一类优化问题的分解算法

讨论一类大规模系统的优化问题,提出一种递阶优化方法．该方法首先将原问题转化为多目标优化问题,证明了原问题的最优解在多目标优化问题的非劣解集中,给出了从多目标优化问题的解集中挑出原问题最优解的算法,建立了算法的理论基础．仿真结果验证了算法的有效性．

     

基于新型双目标模型的约束优化进化算法

利用双目标模型求解约束优化问题时,由于它们的最优解集并不相等,因此需要增加特殊机制确保求解双目标问题的算法收敛到原问题的最优解.为克服这一缺点,本文首先将约束优化问题转化为新的双目标优化模型,并证明了新模型的最优解集与原问题的最优解集相等.其次,以简单的差分进化为搜索算法,基于多目标Pareto支配关系的非支配排序为选择准则,提出了求解新模型的差分进化算法.最后,用10个标准测试函数的数值试验说明了新模型及求解算法的有效性.     

一种优化模糊神经网络的多目标微粒群算法

模糊神经网络优化是一个多目标优化问题．通过对模糊神经网络和微粒群算法的深入分析,提出了一种多目标微粒群算法．在算法中将网络的精确性和复杂性分别作为目标进行优化,再用一种启发性分量加权均值法来选取个体极值和全局极值．算法能够引导粒子较快地向非劣最优解区域移动并最终获得多个非劣最优解,为模糊神经网络的精确性和复杂性的折中寻优问题提供了一种解决方法．茶味觉信号识别的仿真实验验证了该算法的有效性．     

基于Pareto熵的多目标粒子群优化算法

粒子群优化算法因形式简洁、收敛快速和参数调节机制灵活等优点,同时一次运行可得到多个解,且能逼近非凸或不连续的Pareto最优前端,因而被认为是求解多目标优化问题最具潜力的方法之一.但当粒子群优化算法从单目标问题扩展到多目标问题时,Pareto最优解集的存储与维护、全局和个体最优解的选择以及开发与开采的平衡等问题亦随之出现.通过目标空间变换方法,采用Pareto前端在被称为平行格坐标系统的新目标空间中的分布熵及差熵评估种群的多样性及进化状态,并以此为反馈信息来设计进化策略,使得算法能够兼顾近似Pareto前端的收敛性和多样性.同时,引入格占优和格距离密度的概念来评估Pareto最优解的个体环境适应度,以此建立外部档案更新方法和全局最优解选择机制,最终形成了基于Pareto熵的多目标粒子群优化算法.实验结果表明：在IGD性能指标上,与另外8种对等算法相比,该算法在由ZDT和DTLZ系列组成的12个多目标测试问题集中表现出了显著的性能优势.     

MOPSO算法及其在水库优化调度中的应用

提出了一种新的多目标粒子群优化(MOPSO)算法，该算法采用自适应网格方法来估计非劣解集中粒子的密度信息、平衡全局和局部搜索能力的Pareto最优解的搜索机制、删除品质差的多余粒子的Archive集的修剪技术。通过对三峡梯级多目标优化调度问题的计算，表明该算法是求解大规模复杂多目标优化问题的一种有效手段。     

基于一种新模型的多目标遗传算法及性能分析

在多目标优化中,各目标通常相互冲突,其最优解往往有无穷多个,如何在最优解集中求出一组分布均匀且数量多的Pareto最优解供决策者选择十分重要.本文给出了多目标优化的一种新解法.首先定义了种群序值的理想方差和种群密度的方差,然后把目标个数任意的多目标函数优化问题Ⅰ转化成了用种群序值的理想方差和种群密度的方差构成的两个目标函数的优化问题Ⅱ,并对转化后的优化问题Ⅱ提出了一种新的多目标遗传算法(RDMOEA).计算机仿真表明RDMOEA算法对不同的实验函数均可求出在最优解集合中分布均匀且数量充足的Pareto最优解.     

改进非支配排序进化算法在下料问题中的应用

针对一维下料问题,提出了减少废料、减少下料设置时间和减少可回收余料的三目标优化模型,用改进的非支配排序进化算法求出问题的Pareto最优解集,运用逼近理想解方法从解集中选出一个满意解作为下料方案,各优化目标的权重用CRITIC法算出。仿真实验证明了所提出的方法可以有效解决该类多目标下料问题。     

基于Pareto的多目标优化免疫算法

免疫算法具有搜索效率高、避免过早收敛、群体优化、保持个体多样性等优点。将其应用于多目标优化问题,建立了一种新型的基于Pareto的多目标优化免疫算法(MOIA)。算法中,将优化问题的可行解对应抗体,优化问题的目标函数对应抗原,Pareto最优解被保存在记忆细胞集中,并利用有别于聚类的邻近排挤算法对其进行不断更新,进而获得分布均匀的Pareto最优解。文章最后,对MOIA算法与文献[3]中SPEA算法进行仿真,通过比较两者的收敛性和分布性,得到了MOIA优于SPEA的结论。     

