A parallel computing application of the genetic algorithm for lubrication optimization

This study investigated the performance of parallel optimization by means of a genetic algorithm (GA) for lubrication analysis. An air-bearing design was used as the illustrated example and the parallel computation was conducted in a single system image (SSI) cluster, a system of loosely network-connected desktop computers. The main advantages of using GAs as optimization tools are for multi-objective optimization, and high probability of achieving global optimum in a complex problem. To prevent a premature convergence in the early stage of evolution for multi-objective optimization, the Pareto optimality was used as an effective criterion in offspring selections. Since the execution of the genetic algorithm (GA) in search of optimum is population-based, the computations can be performed in parallel. In the cases of uneven computational loads a simple dynamic load-balancing scheme is proposed for optimizing the parallel efficiency. It is demonstrated that the huge amount of computing demand of the GA for complex multi-objective optimization problems can be effectively dealt with by parallel computing in an SSI cluster.     

可重构装配线多目标优化调度研究

针对可重构装配线调度存在的问题,综合考虑影响可重构装配线调度的三个主要因素,即最小化空闲和未完工作业量、均衡零部件的使用速率、最小化装配线重构成本,建立了可重构装配线多目标优化调度的数学模型。提出了一种基于Pareto多目标遗传算法的可重构装配线优化调度方法,该算法综合运用了群体排序技术、小生境技术、Pareto解集过滤及精英保留策略,并采用了交叉概率和变异概率的自适应重构策略。实例仿真表明该算法具有比其他遗传算法更高的求解质量。

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面向绿色设计的材料选择多目标优化决策

为解决绿色设计中材料选择的多目标优化问题,提出一种将神经网络与遗传算法集成的求解决策模型。该模型以材料的力学性能、工艺性能、经济属性和生命周期的环境属性等为优化目标,利用人工神经网络进行系统建模,并为遗传算法找到适应度函数及求得目标函数值的方法,进而利用遗传算法进行多目标优化。采用生态指数方法定量分析材料在其生命周期内对环境的影响。以某个电冰箱壳体材料的选择为例,证明该多目标决策模型对绿色设计中的材料选择有重要指导作用。     

基于降维的驾驶员侧约束系统高维目标优化

为解决将高维目标变为单目标优化时各子目标不能同时较优,而多目标算法直接用于高维目标优化时又存在难以找到一个有代表性的Pareto非劣解集问题,在某轿车驾驶员侧约束系统的优化过程中提出了乘员损伤准则与多目标算法协同优化的方法。在已有相关损伤准则基础上根据最新版的FMVSS 208和ECE R94法规提出了适合研究问题的损伤准则;以提出的损伤准则为媒介,将一个高维目标优化问题降为一个低维目标优化问题,通过灵敏度分析、实验设计、多项式近似模型筛选出优化设计变量并得到近似模型,用多目标算法NSGA-Ⅱ对近似模型进行计算得到Pareto非劣解集,将得到的Pareto非劣解集中的每个解代入损伤准则损伤值计算公式,升序排列得到各子目标同时较优而损伤值最小的优化解。最终的优化结果表明：该方法很好地解决了乘员约束系统的高维目标优化问题,优化效果明显。     

Multiple stiffness topology optimizations of continuum structures

This paper presents a new multi-objective topology optimization algorithm for continuum structures under multiple loading cases. An expert evaluation method of weights based on grey system theory is proposed to calculate the objective weights when the compromise programming approach is employed as a multi-objective optimization scheme converting the multi-objective problem to a single objective problem. A modified updating scheme with a self-adaptive move limit for design variables is also suggested, SIMP is regarded as density-stiffness interpolation scheme and the optimality criteria method is used as the optimizer. Numerical instabilities, such as checkerboards and mesh dependencies, are also discussed. The validities of these methods in this paper are demonstrated by some numerical applications.     

