WSC 2004

WSC 2004 Final Abstracts

Analysis Methodology Track

Sunday 1:00:00 PM 2:30:00 PM
Simulation Optimization I

Chair: Russell Cheng (University of Southampton)

Optimization by Simulation Metamodelling Methods
Russell C.H. Cheng and Christine S.M. Currie (University of Southampton)

We consider how simulation metamodels can be used to optimize the performance of a system that depends on a number of factors. We focus on the situation where the number of simulation runs that can be made is limited, and where a large number of factors must be included in the metamodel. Bayesian methods are particularly useful in this situation and can handle problems for which classical stochastic optimization can fail. We describe the basic Bayesian methodology, and then an extension to this that fits a quadratic response surface which, for function minimization, is guaranteed to be positive definite. An example is presented to illustrate the methods proposed in this paper.

Automated Response Surface Methodology for Stochastic Optimization Models with Unknown Variance
Robin P. Nicolai, Rommert Dekker, Nanda Piersma, and Gerrit J. van Oortmarssen (Erasmus University Rotterdam )

Response Surface Methodology (RSM) is an optimization tool that was introduced in the early 50´s by Box and Wilson (1951). In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the objective function. We will present a framework of the RSM procedures that is founded in recognizing local optima in the presence of noise. We emphasize both stopping rules and restart procedures. The results show that considerable improvement is possible over the proposed settings in the existing literature.

Stochastic Approximation with Simulated Annealing as an Approach to Global Discrete-Event Simulation Optimization
Matthew H. Jones and K. Preston White Jr. (University of Virginia)

This paper explores a new approach to global, stochastic, simulation optimization which combines stochastic approximation (SA) with simulated annealing (SAN). SA directs a search of the response surface efficiently, using a conservative number of simulation replications to approximate the local gradient of a probabilistic loss function. SAN adds a random component to the SA search, needed to escape local optima and forestall premature termination. Using a limited set of simple test problems, we compare the performance of SA/SAN with the commercial package OptQuest. Results demonstrate that SA/SAN can outperform OptQuest when properly tuned. Further results demonstrate that a multi-start approach not only greatly improves the coverage and robustness of SA/SAN, but also provides insights potentially useful in directing iterative improvement of the gain coefficients before each new start. This preliminary study is sufficiently encouraging to invite further research on the SA/SAN approach.

Sunday 3:00:00 PM 4:30:00 PM
Simulation Optimization II

Chair: Bruce Schmeiser (Purdue University)

This paper presents a new meta heuristic algorithm based on the search method called simulated annealing, and its application to solving multi objective simulation optimiza-tion problems. Since the simulated annealing search method has been extensively applied as a modern heuristic to solve single objective simulation optimization problems, a modification to this method has been developed in order to solve multi objective problems. The efficiency of this new algorithm was tested on a real case problem modeled under discrete simulation.

Simulation-Based Optimization Using Simulated Annealing With Confidence Interval
Talal M. Alkhamis and Mohamed A. Ahmed (Kuwait University)

This paper develops a variant of Simulated Annealing (SA) algorithm for solving discrete stochastic optimization prob-lems where the objective function is stochastic and can be evaluated only through Monte Carlo simulations. In the proposed variant of SA, the Metropolis criterion depends on whether the objective function values indicate statisti-cally significant difference at each iteration. The differ-ences between objective function values are considered to be statistically significant based on confidence intervals associated with these values. Unlike the original SA, our method uses a constant temperature. We show that the con-figuration that has been visited most often in the first m it-erations converges almost surely to a global optimizer.

Retrospective Approximation Algorithms for the Multidimensional Stochastic Root-Finding Problem
Raghu Pasupathy and Bruce W. Schmeiser (Purdue University)

The stochastic root-finding problem (SRFP) is that of solving a system of q equations in q unknowns using only an oracle that provides estimates of the function values. This paper presents a family of algorithms to solve the multidimensional (q >= 1) SRFP, generalizing Chen and Schmeiser's one-dimensional retrospective approximation (RA) family of algorithms. The fundamental idea used in the algorithms is to generate and solve, with increasing accuracy, a sequence of approximations to the SRFP. We focus on a specific member of the family, called the Bounding RA algorithm, which finds a sequence of polytopes that progressively decrease in size while approaching the solution. The algorithm converges almost surely and exhibits good practical performance with no user tuning of parameters, but no convergence proofs or numerical results are included here.

