Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem

Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this study, we develop a solution framework which integrates multi-objective evolutionary algorithm (MOEA) with multi-objective computing budget allocation (MOCBA) method for the multi-objective simulation optimization problem. We apply it on a multi-objective aircraft spare parts allocation problem to find a set of non-dominated solutions. The problem has three features: huge search space, multi-objective, and high variability. To address these difficulties, the solution framework employs simulation to estimate the performance, MOEA to search for the more promising designs, and MOCBA algorithm to identify the non-dominated designs and efficiently allocate the simulation budget. Some computational experiments are carried out to test the effectiveness and performance of the proposed solution framework.     

金融中的Levy模型及其仿真

近20年来,金融中Levy模型与蒙特卡洛仿真技术日益受到重视. 在连续时间过程的金融建模中带跳跃的Levy模型相比于连续轨道的布朗运动模型能很好地刻画市场的跳跃,更好地拟合金融数据的统计特征,更准确地对衍生品定价. 但是,相较于经典的Black-Scholes模型,用Levy模型对衍生品定价以及求解对冲策略的计算复杂度大大增加. 蒙特卡洛仿真成为Levy模型计算中最重要的方法之一. 首先详细地介绍了Levy模型引入的背景,并引出仿真方法在其中重要的应用价值. 最后,简要地给出了Levy过程仿真及其梯度估计的基本方法.     

Efficient automatic simulation of parallel computation on networks of workstations

Andrews et al. [Automatic method for hiding latency in high bandwidth networks, in: Proceedings of the ACM Symposium on Theory of Computing, 1996, pp. 257-265; Improved methods for hiding latency in high bandwidth networks, in: Proceedings of the Eighth Annual ACM Symposium on Parallel Algorithms and Architectures, 1996, pp. 52-61] introduced a number of techniques for automatically hiding latency when performing simulations of networks with unit delay links on networks with arbitrary unequal delay links. In their work, they assume that processors of the host network are identical in computational power to those of the guest network being simulated. They further assume that the links of the host are able to pipeline messages, i.e., they are able to deliver P packets in time O(P+d) where d is the delay on the link.In this paper we examine the effect of eliminating one or both of these assumptions. In particular, we provide an efficient simulation of a linear array of homogeneous processors connected by unit-delay links on a linear array of heterogeneous processors connected by links with arbitrary delay. We show that the slowdown achieved by our simulation is optimal. We then consider the case of simulating cliques by cliques; i.e., a clique of heterogeneous processors with arbitrary delay links is used to simulate a clique of homogeneous processors with unit delay links. We reduce the slowdown from the obvious bound of the maximum delay link to the average of the link delays. In the case of the linear array we consider both links with and without pipelining. For the clique simulation the links are not assumed to support pipelining.The main motivation of our results (as was the case with Andrews et al.) is to mitigate the degradation of performance when executing parallel programs designed for different architectures on a network of workstations (NOW). In such a setting it is unlikely that the links provided by the NOW will support pipelining and it is quite probable the processors will be heterogeneous. Combining our result on clique simulation with well-known techniques for simulating shared memory PRAMs on distributed memory machines provides an effective automatic compilation of a PRAM algorithm on a NOW.     

Timed Petri nets and prediction to improve the Chandy–Misra conservative-distributed simulation

The main contribution of this paper shows that distributed simulation of timed Petri nets (TPN) can take advantage of their structure to obtain a significant lookahead which is usually difficult to compute with other models. In this paper, we introduce a conservative-distributed simulation with a reduced number of control messages and without deadlock resolution. This approach is based on a part of optimism computed on the prediction time each logical process can determine for its advancement. Obviously this prediction time must be computed easily according to the structure of the simulated logical process. Timed Petri nets meet these requirements and we use their structure to evaluate the depth of the prediction. In conservative-distributed simulation, it is known that the deeper the prediction, the better the efficiency of the simulation. We present a method we have devised based on channel time prediction. We compare its performance to the Chandy–Misra method and to some related Petri nets approaches (Chiola). Experiments carried out on Sun stations show that there is more parallelism and a reduced number of null messages in the cases of deadlock avoidance. Moreover, considering deadlock detection and resolution technique we observe that in many cases no deadlock occurs with less control messages.     

Strategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environment

In Neitzel et al. (Strategies for time-dependent PDE control using an integrated modeling and simulation environment. Part one: problems without inequality constraints. Technical Report 408, Matheon, Berlin, 2007) we have shown how time-dependent optimal control for partial differential equations can be realized in a modern high-level modeling and simulation package. In this article we extend our approach to (state) constrained problems. “Pure” state constraints in a function space setting lead to non-regular Lagrange multipliers (if they exist), i.e. the Lagrange multipliers are in general Borel measures. This will be overcome by different regularization techniques. To implement inequality constraints, active set methods and barrier methods are widely in use. We show how these techniques can be realized in a modeling and simulation package. We implement a projection method based on active sets as well as a barrier method and a Moreau Yosida regularization, and compare these methods by a program that optimizes the discrete version of the given problem. Ira Neitzel’s research was supported by the DFG Schwerpunktprogramm SPP 1253. Uwe Prüfert’s research was supported by the DFG Research Center Matheon. Thomas Slawig’s research was supported by the DFG Cluster of Excellence The Future Ocean and the DFG Schwerpunktprogramm SPP 1253. Website     

差异驱动型评价方法的稳定性及差异凸显能力比较

针对综合评价中方法种类繁多且无统一比较标准的问题,选取了四种突出被评价对象之间差异的评价方法,采用随机模拟的方式分别从评价方法的稳定性及对差异的凸显能力两个方面进行了比较分析。得出了四种方法稳定性由高到低分别为均方差法、最大离差法、熵值法、拉开档次法,且评价方法的稳定性越高,则其对差异的凸显能力反而越差的结论。该研究不仅验证了差异驱动型评价方法的相关特性,为评价者关于评价方法的选取提供了参考意见,而且随机模拟方法的应用,可为类似的多评价方法的比较问题提供技术参考。     

Statistical Analysis Technique of Two-parameter Generalized Exponential Sum Distribution

A new life distribution is proposed, known as ``two-parameter generalized exponential sum distribution". We study the density function and failure rate function, the average failure rate function, the image features and the numerical characteristics of the mean residual life of the distribution. Several methods of calculating point estimation of parameters are discussed. Through the Monte-Carlo simulation, we compare the precision of the point estimations. In our opinion, the best linear unbiased estimation is the most optimal solution of these methods. At the same time, several methods of calculating parameters of interval estimations are given. We also discuss the precision of interval estimations by Monte-Carlo simulation and use the best linear unbiased estimation and the best linear invariant estimation to construct interval estimations which are better than other estimation method. Finally, several simulation examples and a case of maintaining tanks is used to illustrate the application of the methods presented in this paper.     

基于随机模拟试验的参数估计

介绍了数学实验的背景,MATLAB用于数学实验的优势,并利用参数估计的大样本性质,并通过随机模拟方法求出π的近似值和随机变量的数字特征及分布函数.模拟试验结果表明,由该方法得到的估计值与理论值的误差很小.     

The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

拉开档次法稳定性分析及改进

采用随机模拟仿真的方法分别从增添异常对象和极端样本两个方面对拉开档次法的稳定性进行了分析,给出了相关结论。在此基础上,基于“因子分析”提出了拉开档次法的改进方法,算例部分的分析表明该方法因兼顾了同类数据之间的内部差异,能够削弱“异常值”对原始数据的干扰作用,从而进一步提升了方法的稳定性。最后,指出拉开档次法适用于评价指标数目较少的评价问题,而基于“因子分析”的改进方法则适合于数据数目较多且指标有相关关系的评价问题。     

