Least cost estimating with group technology

A twenty-two digit alpha-numeric Group Technology System was established for the Aerospace Group of VSI Corporation. In addition, the planning for least cost processing planning generation has been completed using the Group Technology (G.T.) System. The G. T. System is also being used for the classical applications such as tooling, reduced set ups, process plans, identifying duplicate parts, etc., in addition to the planned least cost method. The least cost method uses a unique empirical production standards system in conjunction with the G. T. Code for its implementation.     

Predicting optimal solution cost with conditional probabilities

Heuristic search algorithms are designed to return an optimal path from a start state to a goal state. They find the optimal solution cost as a side effect. However, there are applications in which all one wants to know is an estimate of the optimal solution cost. The actual path from start to goal is not initially needed. For instance, one might be interested in quickly assessing the monetary cost of a project for bidding purposes. In such cases only the cost of executing the project is required. The actual construction plan could be formulated later, after bidding. In this paper we propose an algorithm, named Solution Cost Predictor (SCP), that accurately and efficiently predicts the optimal solution cost of a problem instance without finding the actual solution. While SCP can be viewed as a heuristic function, it differs from a heuristic conceptually in that: 1) SCP is not required to be fast enough to guide search algorithms; 2) SCP is not required to be admissible; 3) our measure of effectiveness is the prediction accuracy, which is in contrast to the solution quality and number of nodes expanded used to measure the effectiveness of heuristic functions. We show empirically that SCP makes accurate predictions on several heuristic search benchmarks.     

Learning control of finite Markov chains with unknown transition probabilities

For a Markovian decision problem in which the transition probabilities are unknown, two learning algorithms are devised from the viewpoint of asymptotic optimality. Each time the algorithms select decisions to be used on the basis of not only the estimates of the unknown probabilities but also uncertainty of them. It is shown that the algorithms are asymptotically optimal in the sense that the probability of selecting an optimal policy converges to unity.     

转移概率部分未知时滞跳变系统有限时间控制

时滞是许多工业系统的固有特性,会导致系统控制性能的下降,甚至影响系统稳定,而在实际系统中,有限时间系统的特性更值得关注。针对上述情况,对一类具有时滞的马尔可夫跳变系统有限时间控制器设计的问题进行了研究。把转移概率完全已知的条件放宽至部分未知的更一般情形,采用自由权重的方法,保证所得的线性矩阵不等式具有更小的保守性。首先,给出马尔科夫跳变系统有限时间有界性、有限时间 H无穷有界性的判定准则。然后,通过对线性矩阵不等式(LMIs)求解,获得状态观测器和状态反馈控制器的增益矩阵。最后,仿真实例验证所提算法的有效性。     

转移概率部分未知的随机Markov 跳跃系统的镇定控制

研究一类随机Markov跳跃系统的稳定性与镇定控制问题.此类系统跳跃过程的转移概率部分未知,包括转移概率完全已知和完全未知两种情形,因而更具一般性.首先,给出保证随机Markov跳跃系统均方渐近稳定的充分性判据,并设计了相应的状态反馈镇定控制器;然后,基于矩阵的奇异值分解给出了系统静态输出反馈镇定控制器的设计方法,并将其归结为求解一组线性矩阵不等式（LMIs）的可行性问题;最后,通过数值仿真验证了所得结论的正确性.     

Classic group testing with cost for grouping and testing

We generalize the classical group testing problem to incorporate costs associated with pooling and inspection, both of which are significant factors in actual applications. We formulate the expected cost model as a nonlinear integer programming problem, prove several propositions and a theorem concerning when pooling is more efficient than individual testing, and determine the optimal group size such that the expected cost is minimized.     

Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities

This paper addresses the problems of stability and synchronization for a class of Markovian jump neural networks with partly unknown transition probabilities. We first study the stability analysis problem for a single neural network and present a sufficient condition guaranteeing the mean square asymptotic stability. Then based on the Lyapunov functional method and the Kronecker product technique, the chaos synchronization problem of an array of coupled networks is considered. Both the stability and the synchronization conditions are delay-dependent, which are expressed in terms of linear matrix inequalities. The effectiveness of the developed methods is shown by simulation examples.     

An asymptotically optimal learning controller for finite Markov chains with unknown transition probabilities

A learning controller is presented for a Markovian decision problem in which the transition probabilities are unknown. This controller, which is designed to be asymptotically optimal with consideration of a conflict between estimation and control, uses a performance criterion incorporating a tradeoff between them explicitly for determination of a control policy. It is shown that this controller achieves asymptotic optimality in the sense that the relative frequency of applying the optimal policy converges to unity.     

Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities

In this paper, the stability and stabilization problems of a class of continuous-time and discrete-time Markovian jump linear system (MJLS) with partly unknown transition probabilities are investigated. The system under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases — the latter is hereby the switched linear systems under arbitrary switching. Moreover, in contrast with the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via LMIs formulation, and the relation between the stability criteria currently obtained for the usual MJLS and switched linear systems under arbitrary switching, are exposed by the proposed class of hybrid systems. Two numerical examples are given to show the validity and potential of the developed results.     

On some properties of the confidence intervals for unknown probabilities

Some properties of the exact (nonasymptotic) confidence intervals of the unknown probabilities were studied. Consideration was given to the Bernoulli scheme-based experiments and more general experiments including indistinguishable outcomes.     