基于Pareto解集的多目标优化方法及其应用

针对传统多目标优化设计方法的弱点，基于Pareto概念，借助遗传算法所具有的并行搜索特性，引入群体排序技术、小生境技术求得多目标优化问题的Pareto解集，实现了先寻优后决策的求解模式。实际工程算例表明，该模式可同时获得多个Pareto最优解，据此决策能有效弱化设计人员先验知识不足的影响，因而较传统多目标优化方法更为实用有效。     

Optimum design of externally pressurized air bearing using Cluster OpenMP

This study presents a performance evaluation of a new portable parallel programming paradigm, the Cluster OpenMP (CLOMP) for distributed computing, in conducting an optimum design of air bearings. The multi-objective optimization was carried out by using a genetic algorithm (GA) incorporating Pareto optimality criterion. Since the GA is natural parallel evolution algorithm, the computation of the search was carried out in parallel by using the CLOMP. In this study, the performance of a CLOMP cluster of four dual-core computers for the air bearing optimization was compared with a shared-memory processing (SMP) computer equipped with two quad-core processors. To examine the parallel efficiency of the CLOMP in the GA optimization, several multithread applications of various task sizes were tested. It is shown that the air bearing optimization can be effectively dealt with by the CLOMP (parallel efficiency of 96.2-98.8%) as well as the SMP computing (93.1-99.4%) in the studied cases. The CLOMP retains the characteristics of directive-based OpenMP, such as incremental programming and serial-coding compatibility. The verified high parallel efficiency of the CLOMP cluster demonstrates its potential applications of the scalable computing in many tribological optimizations.     

基于NSGA-Ⅱ叉车轮边减速器优化设计

以叉车轮边减速器行星轮系为研究对象,在满足设计要求的前提下,以轮边减速器行星轮系齿圈直径最小,中心距最大和重合度最高为目标建立目标优化数学模型.运用改进的NSGA-Ⅱ对多目标优化并得到Pareto最优解集,利用多指标加权灰靶决策模型选择最优设计方案.优化结果表明：改进遗传算法的运用是可靠有效的,为以后产品优化设计提供新了的设计思路.     

Multi-objective simulation optimization for selection and determination of order quantity in supplier selection problem under uncertainty and quality criteria

Simulation optimization is providing solutions to practical stochastic problems. Supplier selection is one of the most important decisions that determine the survival of an organization. In this paper, a novel multi-objective simulation optimization method to make decisions on selecting the suppliers and determining the order quantities is proposed. Regarding the fact that a real supply chain is multi-objective with uncertain parameters and includes both quantitative and qualitative variables, the proposed method considers these points and is applicable to real-world problems. This method also considers supplier selection and order quantity allocation to each supplier, which are totally related, as an integrated model. The proposed method consists of four basic modules: Cuckoo Optimization Algorithm (COA), Discrete Event Simulation (DES), Supply Chain Model (SCM), and Generalized Data Envelopment Analysis (GDEA). Unlike many multi-objective methods, the proposed method is not limited to the number of objective functions and this is one of its main benefits. It also pays attention to the efficiency of the organization and, at the same time, finding inputs which result in best output amounts. This method, in addition to the convergence criterion, pays special attention to the dispersion of the Pareto frontier as the second criterion for choosing the good solutions. For implementation of the proposed method, the numerical results for the problem of supplier selection in multi-product, multi-customer modes, and uncertain and qualitative variables are discussed and the Pareto frontiers are presented. The proposed method in this paper is compared with a similar method, and the results show the efficiency of the proposed method.     

多目标结构模糊优化的分层序列法

提出了多目标结构模糊优化的分层序列法,首先把原多目标模糊优化问题分解为一系列单目标（ 或多目标） 模糊优化子问题,该子问题用最大最小法求解。最后可以按着目标函数的重要程度给出原问题模糊最优解。最后用一个三杆桁架的最小重量与变形的模糊多目标优化设计问题证明了该方法的正确性     

