基于Pareto遗传算法的高速插秧机变速器优化设计

以某高速插秧机变速器的优化设计为例,将Pareto最优解概念和遗传算法相结合,在遗传算法的基础上引入群体排序技术、小生境技术和Pareto解集过滤器等技术,并针对设计变量都是离散变量的特点,采用先将生成的随机数变换到约束范围后再圆整到最近离散值的方法,构造了适用于求解多目标优化问题的Pa-reto遗传算法,运用该算法获得了变速器在体积最小、中心距最小和总重合度最大目标下的Pareto最优解集。结果表明,采用Pareto遗传算法优化设计的变速器达到了综合优化设计的效果。     

圆柱齿轮传动多目标优化的差分进化算法

针对单级斜齿圆柱齿轮传动机构优化设计问题,建立以体积最小化和重合度最大化为目标的约束多目标优化模型。为提高Pareto前沿的分布均匀性和分布广度,将网格Pareto占优技术与约束多目标差分进化算法结合,设计网格占优约束多目标差分进化算法(ε-CMODE)。根据工程实践需要,将离散约束多目标优化模型映射为约束非负整数规划问题,再改进ε-CMODE算法以求解该模型。最后,给出优化设计实例。结果表明,ε-CMODE算法能有效求解齿轮机构多目标优化问题,得到均匀分布的Pareto前沿,可为设计人员提供多组备选解。     

齿轮减速器的多目标可靠性优化设计

提出一种以可靠度为目标函数和约束条件的多目标齿轮减速器优化设计方法。将可靠性引入齿轮减速器的确定性优化,考虑可靠度为设计目标和设计约束,并将小齿轮齿数作为离散确定性设计变量,进而构造出具有离散变量的多目标可靠性优化设计模型。提出在分支界定算法中嵌套遗传算法构造该优化问题的求解算法。该算法利用分支界定算法的遍历性和遗传算法的全局性,以获得优化问题的全局性解。最后,分别给出齿轮减速器的连续变量确定性解和可靠性解、混合变量确定性解和可靠性解,用以验证方法的有效性。     

基于双极偏好占优的多目标进化算法及其应用

为有效处理决策者能够提供双极偏好信息的多目标优化问题,加快原有算法的收敛速度,借鉴逼近理想解方法和搜索空间区域划分思想,定义了一种新型双极偏好占优关系,并引入到NSGA-Ⅱ算法中,设计了相应的非支配排序策略、种群多样性策略和约束处理策略,提出一种基于双极偏好占优的NSGA-Ⅱ算法（2p-NSGA-Ⅱ）。将该算法应用于求解两桁架结构设计的工程问题,对比仿真实验结果表明了2p-NSGA-Ⅱ算法的有效性。     

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。     

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。     

喷漆机器人喷漆工艺分析及优化研究

根据现今汽车行业的质量标准,分析了汽车喷涂工艺过程中的实际工作条件,建立带约束条件的多目标优化问题的数学模型,并选取用时最短和漆膜厚度方差最小为目标函数,利用非劣排序遗传算法（NSGA-Ⅱ）的优化方法,得到pareto最优解集。结果表明该优化算法能有效地解决多目标非线性约束优化问题。     

数控速度规划中的时间最优凸优化方法

针对数控高速高精加工中的速度规划问题,考虑速度、电机力矩和轮廓误差等约束条件,对以时间最优为目标的凸优化方法进行了研究。建立了包含轮廓误差等约束与速度平滑因子的完整速度规划模型,通过参数离散化使问题转化为静态最优问题。为改善求解效率并保证全局最优解,将离散规划模型中的复杂非凸目标函数和约束通过数学变换最终转化为凸优化问题,得到多项式时间的全局最优解。通过数值仿真实验验证了该方法的有效性,分析了平滑因子的影响与计算效率。     

一种新的多目标工程问题的优化方法

基于多目标优化设计中理想点法及约束法的基本思想，吸取线性加权法中权系数的处理方法，通过构造新的评价函数来求设计者满足的非劣解；并与混合离散变量的组合型法结合起来，从而形成多目标混合离散变量的优化方法。该方法对工程问题优化设计具有普遍的适用性。     