Least cost distance analysis for spatial interpolation

Spatial interpolation allows creation of continuous raster surfaces from a subsample of point-based measurements. Most interpolation approaches use Euclidean distance measurements between data points to generate predictions of values at unknown locations. However, there are many spatially distributed data sets that are not properly represented by Euclidean distances and require distance measures which represent their complex geographic connectivity. The problem of defining non-Euclidean distances between data points has been solved using the network-based solutions, but such techniques have historically relied on a network of connected line segments to determine point-to-point distances. While these vector-based solutions are computationally efficient, they cannot model more complex 2- and 3-dimensional systems of connectivity. Here, we use least-cost-path analyses to define distances between sampled points; a solution that allows for arbitrarily complex systems of connectivity to be interpolated. We used least-cost path distances in conjunction with the inverse distance weighting interpolation for a proof-of-concept interpolation of water temperature data in a complex deltaic river system. We compare our technique to Euclidean distance interpolation, and demonstrate that our technique, which follows connectivity rules, yields are more realistic interpolation of water temperature.     

Stability analysis for discrete delayed Markovian jumping neural networks with partly unknown transition probabilities

This paper addresses the analysis problem of asymptotic stability for a class of uncertain neural networks with Markovian jumping parameters and time delays. The considered transition probabilities are assumed to be partially unknown. The parameter uncertainties are considered to be norm-bounded. A sufficient condition for the stability of the addressed neural networks is derived, which is expressed in terms of a set of linear matrix inequalities. A numerical example is given to verify the effectiveness of the developed results.     

考虑资源闲置成本的多项目调度问题研究

针对资源受限多项目整体进度优化问题,考虑资源分配过程中的资源闲置成本,提出了一种集成工期延迟和资源闲置成本的多目标调度协同优化模型。通过该模型提高了资源的利用效率,理论上实现了多项目在目标成本最小情况下的整体进度方案。综合利用模拟退火算法和遗传算法的优点,设计退火遗传算法对该模型进行求解,通过算例验证了算法和模型的有效性。     

Group testing problem with two defectives

We consider the classical (2,N) group testing problem, i.e., the problem of finding two defectives among N elements. We propose a new adaptive algorithm such that for $N = \left\lfloor {2\tfrac{{t + 1}} {2} - t \cdot 2\tfrac{t} {4}} \right\rfloor $ the problem can be solved in t tests.     

具有数据包丢失及转移概率部分未知的网络控制系统H∞控制

研究一类具有数据包丢失及状态转移概率部分未知的网络控制系统随机稳定性及H∞控制问题．传感器与控制器之间、控制器与执行器之间存在数据包丢失的网络控制系统被建模成具有4个子系统的跳变系统,4个子系统之间的跳变遵行Markov跳变过程,并具有部分未知的跳变概率．利用Lyapunov稳定性定理及线性矩阵不等式的求解方法得到该类系统随机稳定的充分条件,并给出了相应的∞状态反馈控制器的设计方法．数值仿真结果验证了本文方法的正确性和有效性．     

Nonparametric hypothesis testing with small type I or type II error probabilities

For the problem of signal detection in Gaussian white noise, we obtain lower bounds for the asymptotics of moderate deviation probabilities of type I and type II errors. These asymptotics are attained on tests of the χ ² type. Using these lower bounds, we find lower bounds for nonparametric confidence estimation in the moderate deviation zone.     

An optimal stochastic control problem with observation cost

The problem of simultaneously determining an optimal control strategy and an optimal observation strategy for a linear system is considered. Quadratic costs on state and control and an "on-off" type observation cost are assumed. Dynamic programming is used to obtain a solution. An example is provided that shows some interesting relations between the optimal observation strategy and various system parameters.     

A stochastic production planning problem with nonlinear cost

Most production planning models are deterministic and often assume a linear relation between production volume and production cost. In this paper, we investigate a production planning problem in a steel production process considering the energy consumption cost which is a nonlinear function of the production quantity. Due to the uncertain environment, the production demands are stochastic. Taking a scenario-based approach to express the stochastic demands according to the knowledge of planners on the demand distributions, we formulate the stochastic production planning problem as a mixed integer nonlinear programming (MINLP) model.Approximated with the piecewise linear functions, the MINLP model is transformed into a mixed integer linear programming model. The approximation error can be improved by adjusting the linearization ranges repeatedly. Based on the piecewise linearization, a stepwise Lagrangian relaxation (SLR) heuristic for the problem is proposed where variable splitting is introduced during Lagrangian relaxation (LR). After decomposition, one subproblem is solved by linear programming and the other is solved by an effective polynomial time algorithm. The SLR heuristic is tested on a large set of problem instances and the results show that the algorithm generates solutions very close to optimums in an acceptable time. The impact of demand uncertainty on the solution is studied by a computational discussion on scenario generation.     

考虑轧辊成本的轧制计划编制与调整

在分析轧辊车削成本的基础上对轧制计划编制和调整问题进行深入研究, 建立以最小化轧辊车削量为目标的0-1整数规划模型. 针对问题特征, 构造基于替换邻域搜索的两阶段算法: 第1阶段, 对轧制单元实施最佳匹配和交叉使用调整; 第2阶段, 通过搜索轧制单元的轧辊替换邻域, 用车削量较少的轧辊替代车削量较大的轧辊, 从而优化第1阶段的有效解. 通过实际生产数据验证, 两阶段算法能够在满足轧制工艺规程的基础上有效降低轧辊车削量, 算法和模型均可行且有效.