Dynamic balancing of planar mechanisms using genetic algorithm

This paper presents an optimization technique to dynamically balance the planar mechanisms in which the shaking forces and shaking moments are minimized using the genetic algorithm (GA). A dynamically equivalent system of point-masses that represents each rigid link of a mechanism is developed to represent link’s inertial properties. The shaking force and shaking moment are then expressed in terms of the point-mass parameters which are taken as the design variables. These design variables are brought into the optimization scheme to reduce the shaking force and shaking moment. This formulates the objective function which optimizes the mass distribution of each link. First, the problem is formulated as a single objective optimization problem for which the genetic algorithm produces better results as compared to the conventional optimization algorithm. The same problem is then formulated as a multi-objective optimization problem and multiple optimal solutions are created as a Pareto front by using the genetic algorithm. The masses and inertias of the optimized links are computed from the optimized design variables. The effectiveness of the proposed methodology is shown by applying it to a standard problem of four-bar planar mechanism available in the literature.     

多方案经营过程模型选择策略

经营过程建模的目的是为了经营过程的分析及重构。在经营过程中，由于存在约束、不确定性和不可精确估量等因素，其评价值常常是模糊的，评价目标不单一。因而存在一个对各种方案过程模型选择的问题，这个问题可以转化为多目标模糊最短路的问题。讨论了多目标模糊最短路径的算法与Pareto解空间问题，提出了基于模糊推理引擎选择多个Pareto解的策略。提出了经营过程设计框架，从而解决了企业内、企业间经营过程及供应链优化设计问题。     

基于多属性决策的气动隐身多目标优化

针对多目标优化结果排序与选择的多属性决策(Multi-attribute decision making,MADM)问题,将多目标优化与MADM相结合,提出基于MADM的多目标优化方法,并将该方法应用于跨声速前掠翼(Forward-swept wing,FSW)气动隐身多目标优化中,优化结果提高了跨声速FSW的气动和隐身性能。采用类别形状函数变换法(Class-shape function transformation,CST)方法对翼型几何外形进行描述,实现FSW气动和隐身多学科优化设计模型的参数化描述。建立基于N-S方程的计算流体力学方法的FSW气动分析模型和基于矩量法的计算电磁学方法的FSW隐身分析模型。将Pareto多目标遗传算法得到的Pareto非劣解集构成MADM矩阵,采用基于模糊熵权的改进的逼近理想解的排序法(Modified technique for order preference by similarity to ideal solution,M-TOPSIS)方案评价方法进行Pareto非劣解排序,最终确定最佳的Pareto非劣解。研究结果验证了所提出方法的有效性,为多目标优化问题提供了一种新的解决途径。     

A new multi-objective ant colony algorithm for solving the disassembly line balancing problem

The disassembly line is the best choice for automated disassembly of disposal products. Therefore, disassembly line should be designed and balanced so that it can work as efficiently as possible. In this paper, a mathematical model for the multi-objective disassembly line balancing problem is formalized firstly. Then, a novel multi-objective ant colony optimization (MOACO) algorithm is proposed for solving this multi-objective optimization problem. Taking into account the problem constraints, a solution construction mechanism based on the method of tasks assignment is utilized in the algorithm. Additionally, niche technology is used to embed in the updating operation to search the Pareto optimal solutions. Moreover, in order to find the Pareto optimal set, the MOACO algorithm uses the concept of Pareto dominance to dynamically filter the obtained non-dominated solution set. To validate the performance of algorithm, the proposed algorithm is measured over published results obtained from single-objective optimization approaches and compared with multi-objective ACO algorithm based on uniform design. The experimental results show that the proposed MOACO is well suited to multi-objective optimization in disassembly line balancing.     

