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.     

Concurrent multi-objective tolerance allocation of mechanical assemblies considering alternative manufacturing process selection

Concurrent design of tolerances by considering both the manufacturing cost and quality loss of each component by alternate processes of the assemblies may ensure the manufacturability, reduce the manufacturing costs, decrease the number of fraction nonconforming (or defective rate), and shorten the production lead time. Most of the current tolerance design research does not consider the quality loss. In this paper, a novel multi-objective optimization method is proposed to enhance the operations of the non-traditional algorithms (Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO)) and systematically distribute the tolerances among various the components of mechanical assemblies. The problem has a multi-criterion character in which three objective functions, one constraint, and three variables are considered. The average fitness factor method and normalized weighted objective function method are used to select the best optimal solution from Pareto-optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto-optimal fronts. Two more multi-objective performance measures namely optimizer overhead and algorithm effort are used to find the computational effort of NSGA-II and MOPSO algorithms. The Pareto-optimal fronts and results obtained from various techniques are compared and analysed. Both NSGA-II and MOPSO algorithms are best for this problem.     

Product configuration optimization using a multiobjective genetic algorithm

Product configuration is one of the key technologies in the environment of mass customization. Traditional product configuration technology focuses on constraints-based or knowledge-based application, which makes it very difficult to optimize design of product configuration. In this paper, an approach based on multiobjective genetic algorithm is proposed to solve the problem. Firstly, a configuration-oriented product model is discussed. A multiobjective optimization problem of product configuration according to the model is described and its mathematical formulation is designed. Secondly, a multiobjective genetic algorithm is designed for finding near Pareto or Pareto optimal set for the problem. A matrix method used to check constraint is proposed, and the coding and decoding representation of the solution are designed, then a new genetic evaluation and select mechanism is proposed. Finally, performance comparison of the proposed genetic algorithm with three other genetic algorithms is made. The result shows that the proposed genetic algorithm outperforms the other genetic algorithms in this problem.     

基于多目标遗传算法的水陆两栖可变形机器人结构参数设计方法

水陆两栖可变形机器人是一种兼具变形能力与两栖环境适应能力的新型移动机器人。在其机构设计中,结构参数直接影响该机器人在任务环境中的各项机动性能。针对水陆两栖可变形机器人工作环境复杂性和任务多变性,提出一种基于多目标遗传算法的机器人结构参数设计方法,以得到该型机器人在两栖环境中的最优的综合性能。在水陆两栖可变形机器人陆地环境和水环境中运动学和动力学模型基础上,建立两栖环境中机器人的机动性能指标函数与结构参数的映射关系,并在此基础之上构建面向水陆两栖可变形机器人的结构参数设计的多目标优化问题。利用多目标遗传算法得到该多目标机构参数设计问题的Pareto最优解集,并且通过组合赋权方法确定各目标决策属性的权重,从Pareto最优解集中得到符合设计要求的水陆两栖可变形机器人的各项机构参数最优解,进而指导机器人最终结构参数设计。根据最终得到的结构参数研制出水陆两栖可变形机器人样机Amoeba-II,并在两栖环境下进行样机的各项性能试验,最终验证了基于多目标遗传算法的机器人结构参数设计方法的有效性以及在机器人设计中的适用性。     

基于双层配置体系的产品配置算法研究

在大规模定制生产模式下,产品配置遇到了复杂模糊配置数据的处理问题,为此,提出了基于实例重用的产品配置模糊求解技术,设计了基于多目标遗传算法的产品配置优化算法.将产品配置过程划分为部件配置与零件配置两部分,利用典型条件概率解决产品配置领域的部件模糊配置问题,设计了基于非支配排序遗传算法-Ⅱ,求解以成本、时间和库存为优化目标的零件配置,并结合两者建立完整的产品配置求解算法体系.该算法有效地解决了复杂产品配置中模糊数据处理及配置组合爆炸的问题.     

