基于小生境改进粒子群算法的几何约束求解

几何约束问题可以等价为求解非线性方程组问题。几何约束问题先被转化为一个优化问题。采用基于小生境改进粒子群优化算法来求解该优化问题。由于经典粒子群优化算法容易陷入局部最优,出现早熟现象。为此,基于小生境原理,提出一种小生境改进粒子群优化算法(niche improved particle swarm optimization,NIPSO)。该算法在进行速度和位置更新后,根据小生境数确定个体历史最好位置中的孤立点。然后对所有个体历史最好值差于孤立点值的粒子使用交叉和选择算子进行更新。实验表明,该方法可以提高几何约束求解的效率和收敛性。     

基于多色集合约束模型的车间层印刷电路板组装优化

针对多组装设备、多组装任务的车间层印刷电路板（PCB）组装优化问题，提出了一种将多色集合与遗传算法（GA）相结合的新的优化方法。基于多色集合理论，用数值围道矩阵描述了复杂PCB组装工艺流程中组装优化问题的设备资源约束和工艺约束，建立了PCB组装的优化约束模型。约束模型使得遗传算法始终在有效解空间中进行搜索，不仅简化了GA适应度值的计算，还可通过约束模型的简单修改，动态描述受设备故障和组装任务变化等因素影响的车间层组装优化问题。实例计算结果表明，该方法能显著提高车间层PCB组装优化问题的求解效率，实现车间层PCB组装的动态优化。     

最小化板坯盈余问题的约束满足求解算法

针对热轧薄板生产中板坯设计环节的最小化板坯盈余问题,建立了问题的约束满足优化模型;通过0-1背包问题的多项式归结,证明了问题的NP难复杂性。针对问题的特殊性质,给出了变量选择策略和值选择策略,在此基础上,提出了基于约束满足的求解算法;通过数据实验进一步验证了算法的可行性和有效性。     

基于KS函数求解多约束优化问题研究

针对机械优化设计中常见的多约束优化问题，提出了一种求解新方法：利用KS函数的凝聚特性，将优化问题中的全部或部分约束凝聚为一个近似的、逼近精度仅由一个参数控制的约束，然后，再对约束压缩后的优化问题选用适当的约束优化方法求解。三维空间中一例可行域的图形给出了约束凝聚的几何解释。实例证明，由于压缩了求解规模，此法收敛稳定且速度快。     

产能及周期约束下制造系统能力配置优化

定制型装备制造系统设备能力配置优化属于非线性整数规划问题。由于产能、周期约束均无法封闭表达等原因,其精确解求取非常困难。为此,提出一种目标函数最优值上、下界逐步逼近的近似优化方法。描述了定制型装备制造系统能力配置问题,并以最小化设备投资为目标建立了数学模型;介绍了数学分析与仿真优化相结合的近似优化方法整体思路;阐述了目标函数最优值初始上、下界的获取,逐步改进直至逼近目标函数最优值的过程。通过实例验证了所提方法,并与产能单约束能力配置结果进行了对比。分析表明考虑周期约束将增加设备投资,所提方法和所获结果可为企业优化配置资源提供决策支持。     

优化法求解几何约束的问题

几何约束的求解对于变量设计系统是最为关键的问题，提出用优化求解的方法来求解循环约束，一定程度上克服了Newton-Raphson算法的不稳定性，且可较容易地求解欠约束和过约束的问题。     

网络化协作加工设备约束特性及一种优化选择方法

针对网络化协作加工设备优化选择过程中加工设备种类繁多、优选目标多样、设备属性与优选目标之间约束关系复杂等问题,建立了网络化协作加工设备的属性构成模型,在此基础上建立了一种包括网络化协作加工设备属性、优化选择目标及其之间的约束关系的约束特性框架模型,进而基于粗糙集理论建立了获取约束特性函数的数学模型,提出了一种基于约束特性的网络化协作加工设备优化选择方法并进行了算法求解,最后设计并开发了网络化协作加工设备优化选择支持系统,并在重庆某企业进行了试验应用,取得了较好的效果。     

基于单调性分析的智能优化设计系统

提出一种基于单调性分析和计算机符号处理、人工智能技术的智能优化设计系统。并提出一种利用单调性分析的变量边界区间缩小方法，通过系统的测试、分解等，在不需求助于传统的优化方法的情况下，判断出许多工程优化问题，包括一些带有非单调性函数的问题的全部松约束和紧约束，从而可以求出问题的全局最优解。     

制造加工约束下连续体拓扑优化的数值实现

针对两类常见的制造加工约束即对称性和重复性下的连续体拓扑优化问题,提出了将敏度值在每轮优化前的修正方法,该方法简单且易于编程实现,实现了对称性或重复性约束条件下连续体拓扑优化设计,通过数值算例对不同制造加工约束下的拓扑结果进行了分析对比,结果表明,研究方法具有可行性和有效性。     

