基于逐次确定换班机会集的乘务调度列生成方法

传统列生成方法在求解乘务调度问题时,由于搜索二叉树的节点数呈指数级增长使其难以解决大规模问题。为避免搜索整个树节点,提出一种逐次缩小问题规模的迭代优化方法。针对乘务调度问题提出带有换班机会选择的最小费用网络流模型。利用Dantzig-Wolfe分解原理,将该模型转化为带有换班机会选择的集覆盖模型,并采取列生成方法求解其线性松弛解,以得到原问题的下界。在求解整数解时,利用线性松弛解信息,逐次确定不被使用的换班机会集,将问题转化为一系列规模逐次缩小的乘务调度问题。对城市公交中的多组乘务调度实例进行计算,将结果与问题下界和常用遗传算法的结果进行比较,表明大多数实例都能在合理的时间内取得最优解或近优解。     

不确定可重入定点装配车间集成生产计划与调度

为满足工厂—车间一体化管理需求,研究了不确定可重入定点装配车间生产计划与调度集成优化问题。在分析车间装配特点的基础上,利用期望值描述不确定可重入情况,建立了双层生产计划与调度集成优化随机期望值模型,上层为能力约束的生产计划模型,下层为不确定可重入定点装配车间调度模型。提出了一种具有双层结构的交替迭代式改进遗传算法,上层用精英遗传算法求解生产计划,代入下层后采用基于随机模拟技术的遗传模拟退火算法求解生产调度,然后将调度结果返回上层重新求解新计划,如此不断交替迭代以实现计划与调度的同时优化。通过算例仿真验证了模型及算法的有效性。为制定不确定可重入定点装配车间生产计划与调度提供了一种合理可行的方法。     

虚拟企业中细粒度协同设计任务的不确定调度及GA求解

不确定性资源受限项目调度(URCPSP)是目前研究的热点,处理时间为区间数的任务调度属于URCPSP.针对虚拟企业中细粒度协同设计任务的不确定调度,文中建立了其模型,提出了采用"可能度水平"的方法将其转化为确定性规划,并采用遗传算法进行求解,给出了该遗传算法的结构,并提出了"染色体按资源分段、段内按任务序排列"的编码等具体操作方法.通过实例来说明该不确定调度的具体实现方法,分析表明该方法具有较好的参考价值.     

基于发电计划和设备检修计划的实时调度智能安全校核

针对发电计划和设备检修计划对实时调度的校核影响进行了分析。对机组检修与安全约束调度的关系和步骤进行了梳理。建立了以安全调度为目标以及以竞标机组为目标的多目标检修计划优化模型,约束条件以直流潮流作为实时在线校核。利用二进制遗传算法以及原始对偶内点法对模型进行联合求解。通过 30 节点系统进行仿真分析,说明了该模型的有效性。     

考虑系统阻塞-失负荷成本的电网风险评估

引入阻塞成本和失负荷成本作为电网风险评估的度量,并通过节点边际电价进行计算,建立了直流潮流下的电网动态经济调度模型。通过多次模拟系统的故障运行场景,判断系统是否过载并在必要时进行切负荷,计算并统计形成系统的风险指标值,以此分析并评估系统运行风险。基于IEEE118节点系统的算例证明了所提方法的有效性。     

基于改进遗传算法的不确定加工时间Flow-Shop鲁棒调度

对不确定加工时间环境下的Flow-shop调度问题进行了研究,利用六点模糊数对不确定加工时间进行描述,以最大完工时间和最大完工时间跨度的权重和为鲁棒性测度构建模糊加工时间Flow-shop调度模型。提出了模型求解的改进遗传算法,算法采用单染色体遍历操作代替染色体交叉操作,用以增强种子代繁衍的确定性,最后仿真分析验证了算法的有效性。     

考虑风电辅助调频的弱鲁棒调度模型

为解决传统鲁棒在处理风电不确定性上存在过度保守的问题,将弱鲁棒原理应用到含风电电力系统调度中。用区间鲁棒不确定集合描述风场功率预测误差的不确定性,并建立了风电参与辅助调频情况下的风场备用、传统机组备用等约束条件,提出了一种考虑风电辅助调频的弱鲁棒经济调度模型,通过调度传统机组和风电场以保证系统安全运行,同时满足了一定经济恶化容忍度;在含风电场的IEEE30节点算例中,对比分析了基准场模型、传统鲁棒模型和弱鲁棒调度模型三者的调度结果。算例结果表明:考虑辅助调频能够提高调度解的可行度,且与传统鲁棒模型相比,弱鲁棒具有更好的经济性。     

