基于广义罚函数可行性准则的DE算法对不确定数据的处理

针对不确定数据集成效率低的问题,构造基于区域分割的广义罚函数可行性准则,分析了分割搜索区域的迭代点特征和可行性准则的性质与优势,据此提出一种基于广义罚函数可行性准则改进的DE算法(DE-GPFFC算法).机器学习数据集UCI中不确定数据集的数值结果显示:不确定数据集中最优可行点趋向概率0.5分布,其他数据点趋向概率0,1分布,其中趋向于概率0.5分布的数据点位于可行域int(D),其他数据点位于非可行域out(D).DE-GPFFC算法使得不确定数据集在可行域边界Round(D)进行跨区域搜索,有效提高了不确定数据分类集成效率.     

基于空间收缩技术的约束多目标进化算法

约束多目标进化算法在求解不可行域较大的优化问题时对不可行域的合理探索不仅有助于种群快速收敛于可行区域内的最优解,还能减少无潜力不可行域对算法性能的影响.因此,提出一种基于空间收缩技术的约束多目标进化算法(CMOEA-SST).首先,提出自适应精英保留策略对PPS算法的Pull阶段初始种群进行改进,增加Pull阶段初始种群的多样性和可行性;其次,在进化过程中采用空间收缩技术逐渐缩小搜索空间,减少无潜力不可行域对算法性能的影响,使算法在兼顾收敛性和多样性的同时提高收敛精度.为验证所提算法性能,将该算法与四个代表性算法C-MOEA/D、ToP、C-TAEA、PPS在LIRCMOP系列测试问题上进行仿真对比.实验结果表明,CMOEA-SST在处理不可行域较大约束优化问题时具有更好的收敛性和多样性.     

基于空间收缩技术的约束多目标进化算法

约束多目标进化算法在求解不可行域较大的优化问题时对不可行域的合理探索不仅有助于种群快速收敛于可行区域内的最优解,还能减少无潜力不可行域对算法性能的影响.因此,提出一种基于空间收缩技术的约束多目标进化算法(CMOEA-SST).首先,提出自适应精英保留策略对PPS算法的Pull阶段初始种群进行改进,增加Pull阶段初始种群的多样性和可行性;其次,在进化过程中采用空间收缩技术逐渐缩小搜索空间,减少无潜力不可行域对算法性能的影响,使算法在兼顾收敛性和多样性的同时提高收敛精度.为验证所提算法性能,将该算法与四个代表性算法C-MOEA/D、ToP、C-TAEA、PPS在LIRCMOP系列测试问题上进行仿真对比.实验结果表明,CMOEA-SST在处理不可行域较大约束优化问题时具有更好的收敛性和多样性.     

鲁棒后退时域控制中HJI方程的数值解法及控制器设计

本文讨论了由不确定非线性系统鲁棒后退时域控制(robust receding horizon control,RRHC)策略导出的Hamilton-Jacobin-Isaac(HJI)方程的求解,提出了一种新的带反曲变换的有限差分算法计算值函数,所提出算法对HJI方程的求解是一种稳定且收敛的算法.同时提出基于边界值迭代的加速过程,加速优化问题的求解,在花费更少计算时间的前提下,提高计算精度.所求得的值函数可直接应用于一类不确定非线性系统鲁棒后退时域控制器的设计,在控制器设计中,传统鲁棒后退时域控制策略中的有限时域被扩展到无限时域,求得的控制器可实时实现,避免对初始点可解性的依赖以及反复在线优化问题.     

并行计算和稀疏存储在模糊积分上的应用

近年来很多学者开展了模糊积分的相关研究,并将模糊积分应用于各种分类问题,而模糊测度的确定则是模糊积分计算的重点和难点。本文将并行计算和稀疏存储应用在模糊积分求解上,分别解决模糊积分计算中的时间复杂度和空间复杂度问题,并提出一种高效率模糊积分算法—基于并行和稀疏框架的模糊积分(Parallel and Sparse Frame Based Fuzzy Integral,简称PSFI)。实验表明,随着计算资源的增加,PSFI算法的加速比和效率下降较低。在变量存储上,PSFI算法在较多特征的数据集上对存储空间减少数千倍。最后,本文提出的PSFI算法相比之前提出的多重模糊积分(Multiple Nonlinear Integral, MNI)算法,有较高的分类准确率。     

