基于仿真试验和Kriging模型的多目标优化问题全局优化算法

针对复杂工程系统的多目标仿真优化问题,基于Kriging模型,提出一种将优化过程与试验过程相结合的全局多目标优化算法。该算法利用构造的加点准则序贯选取能应对约束和逼近真实Pareto解集的试验点,只需少量仿真试验就能得到优化问题的高精度Pareto解集。考虑试验点的可行性概率、间隔距离和Kriging模型的不确定性,设计亦能有效辨识非连通可行域的加点准则;提出以最大化试验点的期望超体积改进和可行性概率为目标的近似Pareto解集改进准则,使新试验点兼顾改进近似Pareto解集的质量和精确刻画可行域边界。通过三个数值算例将所提算法与已有算法进行比较,计算结果验证了所提算法的有效性和高效性。     

多目标拆卸线平衡问题的Pareto遗传模拟退火算法

针对传统方法求解多目标拆卸线平衡问题时求解结果单一、无法平衡各目标等不足,提出一种基于Pareto解集的多目标遗传模拟退火算法。该算法融合了遗传操作的快速全局搜索能力和模拟退火操作较强的局部搜索能力,对遗传操作的结果进行模拟退火操作,避免了算法陷入局部最优。结合多目标优化问题的特点,改进了模拟退火操作的Metropolis准则。根据拆卸序列之间的Pareto支配关系得到非劣解,并采用拥挤距离评价非劣解,实现了拆卸序列的精英保留,进而将非劣解添加到种群中,加快了算法的收敛速度。基于25项拆卸任务算例,通过与现有的6种单目标算法进行对比,验证了所提算法的有效性,并将所提算法应用于某拆卸线实例中,求得10种平衡方案,结果表明所提算法较Pareto蚁群算法更具优势。     

-种基于Pareto解集的无约束条件的多目标粒子群算法

鉴于多目标优化问题的广泛存在性以及目前关于它的研究还较少,且没有一种很好的、通用的多目标PSO算法,本文提出了一种基于Pareto解集的多目标粒子群算法.通过采用一个"记忆体"来存储当前得到的Pareto最优解,对每次迭代得到的Pareto解集里的解两两进行比较以选取一个较优的解作为更新方程中当前最优解,这样可以更好的引导粒子群进行下一步的寻优操作,最终得到一个完整的Pareto最优解集.几个测试函数的仿真实验结果也表明了该算法取得了很好的效果.     

供应链环境下产能优化配置问题的混合粒子群算法

针对供应链环境的协作特征,研究以下游企业需求为导向的产能优化配置,建立了以最大化企业盈利、设备利用率以及下游企业需求饱和度为目标的问题模型,并设计了基于精英集的多目标粒子群算法。算法结合模型的约束特征,采用约束满足技术生成初始解,基于惩罚函数的思想设计适应度函数,并对不可行解提出了修复规则;针对多目标优化特征,在求解过程中通过建立精英集来保存非劣解,并基于Pareto最优的概念更新精英集,利用基于k-means聚类的精英集裁剪策略,来保证精英集规模和粒子的分布性。实验结果表明了模型和算法的可行性和有效性。     

解决多目标优化问题的一种粒子群优化算法

优化设计已发展成为一种有效的新型工程设计方法.粒子群优化算法作为一种新型优化算法,逐渐被用于解决多目标优化问题.但目前研究还较少,本文提出了一种基于Pareto解集的多目标粒子群优化算法.采用一个"记忆体"来存储当前得到的Pareto最优解,对当前所得到的Pareto最优解进行相互比较,以确定一个较优的微粒作为微粒群更新方程中的全局极值,由此来引导其它粒子尽快向最优靠拢,达到算法收敛的目的.测试函数的仿真实验结果表明该算法取得了很好的效果.     

单曲柄双摇杆扑翼机构多目标优化设计

对单曲柄双摇杆仿生扑翼机构进行多目标优化设计,可为机构实际应用提供多组备选解。在单曲柄双摇杆机构运动分析的基础上,建立其约束多目标优化模型。其中,以最小化左右扑翼角之差的最大值和最大化扑翼角幅值为目标,以满足Grashof准则、力传递性能和仿生学规律等为约束条件。采用一种改进多目标进化算法——扇形采样约束多目标差分进化算法求解该多目标优化问题,得到多组满足约束条件的Pareto最优解。最后,对Pareto最优解和被支配解进行比较分析,结果表明,前者的目标函数值优于后者。     

基于模糊偏好的多目标粒子群算法的应用研究

研究了基于模糊偏好的多目标粒子群算法,算法将种群的最优解集进行Pareto排序,并动态更新Pareto解集,使其更快速的靠近Pareto前沿,对非劣解进行模糊评价,根据目标偏好的模糊信息,来确定折衷解的满意解。经典算例验证,该算法在计算时间及非劣解质量上,要优于多目标遗传算法。     

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。     

基于近似模型管理的微小卫星结构多目标优化设计

针对某型号微小卫星结构多目标优化的特性,在基于信赖域近似模型管理的基础上,提出了一种新型的近似模型管理框架。选取正交试验法和Kriging近似法用于构建近似模型,选取基于拥挤距离的粒子群多目标优化算法作为核心算法,并通过最大最小距离策略来保证信赖度计算的准确性与合理性,从而确保获取与高精度模型一致的非劣解集。所选的五组优化结果显示,卫星结构质量均有不同程度的减小, 最大减幅达到14.1%,同时整星前三阶固有频率较优化前明显提高。该近似模型管理框架在微小卫星结构多目标优化设计中的成功运用验证了其有效性及合理性,对于复杂工程多目标优化问题具有一定的工程应用价值。       

基于Kriging模型的多目标代理优化算法其收敛性评估

为提高黑箱系统优化设计的效率,基于Kriging模型、期望超体积改进和可行性概率准则,提出一种改进的多目标代理优化算法.该算法的可行域探索准则包含考虑试验点间距离的项,对可行域非连通的优化问题也有效;Pareto解集改进准则以同时优化期望超体积和可行性概率准则为目标,在改进Pareto解集的同时兼顾了对可行域边界的刻画;最后,结合条件模拟方法和随机集理论,提出一种不依赖真实解集的算法收敛性评估方法.通过两个算例将提出的优化算法与已有算法进行对比分析,结果证实了所提算法的高效性及算法收敛性评估方法的可行性.     