不确定条件下的作业车间生产调度综述

在分析了确定性生产调度问题存在的假设前提与实际生产过程中存在的大量干扰因素和相违背情形的基础上,进一步分析了目前解决不确定条件下生产调度问题的建模方法、调度方案以及优化算法的研究现状,并对不确定条件下的生产调度的进一步的研究内容作了展望。     

[供应链调度]分时电价和时变行程时间下的供应链调度

针对单机供应链调度问题,在生产计划和批次配送阶段分别考虑分时电价政策和时变行程时间。以总成本最小为目标建立混合整数规划模型,通过对模型的分析给出了最优解的性质,以此将模型分解为若干个批次的机器调度子问题。对于子问题优化,设计了子集划分启发式算法并证明了算法的最优性。对于主问题的优化,设计了自适应变邻域搜索算法。数值计算结果验证了模型和算法的有效性,证明了供应链集成调度能减少大量的能源消耗。     

带缓冲时间的不确定性作业车间鲁棒调度研究

对机器故障下的作业车间鲁棒调度问题进行了研究。根据威布尔概率分布函数和故障浴盆曲线将不确定的机器故障转化为定量化的故障区间,建立带缓冲时间的性能鲁棒调度优化模型。用遗传算法求解该模型过程中,确立带缓冲时间的鲁棒解码规则,且交叉片段在整个父代中搜索与片段对等的基因,有利于扩大交叉范围。最后的仿真实验表明,优化模型保证了调度的鲁棒性,提出的改进遗传算法对问题求解的有效性。     

A robust design for a closed-loop supply chain network under an uncertain environment

This paper presents a robust design for a multi-product, multi-echelon, closed-loop logistic network model in an uncertain environment. The model includes a general network structure considering both forward and reverse processes that can be used in various industries, such as electronics, digital equipment, and vehicles. Because logistic network design is a time consuming and costly project as well as a strategic and sensitive decision (i.e. the change of such decision is difficult in the future), a robust optimisation approach is adopted to cope with the uncertainty of demand and the return rate described by a finite set of possible scenarios. Hence, to obtain robust solutions with better time, the scenario relaxation algorithm is employed for the proposed model. Numerical examples and a sensitivity analysis are presented to demonstrate the significance and applicability of the presented model. It is shown that solutions resulted from the suggested approach insure more situations, especially in worst case ones. The results show that although the profit values of the robust configuration are less than the deterministic configuration, the robust configuration is more reliable than the deterministic one because the deterministic configuration is infeasible under some demand and return rates (i.e. in the worst cases). Moreover, the results show the computing time superiority of the algorithm compared to the extensive form model as well as optimality of the resulted solutions.     

随机工时下的多目标柔性作业车间鲁棒调度问题

针对工时不确定条件下的多目标柔性作业车间调度问题,采用2个不确定参数描述随机工时的波动程度和约束条件允许违背程度,将不确定条件下的柔性作业车间调度问题模型转换成确定条件下的鲁棒对等问题模型。在算法设计中采用全局非支配解集保存每代进化过程中产生的非支配解,并选择全局非支配解集中的个体参与变异操作。在交叉和变异操作之后,设计了一种基于变邻域结构的局部搜索策略。最后,运用该算法求解经典基准算例,验证了其有效性。     

Robust updating of uncertain damping models in structural dynamics for low- and medium-frequency ranges

This paper deals with the robust updating of uncertain computational models in the context of structural dynamics in the low- and medium-frequency ranges of composite sandwich panels for which experimental results are available. The uncertain computational model is constructed using the non-parametric probabilistic approach which takes into account model and data uncertainties. The formulation of the robust updating problem includes the effects of uncertainties and consists in minimizing a cost function with respect to an admissible set of updating parameters. Updating is performed in two steps using several cost functions and experimental results. The results of the robust updating problem show that the method proposed is efficient for updating the uncertain computational model in both low- and medium-frequency ranges.     