一种三自由度冲压搬运机械手的尺度综合

设计了一种用在管材冲压线上,代替人工完成上、下料动作的三自由度冲压搬运机械手,对该机械手进行工作空间求解和优化设计,以运动学、动力学性能指标为目标函数,以工作空间和静刚度指标为约束条件,以杆件参数和拉簧参数为设计变量,建立机械手的多目标优化模型。用非支配排序遗传算法(Non-dominated Sorting Genetic Algorithm-Ⅱ,NSGA-Ⅱ)求解多目标优化模型,在Pareto最优解集中优先选择降低电动机2极限力矩的解,且所选解不能大幅削弱其他性能指标。将所选解代入运动学、动力学方程中进行理论计算,结果表明,优化后机械手的运动学、动力学性能指标均有了一定程度的改善,为结构设计和运动控制提供了依据。     

柔性剪切蒙皮支撑结构的拓扑优化

为了求解关于柔性剪切蒙皮支撑结构的多目标拓扑优化问题,提出了一种带有多重约束处理能力的位矩阵表示的非支配排序遗传算法。采用位矩阵作为遗传算法的染色体并引入基于矩阵操作的遗传算子,利用Ansys有限元分析获得结构质量、面内剪切性能和面外承载能力等目标。利用Matlab处理结构连通性和面内应变等约束并实现了基于矩阵的优化算法,获得了一系列可行的柔性剪切蒙皮支撑结构,在实际应用中可以根据需要选择合适的结构。从研究结果可以看出,该算法可以给多目标二维结构拓扑优化问题提供可行有效的解。     

Multi-objective optimization of cutting parameters in turning process using differential evolution and non-dominated sorting genetic algorithm-II approaches

Optimization techniques using evolutionary algorithm (EA) are becoming more popular in engineering design and manufacturing activities because of the availability and affordability of high-speed computers. In this work, an attempt was made to solve multi-objective optimization problem in turning by using multi-objective differential evolution (MODE) algorithm and non-dominated sorting genetic algorithm(NSGA-II). Optimization in turning means determination of the optimal set of machining parameters to satisfy the objectives within the operational constraints. These objectives may be minimum tool wear, maximum metal removal rate or any weighted combination of both. The main machining parameters which are considered as variables of the optimization are cutting speed, feed rate, and depth of cut. The optimum set of these three input parameters is determined for a particular job-tool combination of EN24 steel and tungsten carbide during a single-pass turning which minimizes the tool wear and maximizes the metal removal rate after satisfying the constraints of temperature and surface roughness. The regression models, developed for tool wear, temperature, and surface roughness were used for the problem formulation. The non-dominated solution set obtained from MODE was compared with NSGA-II using the performance metrics and reported     

基于NSGA-II算法的超轻型火炮摇架多目标优化设计

针对超轻型火炮摇架减小质量、提高刚度的设计要求,基于有限元法和多目标优化设计方法,建立了摇架多目标优化数学模型。以摇架质量和刚度为优化目标,以摇架强度为约束条件,选择了摇架外形结构尺寸和摇架钢板厚度为设计参数,采用改进非支配排序遗传算法(NSGA-II)作为优化方法。通过优化得到了摇架Pareto最优解集,优化结果对超轻型火炮摇架设计具有指导意义,同时,该优化设计方法为处理薄壁结构优化问题提供了一种新的设计思路。     

基于NSGA Ⅱ的物流配送中车辆路径问题研究

车辆路径问题已经被证明属于NP—Hard问题。针对这一问题建立了多目标优化的数学模型;构造了带精英策略的快速非支配排序遗传算法,以求解车辆路径问题的数学模型,针对物流配送路径优化,将该算法从解决连续问题扩展为解决离散问题;进行了算法设计,提出了离散问题的快速非支配排序和锦标赛选择结合的子代选择方法,并修正了以往的初始群体生成、交叉和变异的方法。通过实例比较证明,该算法可以更好地解决物流配送路径优化的多目标问题,较快找到更优解,避免早熟收敛并改进算法性能,达到较高的搜索效率。     

基于MOPSO的航空发动机分支管路多目标布局优化

分支管路的布局优化属于NP难问题,其多目标优化情况则更加复杂。针对航空发动机分支管路多目标敷设问题,以分支管路长度最小化、分支点数量最小化以及管路平滑度最优为优化目标,建立了基于避障Steiner树的分支管路多目标布局模型。考虑到模型的复杂性,设计基于多目标粒子群优化（Multi-objective particle swarm optimization,MOPSO）的模型求解算法。其中,以分支点数量和坐标作为决策变量;针对分支管路拓扑结构特点,提出一种分支管路平滑度计算方法,结合非支配排序和网格密度计算完成个体多目标评价;通过可视图和测地线处理约束条件;通过多目标粒子群进化计算求得Pareto解集。所建立的分支管路多目标布局模型及求解算法考虑了多端点情况、多目标优化以及避障约束。最后通过管路敷设算例验证了可行性。     