An optimization strategy for die design in the low-density polyethylene annular extrusion process based on FES/BPNN/NSGA-II

An optimization strategy for die design in the polymer extrusion process is proposed in the study based on the finite element simulation, the back-propagation neural network, and the non-dominated sorting genetic algorithm II (NSGA-II). The three-dimensional simulation of polymer melts flow in the extrusion process is conducted using the penalty finite element method. The model for predicting the flow patterns in the extrusion process is established with the artificial neural network based on the simulated results. The non-dominated sorting genetic algorithm II is performed for the search of globally optimal design variables with its objective functions evaluated by the established neural network model. The proposed optimization strategy is successfully applied to the die design in low-density polyethylene (LDPE) annular extrusion process. A constrained multi-objective optimization model is established according to the characteristics of annular extrusion process. The minimum of velocity relative difference, δu, and the minimum of swell ratio, S _w, that, respectively, ensure the extrinsic feature, mechanical property, and dimensional precision of the final products are taken as optimization objectives with a constrained condition on the maximum shear stress. Three important die structure parameters, including the die contraction angle α, the ratio of parallel length to inner radius L/R _i, and the ratio of outer to inner radius R _o /R _i, are taken as design variables. The Phan-Thien–Tanner constitutive model is adopted to describe the viscoelastic rheological characteristics of LDPE whose parameters are fitted by the distributions of material functions detected on the strain-controlled rheometer. The penalty finite element model of polymer melts flowing through out of the extrusion die is derived. A decoupled method is employed to solve the viscoelastic flow problem with the discrete elastic-viscous split-stress algorithm. The simulated results are selected and extracted to constitute the learning samples according to the orthogonal experimental design method. The back propagation algorithm is adopted for the training and the establishment of the predicting model for the optimization objective. A Pareto-optimal set for the constrained multi-objective optimization is obtained using the constrained NSGA-II, and the optimal solution is extracted based on the fuzzy set theory. The optimization for die parameters in the annular extrusion process of low-density polyethylene is performed and the optimization objective is successfully achieved.     

基于改进非支配排序遗传算法的正铲挖掘机工作装置优化设计*

采用多目标进化算法对正铲挖掘机工作装置进行优化设计,目标是水平直线挖掘铲斗切削后角变化量、主要挖掘区域内纵向斗杆挖掘最大挖掘力和纵向铲斗挖掘最大挖掘力3个性能指标。针对NSGA-II处理具有复杂Pareto最优前端优化问题能力不足的问题,提出动态拥挤排序策略,提高算法求解的多样性,引入差分算子和柯西变异算子,提高算法的全局寻优能力。使用ZDT系列测试函数对改进算法进行测试研究,结果表明改进算法的收敛性指标和多样性指标均有很大提高,能够很好地处理具有复杂Pareto最优前端的优化问题。基于改进的优化算法对正铲挖掘机工作装置进行优化设计,并利用理想解法得到了最满意优化方案,优化结果表明了改进算法应用于实际工程问题的有效性和可行性。     

单平台下参数化产品族设计的两阶段智能优化算法

基于对参数化产品族优化设计问题特性的分析,提出了单平台下参数化产品族的两阶段优化设计方法。针对单平台产品族优化设计的特征,给出了单平台下参数化产品族优化设计的一般数学模型,在此基础上提出了平台变量值预先设定时的产品族优化模型,给出了采用拥挤距离排序的多目标约束遗传算法（CDSMOGA）对该模型进行优化求解的过程。对单平台下平台变量值已知时的通用电动机产品族优化数学模型进行了仿真运算。对比仿真结果与国内外文献中的相关结果发现,所提出的方法能够显著改善产品族的整体性能,在参数化产品族的优化设计上是有效的。     

Performance enhancement of axial fan blade through multi-objective optimization techniques

This paper presents an axial fan blade design optimization method incorporating a hybrid multi-objective evolutionary algorithm (hybrid MOEA). In flow analyses, Reynolds-averaged Navier-Stokes (RANS) equations were solved using the shear stress transport turbulence model. The numerical results for the axial and tangential velocities were validated by comparing them with experimental data. Six design variables relating to the blade lean angle and the blade profile were selected through Latin hypercube sampling of design of experiments (DOE) to generate design points within the selected design space. Two objective functions, namely, total efficiency and torque, were employed, and multi-objective optimization was carried out, to enhance the performance. A surrogate model, Response Surface Approximation (RSA), was constructed for each objective function based on the numerical solutions obtained at the specified design points. The Non-dominated Sorting of Genetic Algorithm (NSGA-II) with local search was used for multi-objective optimization. The Pareto-optimal solutions were obtained, and a trade-off analysis was performed between the two conflicting objectives in view of the design and flow constraints. It was observed that, by the process of multi-objective optimization, the total efficiency was enhanced and the torque reduced. The mechanisms of these performance improvements were elucidated by analysis of the Pareto-optimal solutions.     

