particles search a- long descent direction when they were away from Pareto front, and search along non-dominated direction while they were near Pareto front Simulation results of benchmark functions show that H-MOPSO has better performance com- pared with MOPSO,NSGA-II and MOEA/D. The solving of supplier selection problem further validates its effective- ness.
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.
A multi-objective reliable programming model for disruption in supply chain  [PDF]
Ebrahim Teimuory,Fateme Bozorgi Atoei,Emran Mohammadi,Ali Bozorgi Amiri
Management Science Letters , 2013, DOI: 10.5267/j.msl.2013.03.028
Abstract: One of the primary concerns on supply chain management is to handle risk components, properly. There are various reasons for having risk in supply chain such as natural disasters, unexpected incidents, etc. When a series of facilities are built and deployed, one or a number of them could probably fail at any time due to bad weather conditions, labor strikes, economic crises, sabotage or terrorist attacks and changes in ownership of the system. The objective of risk management is to reduce the effects of different domains to an acceptable level. To overcome the risk, we propose a reliable capacitated supply chain network design (RSCND) model by considering random disruptions risk in both distribution centers and suppliers. The proposed study of this paper considers three objective functions and the implementation is verified using some instance.
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。
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