Control Variate Remedies

We consider noisy optimization and some traditional variance reduction techniques aimed at improving the convergence rate, namely (i) common random numbers (CRN), which is relevant for population-based noisy optimization and (ii) stratified sampling, which is relevant for most noisy optimization problems. We present artificial models of noise for which common random numbers are very efficient, and artificial models of noise for which common random numbers are detrimental. We then experiment on a desperately expensive unit commitment problem. As expected, stratified sampling is never detrimental. Nonetheless, in practice, common random numbers nonetheless provided, by far, most of the improvement.

We consider the problem of stochastic simulation optimization with common random numbers over a numerical search domain. We propose the Knowledge Gradient for Common Random Numbers (KG-CRN) sequential sampling algorithm, a simple elegant modification to the Knowledge Gradient that incorporates the use of correlated noise in simulation outputs with Gaussian Process meta-models. We compare this method against the standard Knowledge Gradient and a more recently proposed variation that allows for pairwise sampling. Our method significantly outperforms both baselines under identical laboratory conditions while greatly reducing computational cost compared to pairwise sampling.

A widely applied method of experimental design in stochastic simulation is to use the same pseudo random-number stream for each of the systems or alternatives to be compared. If there are only two alternatives, there is a well-known simple method of statistical analysis. This paper presents Graybill's3 extension of that analysis technique to the case of several systems or alternatives and points out its applicability in the simulation environment. The technique is illustrated using a stochastic simula tion model of a small inventory system. An empirical comparison with other methods of design and analysis is included.

Parametric sensitivity of biochemical networks is an indispensable tool for studying system robustness properties, estimating network parameters, and identifying targets for drug therapy. For discrete stochastic representations of biochemical networks where Monte Carlo methods are commonly used, sensitivity analysis can be particularly challenging, as accurate finite difference computations of sensitivity require a large number of simulations for both nominal and perturbed values of the parameters. In this paper we introduce the common random number (CRN) method in conjunction with Gillespie's stochastic simulation algorithm, which exploits positive correlations obtained by using CRNs for nominal and perturbed parameters. We also propose a new method called the common reaction path (CRP) method, which uses CRNs together with the random time change representation of discrete state Markov processes due to Kurtz to estimate the sensitivity via a finite difference approximation applied to coupled reaction paths that emerge naturally in this representation. While both methods reduce the variance of the estimator significantly compared to independent random number finite difference implementations, numerical evidence suggests that the CRP method achieves a greater variance reduction. We also provide some theoretical basis for the superior performance of CRP. The improved accuracy of these methods allows for much more efficient sensitivity estimation. In two example systems reported in this work, speedup factors greater than 300 and 10,000 are demonstrated.

Comparison with a standard is a general multiple comparison problem, where each system is required to be compared with a single system, referred to as a ‘standard’, as well as with other alternative systems. Screening procedures specially designed to be used for comparison with a standard have been proposed to find a subset that includes all the systems better than the standard in terms of the expected performance. Selection procedures are derived to determine the best system among a number of systems that are better than the standard, or to select the standard when it is equal to or better than the other alternatives. We develop new procedures for screening and selection through the use of two variance reduction techniques, common random numbers and control variates, which are particularly useful in the context of simulation experiments. Empirical results and a realistic example are also provided to compare our procedures with the existing ones.

Gives an overview of the main techniques for improving the statistical efficiency of simulation estimators. Efficiency improvement is typically (but not always) achieved through variance reduction. We discuss methods such as common random numbers, antithetic variates, control variates, importance sampling, conditional Monte Carlo, stratified sampling, and some others, as well as the combination of certain of those methods. We also survey the recent literature on this topic.

Stochastic simulation of fan deltas using parallel multi-stage generative adversarial networks

Traditionally, exactness, numerical stability and speed are the three main criteria for evaluating algorithms for random variate generation. However, it is sometimes required that the algorithms provide correlation between generated variates for the purpose of inducing dependence among the output of simulation runs. The inverse transformation, which produces optimal correlation induction, often performs poorly in terms of the first three criteria. Algorithms based on composition, rejection, and special properties which often excel in terms of the first three criteria, tend to scramble the use of random numbers, causing many attempts at common random numbers, antithetic variates and external control variates to fail. The concept of obtaining correlation via algorithms other than the inverse transformation is examined here. To demonstrate feasibility, previously developed algorithms for Poisson and binomial random variate generation are modified to obtain both positive and negative correlation between runs....