电液比例系统的H_∞鲁棒性控制设计

针对电液比例系统中系统控制数学模型参数时变要求控制器鲁棒性强的特点,通过分析电液比例系统的物理模型,利用线性分式变换(LFT)方法,引入乘性不确定性参数,给出了参数时变的电液比例模型,并得出了具有参数不确定性系统状态空间函数模型。运用线性矩阵不等式(LM I)的H∞控制器的处理方法,设计出基于H∞控制的电液比例系统控制器。利用该控制器可有效的抑制参数时变对系统输出的影响。仿真表明该控制器在较大不确定参数的变动下,控制器仍然能够使系统具有较好的输出性能,结果说明该鲁棒控制器的有效性。     

Identification of uncertain nonlinear systems for robust fuzzy control

In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by S?krjanc et al. (2005) [11] and [12]. With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.     

A robust optimization model for p-median problem with uncertain edge lengths

In this paper, we propose a p-median problem with uncertain edge lengths where uncertainty is characterized by given intervals. The uncertainty in edge lengths may appear in transportation costs or travel times along the edges in any network location problem. Minimax regret approach is a promising tool to cope with uncertainty in network location problems. However, minimax regret algorithms normally suffer from complexity, and they are time consuming. We propose a robust optimization approach to obtain the robust linear counterpart for the same class of the nominal p-median problem. The performance of the proposed model is compared with minimax regret approach through a simple but illustrative example, and results are discussed in more details.     

Minimum weight design of beams against failure under uncertain loading by convex analysis

Under operational conditions, some loads acting on a beam are known (deterministic loads), but there usually exist other loads the magnitude and distribution of which are unpredictable (uncertain loads). If the uncertainty in the loading is not taken into account in the design, the likelihood of failure increases. In the present study beams are designed for minimum weight subject to maximum stress and buckling load criteria and under deterministic and uncertain transverse loads. The uncertain load, which is subject to a constraint on its L ₂ norm, is determined to maximize the normal stress using a convex analysis. The location of the maximum stress is determined under the combination of deterministic and worst-case uncertain loads. The minimum weight design is obtained by determining the minimum cross-sectional area subject to stress and buckling load constraints. Results are given for a number of problem parameters including the axial load, elastic foundation modulus and uncertainty levels.     

参数不确定性汽车的鲁棒最优控制

引入二次多项式平方轮胎模型,建立了车辆的三自由度非线性动力学模型。考虑轮胎参数的不确定性,推导了线性参数不确定性车辆模型,以车辆质心侧偏角和横摆角速度为控制变量,基于线性参数不确定性车辆模型设计了鲁棒最优控制器。利用Matlab/Simulink工具,将此控制器应用于车辆三自由度非线性动力学模型中,并进行了仿真。     

结构凸集—概率混合可靠性分析的新方法

对凸集不确定性和随机变量共存的结构混合可靠性模型行研究,以解决部分参量统计信息不足时的结构可靠性评定问题。基于Info-gap理论,建立一种统一的结构非概率可靠性模型,由此导出一种与概率可靠性方法等价的椭球非概率可靠性模型。用一种特定的椭球凸集模型描述随机变量不确定性,与一般性的凸集模型复合,将凸集不确定性和随机变量共存的混合可靠性问题统一为非概率可靠性问题。基于非概率可靠性方法,提出一种一般性的凸集-概率混合可靠性方法。给出的混合可靠性指标同时具有稳健可靠性和概率可靠性意义,可通过含约束的优化问题求解。算例分析显示,当数据分散性较强或较弱时,已有的混合可靠性方法不能有效度量结构可靠性,新方法更具合理性和适用性。     

A multistage stochastic programming approach in project selection and scheduling

In this paper, the joint problem of project selection and project scheduling under uncertain environment is formulated, analyzed, and solved by multistage stochastic programs. First of all, a general mathematical formulation which can address several versions of the problem is presented. A multi-period project selection and scheduling problem is introduced and modeled by multistage stochastic programs, which are effective for solving long-term planning problems under uncertainty. A set of scenarios and corresponding probabilities is applied to model the multivariate random data process (costs or revenues, available budget, chance of success). Then, due to computational complexity, a scenario tree of the resulted scenarios is constructed by scenario reduction algorithms. Finally, assuming resources of the projects to be limited and renewable, and present worth of profit of projects as the objective, the objective of the problem is maximized. Eventually, a case study is introduced and solved, and the results are presented. The effectiveness of the proposed algorithm is shown by the numerical results.