Multi-objective dynamic optimal trajectory planning of robot manipulators in the presence of obstacles

In this paper, a real-world test problem is presented and made available for the use of evolutionary multi-objective community. The generation of manipulator trajectories by considering multiple objectives and obstacle avoidance is a non-trivial optimisation problem. In this paper two multi-objective evolutionary algorithms viz., elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) algorithm are proposed to address this problem. Multiple criteria are optimised to two simultaneous objectives. Simulations results are presented for industrial robots with two degrees of freedom (Cartesian robot (PP) with two prismatic joints) and six degrees of freedom (PUMA 560 robot), by considering two objectives optimisation. Two methods (normalized weighting objective functions and average fuzzy membership function) are used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find computational effort of NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.     

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     

无公用平台下的参数化产品族多目标智能优化

在忽略产品间共性约束的条件下,参数化产品族整体性能的优化实际上等价于产品族内系列产品的独立优化。基于参数化产品族优化问题的复杂性,提出了一种基于拥挤距离排序的多目标多约束遗传算法（CDSMOGA）,并将其用于求解无公用平台下的产品族优化问题。通用电动机产品族设计实例的仿真试验结果表明,CDSMOGA所得产品族优化设计方案整体性能显著优于被比较方案,验证了该方法的有效性和可行性。     

Multi-objective optimization of collaborative manufacturing chain with time-sequence constraints

To realize the sharing and optimization deployment of manufacturing resources, a concept of collaborative manufacturing chain (CMC) is proposed for the manufacturing of complex products in a networked manufacturing environment. To acquire the optimal CMC, a multi-objective optimization model is developed to minimize the comprehensive cost and the whole production load with time-sequence constraints. Non-dominated sorting genetic algorithm (NSGA-II) is applied to solve optimization functions. The optimal solution set of Pareto is obtained. The technique for order preference by similarity to ideal solution (TOPSIS) approach is then used to identify the optimal compromise solution from the optimal solution set of Pareto. Simulation results obtained in this study indicate that the proposed model and algorithm are able to obtain satisfactory solutions.     

基于多目标遗传算法的产品优化配置研究

针对产品配置设计存在的问题，提出一种基于多目标遗传算法的产品优化配置方法，设计了相应编码解码方案和适应度计算方法，在具体算法中，对小生境的范围确定和精英策略提出改进。仿真实验证明，该算法可行有效，优于其他遗传算法。     

多目标柔性作业车间调度决策精选机制研究

针对多目标柔性作业车间调度优化无法找到唯一最优解的问题，提出多目标遗传算法和层次分析法模糊综合评判的分阶段优化策略。提出优化阶段和精选阶段的优化任务，优化阶段选出一组Pareto解集，精选阶段从Pareto解集中选出最优解；在精选阶段运用层次分析法和模糊评判集成的策略精选调度决策。决策算例证明提出的方法是可行的，可很好地帮助决策者选择出一个最满意的解。     

基于多目标优化的乘用车后排座椅轻量化设计

提出第二代非劣排序遗传算法(NSGA-II)结合响应面法(RSM)-径向基神经网络方法(RBF)混合近似模型和逼近理想解排序(TOPSIS)方法对某乘用车后排座椅进行结构-材料一体化多目标轻量化设计研究。结合有限元理论建立仿真模型,并通过行李箱碰撞试验验证仿真模型的正确性,根据工程经验和座椅靠背骨架吸能分析确定了6个优化部件厚度、材料的设计变量及取值范围;采用RSM-RBF混合近似模型方法拟合设计变量与响应之间的关系;利用NSGA-Ⅱ算法对优化问题进行求解,得到Pareto最优解集。最后采用基于熵权TOPSIS方法对Pareto最优解集进行排序确定最佳折中解。结果表明:在满足各项安全性能法规的前提下,乘用车后排座椅减重3.57 kg。     