逆向工程中基于几何约束的汽车零部件模型重建

结合汽车变速籀、发动机零部件的精密测量和数字建模，考虑零部件实物模型中的隐含约束关系，提出了基于几何约束的模型重建和优化求解方法。该方法把约束按照优先等级顺序添加到约束图中，应用自由度分析法建立协调的约束系统，把复杂约束问题分解为约束子问题进行求解。将该方法应用于变速箱零部件模型重建中，所得到的几何模型较好地反映了原始设计意图，满足产品装配精度要求。     

基于惩罚和修复策略的约束优化遗传算法

约束优化问题中最难以解决的就是约束处理问题,将惩罚函数法与修复策略相结合应用于非线性约束优化遗传算法之中,使得约束优化问题在惩罚函数和修复算子的协同作用下收敛于全局最优,有效避免了迭代过程中大量非可行解的产生,解决了在遗传算法约束优化问题中单独使用惩罚和修复方法时一些难以解决的问题。基于随机方向法构造的修复算子作用效果显著,采用多个测试函数对算法进行检验,均能较好地收敛于可行域中的最优解,验证了算法的可靠性。     

扩展拉格朗日乘子粒子群算法解决工程优化问题

工程上很多优化问题,如容器设计、波纹管、板翅式换热器的结构优化设计等,皆为非线性约束优化设计问题,常采用惩罚函数法处理约束条件;为获得问题最优解,该方法需要合理确定初始惩罚因子,且需要动态惩罚因子无穷大。扩展拉格朗日乘子法是一种改进的惩罚函数法,可以克服惩罚函数法的不足,获得全局最优解,但目前对其研究和应用有限。对拉格朗日乘子法与粒子群算法相结合处理非线性约束问题进行研究,提出惩罚因子更新策略,确定扩展拉格朗日乘子粒子群算法合理的操作过程。标准测试函数结果显示：提出的方法及策略实现了扩展拉格朗日乘子粒子群算法解决非线性约束问题,并得到了问题的全局最优解;其在容器及波纹管系列优化设计中的应用进一步显示,提出的方法在处理非线性约束工程实际问题时,运行稳定可靠,可快捷获得问题的全局最优解或近似最优解。     

基于混合遗传算法的齿轮传动优化设计

以体积最小为目标函数,建立了齿轮传动优化设计数学模型,并用外部惩罚函数法将该问题转化为无约束优化问题。针对遗传算法的局限性,采用整数编码和实数编码结合的混合编码,并调整了适应函数,采用随机多父辈适应函数值加权交叉和自适应变异操作,结合了模拟退火算法,给出了初温的确定方法,从而形成了混合遗传算法。该算法能够有效地减少不可行解的产生,提高收敛速度,避免早熟收敛。算例说明,该优化方法有效、实用。     

Concept optimization for mechanical product using Genetic Algorithm

Conceptual design is the first step in the overall process of product design. Its intrinsic uncertainty, imprecision, and lack of information lead to the fact that current conceptual design activities in engineering have not been computerized and very few CAD systems are available to support conceptual design. In most of the current intelligent design systems, approach of principle synthesis, such as morphology matrix, bond graphic, or design catalogues, is usually adopted to deal with the concept generation, in which optional concepts are generally combined and enumerated through function analysis. However, as a large number of concepts are generated, it is difficult to evaluate and optimize these design candidates using regular algorithm. It is necessary to develop a new approach or a tool to solve the concept generation. Generally speaking, concept generation is a problem of concept synthesis. In substance, this process of developing design candidate is a combinatorial optimization process, viz., the process of concept generation can be regarded as a solution for a state-place composed of multi-concepts. In this paper, genetic algorithm is utilized as a feasible tool to solve the problem of combinatorial optimizalion in concept generation, in which the encoding method of morphology matrix based on function analysis is applied, and a sequence of optimal concepts are generated through the search and iterative process which is controlled by genetic operators, including selection, crossover, mutation, and reproduction in GA. Several crucial problems on GA are discussed in this paper, such as the calculation of fitness value and the criteria for heredity termination, which have a heavy effect on selection of better concepts. The feasibility and intellectualization of the proposed approach are demonstrated with an engineering case. In this work concept generation is implemented using GA, which can facilitate not only generating several better concepts, but also selecting the best concept. Thus optimal concepts can be conveniently developed and design efficiency can be greatly improved.     