高重合度圆柱齿轮传动多目标优化设计

以重合度最大、体积最小、弯曲强度相等为目标函数,建立了圆柱齿轮传动多目标优化设计数学模型,采用带精英策略的快速非支配排序遗传算法(NSGA-Ⅱ)进行优化求解。对高速重载斜齿圆柱齿轮传动进行了高重合度优化设计,得到了Parteto最优解,并从中选择了一个优化方案与原始方案进行对比,结果显示高重合度圆柱齿轮传动的强度有明显提高,体积也有一定的减小。     

Preference adjustable multi-objective NMPC: An unreachable prioritized point tracking method

This paper proposes a new preference adjustable multi-objective model predictive control (PA-MOMPC) law for constrained nonlinear systems. With this control law, a reasonable prioritized optimal solution can be directly derived without constructing the Pareto front by solving a minimal optimization problem, which is a novel development of recently proposed utopia tracking approaches by additionally considering objective preferences with more flexible terminal and stability constraints. The tracking point of the proposed PA-MOMPC law is represented by a parametric vector with the parameters adjustable on the basis of objective preferences. The main result of this paper is that the solution obtained through the proposed PA-MOMPC law is demonstrated to have two important properties. One is the inherent Pareto optimality, and the other is the priority consistency between the solution and the tuning parametric vector. This combination makes the objective priorities tuning process transparent and efficient. The proposed PA-MOMPC law is supported by feasibility analyses, proof of nominal stability, and a numerical case study.     

基于NSGAⅡ的齿轮减速器多目标优化研究

为了解决工程设计中有离散变量、多约束的多目标优化问题,对改进的非占优排序遗传算法(NSGAⅡ)进行了研究,通过基于拥挤距离的非占优排序,提出了离散变量和多约束的处理方法,利用Matlab软件编写了NSGAⅡ的多目标优化程序,并以二级减速器多目标优化设计为例,建立了多目标优化数学模型,运用NSGAⅡ算法求解得到了帕累托最优解集,根据模糊集合理论的有关方法选取了最优解,与传统方法得到的结果相比,体积、失效概率和传动误差都有不同程度的降低。研究结果表明,修改后的NSGAⅡ能用于有效地求解有离散变量、多约束的多目标优化设计问题。     

基于有约束多目标进化算法的冷轧负荷分配分析

冷轧负荷分配问题可以抽象为一个有约束多目标优化问题。为解决此问题,提出了基于环境Pareto支配选择策略的有约束多目标进化算法。该算法更加客观地评价了两个不同解的优劣,利用优秀不可行解加速算法收敛。以等功率裕量、最小轧制能耗、最小综合打滑函数、末机架板形良好轧制力为优化目标,利用有约束多目标进化算法得到了4个目标函数之间的定量关系,使决策者不需要掌握复杂的轧制理论知识就可以直观地掌握轧制规律,并进一步说明了多目标策略在压下负荷分配中的必要性。     

A simulated annealing algorithm to find approximate Pareto optimal solutions for the multi-objective facility layout problem

In this article, we consider the facility layout problem which combines the objective of minimization of the total material handling cost and the maximization of total closeness rating scores. Multi-objective optimization is the way to consider the two objectives at the same time. A simulated annealing (SA) algorithm is proposed to find the non-dominated solution (Pareto optimal) set approximately for the multi-objective facility layout problem we tackle. The Pareto optimal sets generated by the proposed algorithm was compared with the solutions of the previous algorithms for multi-objective facility layout problem. The results showed that the approximate Pareto optimal sets we have found include almost all the previously obtained results and many more approximate Pareto optimal solutions.     

Multi-Objective Optimization of Spur Gearbox with Inclusion of Tribological Aspects

In this paper, a novel multi-objective optimization of a two-stage spur gearbox is carried out with a comprehensive range of constraints. The first objective function aims to reduce the weight/volume and second aims to minimize the power losses in the gearbox. Various design constraints and tribological constraints such as scuffing and wear are included. By using a specially formulated discrete version of NSGA-II optimization code, these objective functions are minimized for three different gear profiles (unmodified profile, smooth meshing, and high load) and for different SAE oil grades. Optimization is first carried out based on standard single objective minimization using regular constraints based on existing literature and then based on multi-objective optimization with comprehensive constraints which include tribological aspects. Finally, these two cases are compared for different gear profiles and oils. The results indicate that there is a high probability of wear failure, for solutions obtained from single objective minimization. The total power loss is reduced by half when using multi-objective compared to single objective optimization.