A genetic algorithmic approach to multi-objective scheduling in a kanban-controlled flowshop with intermediate buffer and transport constraints

In this paper, we consider the problem of extended permutation flowshop scheduling with the intermediate buffers. The Kanban flowshop problem considered involves dual-blocking by both part type and queue size acting on machines, as well as on material handling. The objectives considered in this study include the minimization of mean completion time of containers, mean completion time of part types, and the standard deviation of mean completion time of part types. An attempt is made to solve the multi-objective problem by using a proposed genetic algorithm, called the “non-dominated and normalized distanceranked sorting multi-objective genetic algorithm” (NDSMGA). In order to evaluate the NDSMGA, we have made use of randomly generated flowshop scheduling problems with input and output buffer constraints in the flowshop. The non-dominated solutions for these problems are obtained from each of the existing methods, namely multi-objective genetic local search (MOGLS), elitist non-dominated sorting genetic algorithm (ENGA), gradual priority weighting genetic algorithm (GPWGA), modified MOGLS, and the NDSMGA. These non-dominated solutions are combined to obtain a net non-dominated solution set for a given problem. Contribution in terms of number of solutions to the net non-dominated solution set from each of these algorithms is tabulated, and the results reveal that a substantial number of non-dominated solutions are contributed by the NDSMGA.     

A genetic algorithmic approach to multi-objective scheduling in a Kanban-controlled flowshop with intermediate buffer and transport constraints

In this paper, we consider the problem of extended permutation flowshop scheduling with the intermediate buffers. The Kanban flowshop problem considered involves dual-blocking by both part type and queue size acting on machines, as well as on material handling. The objectives considered in this study include the minimization of mean completion time of containers, mean completion time of part types, and the standard deviation of mean completion time of part types. An attempt is made to solve the multi-objective problem by using a proposed genetic algorithm, called the “non-dominated and normalized distance-ranked sorting multi-objective genetic algorithm” (NDSMGA). In order to evaluate the NDSMGA, we have made use of randomly generated flowshop scheduling problems with input and output buffer constraints in the flowshop. The non-dominated solutions for these problems are obtained from each of the existing methods, namely multi-objective genetic local search (MOGLS), elitist non-dominated sorting genetic algorithm (ENGA), gradual priority weighting genetic algorithm (GPWGA), modified MOGLS, and the NDSMGA. These non-dominated solutions are combined to obtain a net non-dominated solution set for a given problem. Contribution in terms of number of solutions to the net non-dominated solution set from each of these algorithms is tabulated, and the results reveal that a substantial number of non-dominated solutions are contributed by the NDSMGA.     

基于Pareto挖掘的白车身侧碰安全件轻量化优化设计

为提高白车身轻量化优化效果,提出了熵权灰色关联分析法用于挖掘非支配Pareto解集中的最优解。建立了白车身及整车侧碰有限元模型,通过实车侧碰试验验证了所建模型的准确性。以侧碰安全件料厚为设计变量,综合考虑白车身弯扭刚度、振动频率等基本静-动态性能及侧碰安全性能,构建径向基函数神经网络结合Kriging（RBFNN-Kriging）混合近似模型并联合第二代非支配排序遗传算法（NSGA-Ⅱ算法）进行了多目标优化。最后,提出了熵权灰色关联分析法计算所有非支配Pareto解的灰色关联度,并以此为评价指标进行多目标决策。优化决策结果表明：在满足白车身性能设计基线的要求下,白车身侧碰安全件质量减小了2.68 kg,取得了较好的轻量化效果。     

Multi-objective optimization of drive gears for power split device using surrogate models

Power split device (PSD) is a key component in the energy coupling and decoupling of parallel-series hybrid electric vehicle. This paper proposes a multi-objective optimization method to achieve optimal balance solution among the volume, contact stress, and frictional energy dissipation of PSD drive gears, some of which are implicit with respect to design variables. To avoid the time-consuming problem of finite element analysis used to solve nonlinear responses, surrogate models are adopted to generate approximate expressions of design variables. Pareto-optimal solutions of PSD are obtained using multi-island genetic algorithm (MIGA), non-dominated sorting GA-II (NSGA-II), and multi-objective particle swarm optimization algorithm. The performances of PSD before and after optimization are compared. Results indicate that the proposed method is effective, and NSGA-II achieves higher optimizing efficiency in solving the multiobjective optimization problem of PSD than the other algorithms.     

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.