Chaos control in passive walking dynamics of a compass-gait model

The compass-gait walker is a two-degree-of-freedom biped that can walk passively and steadily down an incline without any actuation. The mathematical model of the walking dynamics is represented by an impulsive hybrid nonlinear model. It is capable of displaying cyclic motions and chaos. In this paper, we propose a new approach to controlling chaos cropped up from the passive dynamic walking of the compass-gait model. The proposed technique is to linearize the nonlinear model around a desired passive hybrid limit cycle. Then, we show that the nonlinear model is transformed to an impulsive hybrid linear model with a controlled jump. Basing on the linearized model, we derive an analytical expression of a constrained controlled Poincaré map. We present a method for the numerical simulation of this constrained map where bifurcation diagrams are plotted. Relying on these diagrams, we show that the linear model is fairly close to the nonlinear one. Using the linearized controlled Poincaré map, we design a state feedback controller in order to stabilize the fixed point of the Poincaré map. We show that this controller is very efficient for the control of chaos for the original nonlinear model.     

A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number

A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier–Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes a frequent requirement in the simulation of turbulent flows in complex geometries. The two‐step method is considered here; to obtain a regularization that is second order accurate in space and time, the method computes a low‐order accurate, stable, and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is stable and the accuracy in both space and time is improved after the correction step. We also perform a qualitative test to demonstrate that the method is capable of capturing qualitative features of a turbulent flow, even on a very coarse mesh. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 814–839, 2017     

新股网上申购投资的随机模拟分析

为研究现行制度下新股网上申购投资收益,通过对全流通前后IPOs数据的统计分析,选取2006年6月～2007年12月数据段为研究对象.研究银行间市场回购融资、交易所市场回购融资、现金三种不同资金来源用于新股网上申购的情形,分析不同资金规模的收益回报情况.研究中用分层抽样技术,对新股上市首日售出价和申购日市场回购利率构造三角概率分布,进行随机模拟,得出单个投资者比较合理的新股申购资金规模及收益.结果对于合理设计以新股申购为主要投资对象的理财产品、设定新股申购资金规模、以及对新股申购成本与收益回报的定位等都有重要参考意义.     

Exponential meshes and three‐dimensional computation of a magnetic field

We describe the simulation of an exterior problem using a magnetic field deriving from magnetostatics, with a numerical method mixing the approaches of C. I. Goldstein and L.‐A. Ying. This method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain. On this mesh, we use an edge elements discretization and a recently proposed mixed formulation. In this paper, we provide both a theoretical and numerical study of the method. We establish an error estimate, describe the implementation, propose some preconditioning techniques and show the numerical results. We also compare these results with those obtained from an equivalent boundary elements approach. In this way, we retain that our method leads to a practical numerical implementation, a saving of storage, and turns out to be an alternative to the classical boundary elements method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 595–637, 2003     

Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics

Recent laboratory experiments of Bolles et al. (Phys Rev Fluids 4(1):011801, 2019) demonstrate that an abrupt change in bottom topography can trigger anomalous statistics in randomized surface waves. Motivated by these observations, Majda et al. (Proc Natl Acad Sci 116(10):3982–3987, 2019) developed a theoretical framework, based on deterministic and statistical analysis of the truncated Korteweg-de Vries (TKdV) system that successfully captures key qualitative features of the experiments including the robust emergence of anomalous statistics and heightened skewness in the outgoing wavefield. Here, we extend these parallel experimental and modeling efforts with several new findings that have resulted from a synergetic interaction between the two. By precisely relating model parameters to physical ones, we calibrate the model inverse temperature to the specific conditions present in the experiments, thereby permitting a quantitative comparison. We find theoretically predicted distributions of surface displacement to match the experimental measurements with surprising detail. Prompted by the presence of surface slope in the TKdV Hamiltonian, we present new experimental measurements on surface slope statistics and compare them to model predictions. Analysis of some deterministic trajectories of TKdV elucidates the experimental length and time scales required for the statistical transition to a skewed state. Finally, the theory predicts a peculiar relationship between the outgoing displacement skewness and the change in slope variance, specifically how their ratio depends on the wave amplitude and depth ratio. New experimental measurements provide convincing evidence for this prediction.