基于蒙特卡洛Q值函数的多智能体决策方法

多智能体决策问题是人工智能领域的研究热点.与单智能体决策问题相比,多智能体决策的策略搜索空间更大.分布式局部感知马尔可夫决策过程(Dec-POMDPs)建立了不确定环境下多智能体决策问题的通用模型,自提出以来受到很大关注,但是求解Dec-POMDPs问题计算复杂度高,内存占用大.基于此,提出一种新的Q值函数表示-----蒙特卡洛Q值函数$(Q_MC)$,并从理论上证明$Q_MC$是最优Q值函数$Q^\ast$的上界,能够保证启发式搜索到最优解;运用自适应抽样方法,平衡收敛准确性和求解时间的关系;结合启发式搜索的精确性和蒙特卡洛方法随机抽样的一般性,提出一种基于$Q_MC$的蒙特卡洛聚类/扩展算法(CEMC),CEMC整合了Q值函数求解和策略搜索过程,避免保存所有值函数,只按需求解.实验结果表明,CEMC在时间和内存占用上超过目前性能最好的使用紧凑Q值函数的启发式方法.     

带最小批量约束的计划问题及其拉格朗日松弛算法

针对一类带最小批量约束的计划问题, 提出了基于拉格朗日松弛策略求解算法. 通过拉格朗日松弛策略, 将原问题转为一系列带最小批量约束的动态经济批量W-W(Wagner-Whitin)子问题. 提出了解决子问题且其时间复杂度O(T³)的最优前向递推算法. 对于拉格朗日对偶问题, 用次梯度算法求解, 获得原问题的下界. 若对偶问题的解是不可行的, 通过固定装设变量, 求解一个剩余的线性规划问题来进行可行化处理. 最后, 数据仿真验证了算法的有效性.     

基于动态迁移的ε约束生物地理学优化算法

提出基于动态迁移的ε约束生物地理学优化算法(εBBO-dm).首先,利用ε约束方法来处理约束条件,并根据群体约束违反度的优劣程度对水平参数ε进行自适应调整,充分利用较优不可行个体的有效信息,有效提高对可行域的搜索效率.其次,采用新的ε约束排序机制确定迁入率和迁出率,较好地平衡可行个体与不可行个体之间的关系.再次,为了增强迁移机制的搜索能力,提出新的动态迁移策略.最后,采用分段logistic混沌映射改进物种变异机制,提高了算法的收敛精度.通过对13个标准测试函数的仿真实验表明,εBBO-dm较其他算法在收敛精度和收敛速度上具有明显优势,尤其适合于复杂单目标约束优化问题的求解.     

混合猴群算法求解折扣{0-1}背包问题

针对折扣{0-1}背包问题(D{0-1}KP),当问题规模较大时,精确算法求解比较困难。基于此,将贪心核加速算子与猴群算法融合提出一种混合猴群算法(MMA)用于求解D{0-1}KP问题。同时在MMA算法的爬过程中引入诱导因子,避免爬过程陷入局部最优,再利用修复策略对不可行解进行修复。通过仿真实验,结果表明MMA算法求解大规模D{0-1}KP问题的计算性能有效,求解结果可行。     

改进的差分进化算法在电力经济调度中的应用

以优化发电系统中的发电总费用为目标,结合实际运行中机组的约束条件和阀点效应,建立了电力经济调度(ED)模型,并提出了求解该模型的改进的差分进化算法(ADE)。针对标准差分进化算法存在的种群多样性和收敛性能之间的矛盾,在度量种群多样性的基础上,引入了基于排序的可行解选取递减策略改进变异策略current-to-best。此外,提出一种新颖的等式约束修复机制,确保求解的可行性。最后,利用13个机组的测试系统进行仿真试验,结果证明了ADE算法求解ED模型的有效性。     