梯度策略的多目标GANs帕累托最优解算法

针对基于梯度策略的多目标优化算法无法适用于多目标、高维度的生成对抗网络(Generative Adversarial Nets, GANs)及多目标GANs中利用交叉验证产生次优解,极难求得最优解等问题,提出一种基于梯度策略的多目标GANs帕累托最优解算法。该算法采用硬参数共享方式,将多目标优化分解为多个两目标优化,确定多目标权重参数后,沿着梯度方向进行线性搜索,最终确定帕累托最优解。理论上,在弱条件约束下,证明了所提算法能够确切地产生帕累托最优解。实验上,将所提算法应用到图像处理的常见领域,对比所提算法与原算法的性能。结果表明,当目标数量大于2时,所提算法能够产生明显的性能优势。     

基于不可行度和内分泌原理的多目标粒子群方法

针对有约束条件的多目标优化问题,提出了一种求解带约束的基于内分泌思想的多目标粒子群算法。利用不可行度方法和约束主导原理指导进化过程中精英种群的选择操作和约束条件的处理,根据生物体激素调节机制中促激素和释放激素间的相互作用原理,考虑当前非劣解集中的个体对其最邻近的一类群体的监督控制,引入当前粒子的类全局最优位置来反映其所属类中最好位置粒子对当前粒子的影响。为验证多目标约束优化算法的有效性,对两个典型的多目标优化问题进行了仿真实验,仿真结果表明该算法能较大概率地获得多目标约束优化问题的可行Pareto最优解。     

Extension of dynamic programming to nonseparable dynamic optimization problems

The use of dynamic programming is extended to a general nonseparable class where multiobjective optimization is used as a separation strategy. The original nonseparable dynamic optimization problem is first embedded into a separable, albeit multiobjective, optimization problem where multiobjective dynamic programming using the envelope approach is used as a solution scheme. Under certain conditions, the optimal solution of the original nonseparable problem is proven to be attained by a noninferior solution.     

基于粒子记忆体的多目标微粒群算法*

针对多目标微粒群算法(MOPSO)解的多样性分布问题,提出一种基于粒子记忆体的多目标微粒群算法(dp-MOPSO)。dp-MOPSO算法为每个微粒分配一个记忆体,保存寻优过程中搜索到的非支配pbest集,以避免搜索信息的丢失。采用外部存档保存种群搜索到的所有Pareto解,并引入动态邻域的策略从外部存档中选择全局最优解。利用几个典型的多目标测试函数对dp-MOPSO算法的性能进行测试,并与两种著名的多目标进化算法m-DNPSO、SPEA2进行比较。实验结果表明,dp-MOPSO算法可以更好地逼近真实Pareto沿,同时所得Pareto解分布更均匀。     

Hierarchical control for large-scale systems with general multiple linear-quadratic structure

A class of large-scale linear control systems, where the overall objective function is a nonlinear function of multiple quadratic performance indices, is investigated in this paper. This type of large-scale control problem with a general multiple linear-quadratic structure is nonseparable in the sense of conventional hierarchical control. Hierarchical control is extended in this paper to large-scale nonseparable control problems, where multiobjective optimization is used as a separation strategy. The large-scale general multiple linear-quadratic control problem is embedded, under certain conditions, into a family of the weighted Lagrangian formulation. The weighted Lagrangian formulation is separable with respect to subsystems and can be effectively solved using the interaction prediction approach at the two lower levels in the proposed three-level solution structure. At the third level, the weighting vector for the weighted Lagrangian formulation is adjusted iteratively to search the optimal weighting vector with which the optimal control of the original large-scale nonseparable control problem is attained. One feature of this hierarchical control scheme is a derived analytical solution for the large-scale general multiple linear-quadratic control.     