     

On generating multivariate Poisson data in management science applications

Generating multivariate Poisson random variables is essential in many applications, such as multi echelon supply chain systems, multi‐item/multi‐period pricing models, accident monitoring systems, etc. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix, and therefore are rarely used in management science. Instead, multivariate Poisson data are commonly approximated by either univariate Poisson or multivariate Normal data. However, these approximations are often not adequate in practice. In this paper, we propose a conceptually appealing correction for NORTA (NORmal To Anything) for generating multivariate Poisson data with a flexible correlation structure and rates. NORTA is based on simulating data from a multivariate Normal distribution and converting it into an arbitrary continuous distribution with a specific correlation matrix. We show that our method is both highly accurate and computationally efficient. We also show the managerial advantages of generating multivariate Poisson data over univariate Poisson or multivariate Normal data. Copyright © 2011 John Wiley & Sons, Ltd.     

Lexicography and degeneracy: can a pure cutting plane algorithm work?

We discuss an implementation of the lexicographic version of Gomory’s fractional cutting plane method for ILP problems and of two heuristics mimicking the latter. In computational testing on a battery of MIPLIB problems we compare the performance of these variants with that of the standard Gomory algorithm, both in the single-cut and in the multi-cut (rounds of cuts) version, and show that they provide a radical improvement over the standard procedure. In particular, we report the exact solution of ILP instances from MIPLIB such as stein15, stein27, and bm23, for which the standard Gomory cutting plane algorithm is not able to close more than a tiny fraction of the integrality gap. We also offer an explanation for this surprising phenomenon.     

凝固过程的温度场数值模拟

通过对铸件凝固过程中各换热边界条件的研究,建立了凝固过程的二维非稳态温度场计算数学模型;并运用了有限差分方法对模型进行离散,得到大型方程组,并利用超松驰迭代法(即SOR法)解该方程组,据此,利用Turbo C编制了计算机程序.上机运行结果表明,可较满意地模拟凝固过程温度场的分布.     

Surprising computations

In the course of simulation of differential equations, especially of marginally stable differential problems using marginally stable numerical methods, one occasionally comes across a correct computation that yields surprising, or unexpected results. We examine several instances of such computations. These include (i) solving Hamiltonian ODE systems using almost conservative explicit Runge–Kutta methods, (ii) applying splitting methods for the nonlinear Schrödinger equation, and (iii) applying strong stability preserving Runge–Kutta methods in conjunction with weighted essentially non-oscillatory semi-discretizations for nonlinear conservation laws with discontinuous solutions.For each problem and method class we present a simple numerical example that yields results that in our experience many active researchers are finding unexpected and unintuitive. Each numerical example is then followed by an explanation and a resolution of the practical problem.     

Information dynamics algorithm for detecting communities in networks

The problem of community detection is relevant in many scientific disciplines, from social science to statistical physics. Given the impact of community detection in many areas, such as psychology and social sciences, we have addressed the issue of modifying existing well performing algorithms by incorporating elements of the domain application fields, i.e. domain-inspired. We have focused on a psychology and social network-inspired approach which may be useful for further strengthening the link between social network studies and mathematics of community detection. Here we introduce a community-detection algorithm derived from the van Dongen’s Markov Cluster algorithm (MCL) method [4] by considering networks’ nodes as agents capable to take decisions. In this framework we have introduced a memory factor to mimic a typical human behavior such as the oblivion effect. The method is based on information diffusion and it includes a non-linear processing phase. We test our method on two classical community benchmark and on computer generated networks with known community structure. Our approach has three important features: the capacity of detecting overlapping communities, the capability of identifying communities from an individual point of view and the fine tuning the community detectability with respect to prior knowledge of the data. Finally we discuss how to use a Shannon entropy measure for parameter estimation in complex networks.