Integrated airline scheduling

Airline scheduling is composed of fleet assignment, aircraft maintenance routing, and crew scheduling optimization subproblems. It is believed that the full optimization problem is computationally intractable, and hence the constituent subproblems are optimized sequentially so that the output of one is the input of the next. The sequential approach, however, provides an overall suboptimal solution and can also fail to satisfy the maintenance constraints of an otherwise feasible full problem. In this paper several integrated models for the optimization of airline scheduling are presented for the first time, and solved by applying an enhanced Benders decomposition method combined with accelerated column generation. Solutions of several realistic data sets are computed using the integrated models, which are compared with solutions of the best known approaches from the literature. As a result, the integrated approach significantly reduces airline costs. Finally, a comparison of alternative formulations has shown that keeping the crew scheduling problem alone in the Benders subproblem is much more efficient than keeping the aircraft routing problem.     

Methods for uncertainty propagation in life cycle assessment

Life cycle assessment (LCA) calculates the environmental impact of a product over its entire life cycle. Uncertainty analysis is an important aspect in LCA, and is usually performed using Monte Carlo sampling. In this study, Monte Carlo sampling, Latin hypercube sampling, quasi Monte Carlo sampling, analytical uncertainty propagation and fuzzy interval arithmetic were compared based on e.g. convergence rate and output statistics. Each method was tested on three LCA case studies, which differed in size and behaviour. Uncertainty propagation in LCA using a sampling method leads to more (directly) usable information compared to fuzzy interval arithmetic or analytical uncertainty propagation. Latin hypercube and quasi Monte Carlo sampling provide more accuracy in determining the sample mean than Monte Carlo sampling and can even converge faster than Monte Carlo sampling for some of the case studies discussed in this paper.     

A capacitated hub location problem under hose demand uncertainty

In this study, we consider a capacitated multiple allocation hub location problem with hose demand uncertainty. Since the routing cost is a function of demand and capacity constraints are imposed on hubs, demand uncertainty has an impact on both the total cost and the feasibility of the solutions. We present a mathematical formulation of the problem and devise two different Benders decomposition algorithms. We develop an algorithm to solve the dual subproblem using complementary slackness. In our computational experiments, we test the efficiency of our approaches and we analyze the effects of uncertainty. The results show that we obtain robust solutions with significant cost savings by incorporating uncertainty into our problem.     

基于三维Savitzky-Golay滤波的蒙特卡罗剂量分布去噪

提出了一种基于三维Savitzky-Golay滤波的蒙特卡罗（MC）剂量分布的去噪方法。该方法首先利用MC方法模拟粒子轨迹数目较少时得到剂量的三维分布，然后对该剂量分布用三维Savitzky-Golay平滑滤波方法进行去噪处理。结果表明：采用三维Savitzky-Golay平滑滤波方法去噪，不仅提高了剂量分布的可视性，降低了MC计算剂量分布的不确定性。而且也相应地提高了MC剂量计算方法的计算效率。     

基于随机化Halton序列的粒子滤波算法研究*

为了克服传统粒子滤波蒙特卡洛（MC）随机采样粒子之间的间隙过大与层叠,及其产生的采样效率和滤波精度较低的问题,提出一种基于Halton序列的拟蒙特卡洛（QMC）采样粒子滤波算法。该算法在对Halton序列进行随机化、较好地消除其各维之间相关性的基础上,将之应用于粒子采样过程,以代替蒙特卡洛随机采样,得到用均匀分布粒子近似的后验状态概率密度。仿真证实,算法性能要优于传统粒子滤波算法,改善了采样效率与计算精度,且能克服粒子的退化现象。     

基于时序蒙特卡洛的WSN节点定位算法

针对无线传感器网络（WSN）中的移动节点定位问题,提出了一种将反馈时间序列与蒙特卡洛相结合的定位算法TSMCL（Feedback Time Series-Based Monte Carlo）。该算法基于目标节点1跳范围内的邻居锚节点（至少3个）反馈信号的先后顺序,构建了节点可能的初始采样区域R1,并以区域R1与蒙特卡洛采样区域R2的重叠区作为新的采样区域R,以进一步缩小采样范围、提高采样效率。仿真结果表明：与蒙特卡洛定位算法相比,提出的TSMCL算法能够减少约38%的定位误差,尤其当节点移动速度较高时,算法的收敛速度也得到了显著提升。     