孔群加工路径规划问题的进化求解

孔群加工路径规划对于提高多孔类零件的加工效率和质量具有重要意义。建立了两个孔群加工路径规划问题的数学模型,分别归纳为单目标和多目标组合优化问题,并引入进化蚁群系统算法和人工免疫算法求解单目标组合优化问题。这两种算法均能有效防止解空间的“组合爆炸”问题,计算复杂度的阶次低于Hopfield神经网络算法,且性能优于Hopfield算法。采用多目标解的快速排序技术分别对进化蚁群系统算法和人工免疫算法加以改进,开发出多目标进化蚁群系统算法和多目标人工免疫算法。分析表明,改进算法不增加原算法的计算复杂度,能直接用于求解多目标组合优化问题而无需事先给出目标权值向量,并能一次运行求得问题的多个Pareto最优解。     

Application of the Genetic Algorithm to the Multi-Objective Optimization of Air Bearings

A feasible solution must be obtained in a reasonable time with high probability of global optimum for a complex tribological design problem. To meet this decisive requirement in a multi-objective optimization problem, the popular and powerful genetic algorithms (GAs) are adopted in an illustrated air bearing design. In this study, the goal of multi-objective optimization is achieved by incorporating the criterion of Pareto optimality in the selection of mating groups in the GAs. In the illustrated example the diversity of group members in the evolution process is much better maintained by using Pareto ranking method than that with the roulette wheel selection scheme. The final selection of the optimal point of the points satisfied the Pareto optimality is based on the minimum–maximum objective deviation criterion. It is shown that the application of the GA with the Pareto ranking is especially useful in dealing with multi-objective optimizations. A hybrid selection scheme combining the Pareto ranking and roulette wheel selections is also presented to deal with a problem with a combined single objective. With the early generations running the Pareto ranking criterion, the resultant divergence preserved in the population benefits the overall GA's performance. The presented procedure is readily adoptable for parallel computing, which deserves further study in tribological designs to improve the computational efficiency.     

基于高维多目标候鸟优化算法的柔性作业车间调度

针对柔性作业车间调度问题,提出一种改进的多目标候鸟优化算法来求解考虑完工时间、总拖期、机器总负荷以及总能耗的高维多目标问题。多目标候鸟优化算法在候鸟优化算法的基础上引入基于Pareto支配和参考点的选择算子来给予鸟群选择压力,并用基于属性层次模型和灰色关联分析法的组合权重法从最优解集中选择一个最合适的方案。算例和实例验证了算法的有效性和实用性。     

可逆约束系统参数匹配优化研究

针对可逆约束系统中可逆预紧式安全带与安全气囊优化匹配的问题,建立某车型驾驶员侧约束系统仿真模型,分别对碰撞前自动紧急制动作用下乘员动态响应,以及碰撞中乘员损伤指标进行验证分析。将试验设计,Kriging代理模型以及第二代多目标遗传算法相结合,以可逆约束系统6个关键参数为输入变量,以乘员头、胸、颈、大腿的损伤值为优化目标,开展多目标优化研究,并利用加权损伤指标(Weighted injury criteria,WIC)评价最优匹配方案。结果表明:与优化前相比较,优化后的约束系统能够有效降低乘员损伤值。当碰撞初速度为56 km/h时,最优匹配方案使胸部、颈部、大腿损伤值分别降低6.61%、28.99%、16.12%,WIC值降低4.99%,头部损伤值基本没有变化;将碰撞初速度增大至64 km/h后,最优匹配方案表现出更好的保护效果,乘员头部、胸部、颈部、大腿损伤值分别降低26.19%、33.21%、20.49%、6.11%,WIC值降低28.01%。     

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.     

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.     

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.     

求解物流Web服务组合问题的两阶段多目标蚁群算法

针对基于QoS的物流Web服务组合优化问题,提出了两阶段多目标蚁群优化(TMACO)算法。首先,针对原始数据集中存在被支配候选服务而增加算法求解时间的问题,提出了基于Pareto支配的预优化策略;其次,针对属性权重难以确定的问题,提出了不依赖权重的信息素更新策略和启发信息策略;最后,针对基础蚁群算法容易陷入局部最优的问题,提出了懒蚂蚁策略。实验结果表明,TMACO算法具有良好性能,相对于基础蚁群算法、利用解与理想解距离来更新信息素的改进蚁群算法、遗传算法以及用支配程度作为解的个体评价的改进遗传算法,TMACO算法有更高的寻优能力,能够找到更多更优的非劣解。     

多目标混合流水车间作业调度的演化算法

针对多目标条件下混合流水车间作业调度的优化问题,提出了一种在优化进程中能够动态调整适应度分配的演化算法。该算法采用矩阵编码描述多阶段并行机调度方案,结合问题的优化模型,对每一代Pareto解在各目标方向上的改善程度进行度量,进而通过多目标的选择性权重系数计算种群个体的适应度,以获得在改善指示方向上的选择压力。通过BENCHMARK问题测试和实际算例分析,表明新算法的性能优于现有的求解算法,特别是对于高维多目标优化问题,能够获得较高的演化收敛速度。     

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.