Agent-based simulation provides a methodology to investigate complex systems behavior, such as supply chains, while incorporating many empirical elements relative to both systems structure and agent behavior. While there is a significant amount of simulation and analytical research investigating the impact of information sharing in supply chains, few studies have used empirical demand for the model. This research utilizes empirical distributions in order to determine the demand process faced by distribution centers in a distribution network. Therefore, the distribution centers face independent and heterogeneous demand that is not normal, and exhibits a much larger coefficient of variation than is generally utilized in similar research. With so much complexity and variability, contrasting different inter-organizational information sharing configurations provides an ideal setting for utilizing common random numbers for variance reduction. Comparisons made using this methodology show clear differences between the different information sharing schemes.

Stochastic Simulation of a CumSum Knock Controller

The main objective of this paper is to develop a technique for direct assessment of reservoir flow performance uncertainties. This is achieved via a single stochastic flow simulation that combines a model for local geologic uncertainty with a simple analog for the flow transfer function to estimate the joint probability distribution that characterizes the global uncertainty in flow performance. Our method provides the framework to go directly from local uncertainty, derived using simple spatial interpolation techniques, to flow uncertainty, skipping the intermediate steps of stochastic sequential simulation and not requiring any fine-scale flow simulations.

Quantifying Uncertainty in CFD

The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time-scales.

자동화 컨테이너 터미널에서 안벽크레인, AGV (Automated Guided Vehicle)와 같은 하역장비의 작업은 수많은 요인에 영향을 받으며, 이로 인해 각 장비의 작업시간 예측에 있어 불확실성이 존재한다 이러한 불확실성은 AGV 배차를 어렵게 만들고 작업효율을 떨어뜨리는 주요 원인 중 하나이다. 본 논문에서는 이러한 불확실성에 대처하기 위하여 확률적 시뮬레이션 기반 AGV 배차 알고리즘을 제안한다. 제안 방안은 AGV에 작업을 할당할 때, 할당된 작업의 수행 및 이후 일정 기간 동안의 AGV의 작업에 대해 확률적 시뮬레이션을 여러 번 반복 수행하여 작업할당에 대한 평가치의 확률적 표본을 수집한다. 수집한 표본으로부터 평가의 기대치를 추정하고 이를 이용하여 대안을 평가함으로써 불확실성의 영향을 줄인다. 평가의 신뢰도를 높이기 위해서는 많은 수의 표본을 수집해야 하므로 실시간 제약 하에서 수집 가능한 확률적 표본의 수를 늘리기 위해 이벤트 기반의 고속 시뮬레이션을 디자인하였다. 시뮬레이션 실험을 통해 검증한 결과 불확실성이 있는 환경에서 제안방안의 성능이 정적인 환경을 가정하는 방안보다 뛰어남을 확인하였다. In an automated container terminal, various factors affect the operation of container handling equipment such as quay cranes and AGVs, and thus calculating the exact operation time is nearly infeasible. This uncertainty makes it difficult to dispatch AGVs well. In this paper, we propose a simulation-based AGV dispatching algorithm When dispatching an AGV to an operation, the proposed algorithm conducts multiple stochastic simulation for the succeeding AGV operations for the predetermined period to collect stochastic samples of the result of the dispatching. In the stochastic simulation, the uncertainty of crane operations is represented as a simple probability distribution and the operation time of a crane is determined according to this. A dispatching option is evaluated by the total delay time of quay cranes which is estimated by averaging the quay crane delay of each simulation In order to collect a sufficient number of samples that guarantee the credibility of the evaluation, we devised a high-speed simulator that simulates AGV operation The effectiveness of the proposed algorithm is validated by simulation experiments.

Karst systems show high spatial variability of hydraulic parameters over small distances and this makes their modeling a difficult task with several uncertainties. Interconnections of fractures have a major role on the transport of groundwater, but many of the stochastic methods in use do not have the capability to reproduce these complex structures. A methodology is presented for the quantification of tortuosity using the single normal equation simulation (SNESIM) algorithm and a groundwater flow model. A training image was produced based on the statistical parameters of fractures and then used in the simulation process. The SNESIM algorithm was used to generate 75 realizations of the four classes of fractures in a karst aquifer in Iran. The results from six dye tracing tests were used to assign hydraulic conductivity values to each class of fractures. In the next step, the MODFLOW-CFP and MODPATH codes were consecutively implemented to compute the groundwater flow paths. The 9,000 flow paths obtained from the MODPATH code were further analyzed to calculate the tortuosity factor. Finally, the hydraulic conductivity values calculated from the dye tracing experiments were refined using the actual flow paths of groundwater. The key outcomes of this research are: (1) a methodology for the quantification of tortuosity; (2) hydraulic conductivities, that are incorrectly estimated (biased low) with empirical equations that assume Darcian (laminar) flow with parallel rather than tortuous streamlines; and (3) an understanding of the scale-dependence and non-normal distributions of tortuosity.