A hybrid method of modified NSGA-II and TOPSIS for lightweight design of parameterized passenger car sub-frame

This paper presents a hybrid method integrating modified NSGA-II and TOPSIS, used for lightweight design of the front sub-frame of a passenger car. Firstly, the FE model of the sub-frame is constructed and is validated by modal test. Then, the strength performance of the sub-frame is analyzed under four typical load conditions consisting of braking, acceleration, steady state cornering and vertical bump. After that, a parameterized model of the sub-frame, in which 12 geometric parameters are defined as design variables, is developed based on the mesh morphing technology. Subsequently, modified NSGA-II is employed for multi-objective optimization of the sub-frame considering weight, maximum von-Mises stress and first order natural frequency as three conflicting objective functions. Accordingly, a set of Pareto-optimal solutions are obtained from the optimization process. Finally, the entropy weight theory and TOPSIS method are adopted to rank all these solutions from the best to the worst for determining the best compromise solution. In addition, the effectiveness of the proposed hybrid lightweight design method is demonstrated by the comparisons among baseline design and optimum solutions.     

Multi-objective optimization of cycloidal gear based on segmental modification of pressure angle

In order to get the optimal profile of cycloid gear after sectional modification, a multi-objective optimization design method is proposed that considers both the modification parameters and macro-parameters of the cycloid gear. An algorithm of meshing force, meshing efficiency and anti-gluing ability between the cycloid gear and the pin gear was derived, and the related independent parameters were extracted as optimization variables. Taking high efficiency, high strength and light weight as the objective, the mathematical models of double-objective and three-objective optimization were established, and the influence of key design variable on the objective function was analyzed, and NSGA-II multi-objective genetic algorithm was used to solve the Pareto optimal solution of the optimization mathematical model. Results show that the optimized parameters can significantly improve the meshing efficiency, reduce the volume and meet the design requirements of high strength, high efficiency and lightweight on the premise of ensuring the strength of cycloid gear surface.

     

Evolutionary bi-criteria optimum design of robots based on task specifications

The optimum robot structure design problem based on task specifications is an important one, since it has greater influence on manipulator workspace design, vibrations of the manipulator during operation, manipulator efficiency in the work environment and power consumption. In this paper, an optimization robot structure problem is formulated with the objective of determining the optimal geometric dimensions of the robot manipulators considering the task specifications (pick and place operation). The aim is to minimize torque required for motion and maximize manipulability measure of the robot subject to dynamic, kinematic, deflection and structural constraints with link physical characteristics (length and cross-sectional area parameters) as design variables. In this work, five different cross-sections (hollow circle, hollow square, hollow rectangle, C-channel and I-channel) have been experimented for the link. Three evolutionary optimization algorithms namely multi-objective genetic algorithm (MOGA), elitist nondominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) are used for the optimum structural design of 2-link and 3-link planar robots. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best optimal solution. Two multiobjective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the Pareto optimal fronts. Two more multiobjective performance measures namely optimiser overhead and algorithm effort, are used to find computational effort of optimization algorithm. The results obtained from various techniques are compared and analyzed.     

扇形采样约束多目标差分进化算法及工程应用

工程实践中存在大量约束多目标优化问题(Constrained multi-objective optimization problems, CMOPs),多目标进化算法是求解这类问题的一类有效方法。引入扇形采样技术,将二次变异双种群差分进化算法和约束处理方法相结合,设计求解CMOPs的进化算法——基于扇形采样的约束多目标差分进化算法(Sector-sampling-based constrained multi-objective differential evolution algorithm, SS-CMODE)。扇形采样可避免耗时的非劣操作,且能保证Pareto最优解集的良好逼近性和多样性。通过3个典型CMOPs的对比测试,表明SS-CMODE的解集均匀性和计算效率明显优于对比算法。以J23-80机械压力机使用的双曲柄串联机构多目标优化为例,研究新算法求解工程问题的有效性。以锻冲工作阶段平均速度波动最小和力传动性能最优为目标,建立机构的约束多目标优化模型,再应用SS-CMODE求解该问题。结果表明,该算法能求出多组满足约束条件的Pareto最优解,且解集均匀性良好。