基于蚁群优化的多目标社区检测算法

蚁群优化算法作为单目标优化问题,由于只有一个目标函数,通常会将解限制到特定的范围内。当优化的目标不恰当时,算法可能失效,比如分辨率限制问题。我们将多目标优化的思想与传统的用于社区检测的蚁群优化算法相结合,增加了目标函数个数,即增加了解的评价指标数目。该算法引入多目标策略,提出多目标ACO算法,该算法在一次运行过程中会产生一组Pareto最优解。并在三个真实世界网络证明该算法的有效性和准确性。     

一种基于新的模型的多目标存档遗传算法

在多目标优化中,如何在最优解集中获得一组分布均匀且质量较好的代表解是十分重要的。文中给出了种群个体的序和解的均匀性分布定义,在此基础上又给出了解的序值方差和U-度量方差,然后把对任意多个目标函数的优化问题转化成对两个目标函数的优化问题,并对转化后的优化问题提出了一种新的多目标存档遗传算法,并证明了其全局收敛性。数据实验比较表明该算法能找到问题的数量更多、分布更广、更均匀的Pareto最优解。     

Multi-objective reliability-redundancy allocation problem using particle swarm optimization

This paper considers the multi-objective reliability redundancy allocation problem of a series system where the reliability of the system and the corresponding designing cost are considered as two different objectives. Due to non-stochastic uncertain and conflicting factors it is difficult to reduce the cost of the system and improve the reliability of the system simultaneously. In such situations, the decision making is difficult, and the presence of multi-objectives gives rise to multi-objective optimization problem (MOOP), which leads to Pareto optimal solutions instead of a single optimal solution. However in order to make the model more flexible and adaptable to human decision process, the optimization model can be expressed as fuzzy nonlinear programming problems with fuzzy numbers. Thus in a fuzzy environment, a fuzzy multi-objective optimization problem (FMOOP) is formulated from the original crisp optimization problem. In order to solve the resultant problem, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker regarding cost and reliability goals and then particle swarm optimization is applied to solve the resulting fuzzified MOOP under a number of constraints. The approach has been demonstrated through the case study of a pharmaceutical plant situated in the northern part of India.     

一种多目标人工蜂群算法

为将标准人工蜂群算法有效应用到多目标优化问题中,设计了一种多目标人工蜂群算法。其进化策略在利用精英解引导搜索的同时结合正弦函数搜索操作来平衡算法对解空间的开发与开采行为。另外,算法借助了外部集合来记录与维护种群进化过程中产生的Pareto最优解。理论分析表明:针对多目标优化问题,本算法能收敛到理论最优解集合。对典型多目标测试问题的仿真实验结果表明:本算法能有效逼近理论最优,具有较好的收敛性和均匀性,并且与同类型算法相比,本算法具有良好的求解性能。     

Multi-objective decision support system in numerical reliability optimization of modern electronic packaging

Nowadays, numerical prototyping methods in electronic packaging are widely used. This is mainly due to cost and time reduction and improved functionality and reliability of final products. Recently, there has been a lot of interest and work conducted on advanced numerical optimization, which can be directly applied to prototyping. So far, the optimization is focused on one criteria while neglecting problem of multi-objectivity, which is not the best approach from practical point of view. Nevertheless, such an approach is jusitified from the point of view of complex analysis, interdisciplinary issues and reduced accuracy of numerical models. In reality, there are usually many criteria which, in order to solve the problem, have to be taken into consideration. There are many multi-objective methods, of which the Pareto set approach is mostly cited in the literature. The “problem” of multi-objective optimization is that not a single optimal solution has resulted but the set of equivalent optimal solutions. This set of equivalent optimal solutions is referenced as “the Pareto set”. From the mathematical point of view, every value from this set can be treated as optimal for certain assumed constraints. However, there could be some additional conditions which cannot be applied to optimization process and some of the results from the Pareto set are more likely (i.e., the fabrication process will be more repeatable) then the others. So, the question is: which value from the Pareto set should be taken to further processing? There are two possibilities: asking an expert for the advice or use the decision making system. Decision making methods based on multi-objective optimization could be referenced as “Multiple criteria decision making” (MCDM) or “Multiple criterial decision aid” (MCDA) systems. There are several groups of these methods: (a) mathematical multi-objective programming, (b) artificial intelligence methods, (c) simple arithmetic methods, and (d) advanced mathematical methods. The current paper will focus on designing and application of the decision support system for multi-objective numerical reliability optimization of electronic packaging. The work will be based on the self developed numerical tool based on Python Scrippting language and will present its application to selected microelectronic packages based on its numerical model elaborated in ABAQUS.     

基于ADEMO/D-ENS的飞控系统性能指标分配方法

针对目前飞行控制系统设计中部件/组件性能参数的确定存在反复多次迭代的问题,对飞控系统性能指标的分配进行了研究。通过对性能指标分配过程进行建模,确定了分配过程属于多目标优化问题。基于Tchebycheff方法将多目标优化问题转化为单目标优化子问题集合,基于自适应差分进化算法得到的单目标优化子问题集合的最优解即为多目标优化问题Pareto最优解,同时采用惩罚因子保持差分进化算法种群的多样性。通过仿真与性能指标未分配的系统进行对比,结果表明分配后的系统具有更好的动态性和跟踪性,说明所提出的分配方法是正确的、可行的,并能够为工程应用提供一定的理论指导。