一种改进遗传算法及在结构优化设计中的应用

针对简单遗传算法中的线性适应度、恒定交叉与变异概率等不能动态地适应整个寻优过程，提出采用非线性适应度与自适应交叉、变异概率的改进遗传算法。以典型的遗传算法测试函数验证改进遗传算法的有效性与可行性，最后将改进遗传算法用于离散变量桁架结构优化设计，计算结果表明改进遗传算法是可行、有效的。     

Data-driven RLV multi-objective reentry trajectory optimization based on new QABC algorithm

In recent years, big data and cloud technology have been widely used in information extraction and optimization decision. An improved artificial bees colony (ABC) algorithm called QABC is proposed for optimum design of the reusable launch vehicle (RLV) reentry trajectory. Because of poor convergence property of classical ABC algorithm in solving constrained nonlinear optimization problems (CNOPs), several modifications are carried out in this paper. The modifications include a quantum delta potential well model, two dynamic tolerance mechanisms, and a general generation mechanism of selection probability which is associated with the fitness of food source. In this paper, taking RLV three-dimension reentry trajectory design as an application example, a single-objective/multi-constraints optimization model was established with physical programming (PP) method and static penalty function method, in which four objectives (maximum range, minimum heat load, minimum heat flux (MHF), minimum oscillation) and five constraints (dynamic pressure, overload, heat flow, terminal altitude, and terminal velocity) were taken into account. Four single objective trajectory designs and two typical multi-objective trajectory designs with different preference structures were resolved, and the results showed that the optimization model founded by PP method was effective and flexible to reflect the designers preference. The improved algorithm, QABC, show excellent performance in solving RLV reentry trajectory optimization problem and a good prospect in other engineering applications.     

大型产品结构优化问题的病毒进化遗传算法

针对一种大型产品结构的质量－成本优化问题，设计了一种病毒进化遗传算法，提出了相应的编码解码方案和适应度的计算。病毒进化遗传算法是一种协同进化算法，既实现了遗传操作在父子代群体间纵向继承进化信息进行全局搜索的功能，也实现了病毒感染操作在同一代群体中横向传播进化信息进行局部搜索的功能，从而可以比遗传算法较快获得问题的满意解。最后给出了病毒进化遗传算法的试验仿真结果。     

非稳态罚函数遗传算法及其用于机械/结构系统的健壮性设计

在机械 /结构的优化设计中 ,普遍存在约束的作用 ,且最优解往往位于可行域的边界上。由于外界环境的变化或人为因素造成设计变量扰动 ,可能使设计成为不可行。本文提出了一种基于设计变量敏感性的健壮性设计方法 ,并用非稳态罚函数遗传算法来实现多目标优化设计。     

Effect of manufacturing tolerances on indexing accuracy and synthesis of the Geneva Mechanism

Machine tools used for batch and mass production are generally equipped with the Geneva Mechanism for indexing. One of the factors affecting the machining accuracy in these machine tools is the positional accuracy of the tools with respect to the work which, in turn, is affected by the indexing accuracy of the indexing mechanism. This paper discusses the effect of manufacturing tolerances on indexing accuracy. It is observed that indexing accuracy is different for constrained and unconstrained designs corresponding to the same value of tolerance. Results regarding indexing accuracy for different values of tolerances in constrained designs are recorded and suggest that, in the case of constrained designs, careful allocation of tolerances on design parameters is needed. The method of tolerance allocation suggested by Choubey and Atluri⁸ is followed. Synthesis of a six-slot Geneva Mechanism incorporating manufacturing tolerances and following stochastic non-linear programming and the exterior penalty function method is carried out to study these effects. Practical implications of the effects of manufacturing tolerances on indexing accuracy and synthesis of Geneva drives are discussed, giving suitable examples     

Optimal Placement of Active Members in Truss Adaptive Structures

The mathematical model of optimal placement of active members in truss adaptive structures is essentially a nonlinear multi-objective optimization problem with mixed variables,it is usually much difficult and costly to be solved.In this paper,the optimal location of active members is treated in terms of(0,1)discrete variables.Structural member sizes,control gains,and(0,1)placement variables are treated simultaneously as design variables.Then,a succinct and reasonable compromise scalar model,which is transformed from original multi-objective optimization,is established,in which the(0,1)discrete variables are converted into an equality constraint.Secondly,by penalty function approach,the subsequent scalar mixed variable compromise model can be formulated equivalently as a sequence of continuous variable problems.Thirdly,for each continuous problem in the sequence,by choosing intermediate design variables and temporary critical constraints,the approximation concept is carried out to generate a sequence of explicit approximate problems which enhance the quality of the approximate design problems.Considering the proposed method,a FORTRAN program OPAMTAS2.0 for optimal placement of active members in truss adaptive structures is developed,which is used by the constrained variable metric method with the watchdog technique(CVMW method).Finally,a typical 18 bar truss adaptive structure as test numerical examples is presented to illustrate that the design methodology set forth is simple,feasible,efficient and stable.The established scalar mixed variable compromise model that can avoid the ill-conditioned possibility caused by the different orders of magnitude of various objective functions in optimization process,therefore,it enables the optimization algorithm to have a good stability.On the other hand,the proposed novel optimization technique can make both discrete and continuous variables be optimized simultaneously.