Robust optimization of structural dynamic characteristics based on adaptive Kriging model and CNSGA

Dynamic characteristics greatly influence the comprehensive performance of a structure. But they are rarely included as objectives in traditional robust optimization of structures. In this study, a robust optimization model including both means and standard deviations of dynamic characteristic indices in the objective and constraint functions is constructed for improving the structural dynamic characteristics and reducing their fluctuations under uncertainty. Adaptive Kriging models are employed for the efficient computation of dynamic characteristics. An intelligent resampling technology is proposed to save computational costs and accelerate convergence of Kriging models, which takes full advantage of the test points for precision verification, the sample points within the local region of the biggest relative maximum absolute error and the near-optimal point to improve the global and local precision of Krigings. The high efficiency of proposed intelligent resampling technology is demonstrated by a numerical example. Finally, an efficient algorithm integrating adaptive Kriging models, Monte Carlo (MC) method, constrained non-dominated sorting genetic algorithm (CNSGA) is proposed to solve the robust optimization model of structural dynamic characteristics. Kriging models are interfaced with MC method to efficiently compute the fitness of individuals during CNSGA. The implementation of proposed methodology is explained in detail and highlighted by the robust optimization of a cone ring fixture with lots of circumferentially distributed holes in a large turbo generator aimed at moving its natural frequencies away from the exciting one. The comparison of the optimized design with the initial one demonstrates that the proposed methodology is feasible and applicable in engineering practice.     

基于RMC的蒙特卡罗程序性能优化

蒙特卡罗MC方法是核反应堆设计和分析中重要的粒子输运模拟方法。MC方法能够模拟复杂几何形状且计算结果精度高,缺点是需要耗费大量时间进行上亿规模粒子模拟。如何提高蒙特卡罗程序的性能成为大规模蒙特卡罗数值模拟的挑战。基于堆用蒙特卡罗分析程序RMC,先后开展了基于TCMalloc动态内存分配优化、OpenMP线程调度策略优化、vector内存对齐优化和基于HDF5的并行I/O优化等一系列优化手段,对于200万粒子的算例,使其总体性能提高26.45%以上。     

A new algorithm for importance analysis of the inputs with distribution parameter uncertainty

Importance analysis is aimed at finding the contributions by the inputs to the uncertainty in a model output. For structural systems involving inputs with distribution parameter uncertainty, the contributions by the inputs to the output uncertainty are governed by both the variability and parameter uncertainty in their probability distributions. A natural and consistent way to arrive at importance analysis results in such cases would be a three-loop nested Monte Carlo (MC) sampling strategy, in which the parameters are sampled in the outer loop and the inputs are sampled in the inner nested double-loop. However, the computational effort of this procedure is often prohibitive for engineering problem. This paper, therefore, proposes a newly efficient algorithm for importance analysis of the inputs in the presence of parameter uncertainty. By introducing a ‘surrogate sampling probability density function (SS-PDF)’ and incorporating the single-loop MC theory into the computation, the proposed algorithm can reduce the original three-loop nested MC computation into a single-loop one in terms of model evaluation, which requires substantially less computational effort. Methods for choosing proper SS-PDF are also discussed in the paper. The efficiency and robustness of the proposed algorithm have been demonstrated by results of several examples.     

流程工业配料过程的随机优化模型及求解算法

针对配料过程原料质量参数存在的不确定性,以原料消耗成本最小为优化目标,将不确定质量参数以随机数的形式引入质量指标约束中,建立了一种配料过程随机优化模型．考虑传统蒙特卡洛抽样方法的不足,采用一种更高效的Hammersley sequence sampling（HSS）技术,获得随机优化模型对应的期望值优化模型．将HSS技术用于遗传算法的种群初始化和交叉、变异操作,以保证种群分布的均匀性,实现随机优化问题的有效求解．工业应用实验结果表明,所提方法不仅能够有效降低原料的消耗成本,而且能够保证产品质量指标满足生产要求,优化结果具有较好的鲁棒性,为配料过程的随机优化控制提供了一个优化模式．