A Meta-Heuristic Based on Simulated Annealing for Solving Multiple-Objective Problems in Simulation Optimization
Eduardo Alberto Avello, Felipe F. Baesler, and Reinaldo J. Moraga (Universidad del BioBio)

Monday 10:30:00 AM 12:00:00 PM
Simulation Optimization III

Chair: Sigrun Andradottir (Georgia Tech)

Global Likelihood Optimization Via the Cross-Entropy Method, with an Application to Mixture Models
Zdravko Botev and Dirk P Kroese (The University of Queensland)

Global likelihood maximization is an important aspect of many statistical analyses. Often the likelihood function is highly multi-extremal. This presents a significant challenge to standard search procedures, which often settle too quickly into an inferior local maximum. We present a new approach based on the cross-entropy (CE) method, and illustrate its use for the analysis of mixture models.

Efficient Simulation-Based Discrete Optimization
Seth D. Guikema, Rachel A. Davidson, and Zehra Çaðnan (Cornell University)

In many practical applications of simulation it is desirable to optimize the levels of integer or binary variables that are inputs for the simulation model. In these cases, the objective function must often be estimated through an expensive simulation process, and the optimization problem is NP-hard, leading to a computationally difficult problem. We investigate efficient solution methods for this problem, and we propose an approach that reduces the number of runs of the simulation by using ridge regression to approximate some of the simulation calls. This approach is shown to significantly decrease the computational cost but at a cost of slightly worse solution values.

Simulation Optimization Using Balanced Explorative and Exploitative Search
Andrei A. Prudius and Sigrun Andradottir (Georgia Institute of Technology)

We present a new random search method for solving simulation optimization problems. Our approach emphasizes the need for maintaining the right balance between exploration and exploitation during various stages of the search. Exploration represents global search for promising solutions within the entire feasible region, while exploitation involves local search of promising subregions. Preliminary numerical results are provided that show the performance of the method applied to solve deterministic and stochastic optimization problems.

Monday 1:30:00 PM 3:00:00 PM
Simulation Methodology and Application

Chair: John Shortle (George Mason University)

Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we report some of the recent progress we had in broadening the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. We first describe the method and the class of stochastic mathematical programs with complementarity constraints that we are interested in solving and then outline a set of sufficient conditions for its almost-sure convergence. We also illustrate an application of the method to solving a toll pricing problem in transportation networks. These developments also make it possible to solve certain stochastic bilevel optimization problems and Stackelberg games, involving expectations or steady-state functions, using simulation.

Make-to-Stock Systems with Backorders: IPA Gradients
Yao Zhao and Benjamin Melamed (Rutgers University)

We consider single-stage, single-product Make-to-Stock systems with random demand and random service (production) rate, where demand shortages at the inventory facility are backordered. The Make-to-Stock system is modeled as a stochastic fluid model (SFM), in which the traditional discrete arrival, service and departure stochastic processes are replaced by corresponding stochastic fluid-flow rate processes. IPA (Infinitesimal Perturbation Analysis) gradients of various performance metrics are derived with respect to parameters of interest (here, base-stock level and production rate), and are showed to be unbiased and easy to compute. The (random) IPA gradients are obtained via sample path analysis under very mild assumptions, and are inherently nonparametric in the sense that no specific probability law need be postulated. The formulas derived can be used in simulation, as well as in real-life systems.

Generating Scheduling Constraints for Discrete Event Dynamic Systems
Wai Kin Chan and Lee W. Schruben (University of California, Berkeley)

In most scheduling literature, constraints are seemingly generated in an ad-hoc manner using intuitive arguments. This could result in overlooking some constraints or including unnecessary constraints. Schruben (2000) has shown how the dynamics of some discrete event systems can be modeled as the solutions of optimization programs. In this paper, we use this idea to generate mathematical programming models systematically for scheduling resources in discrete event dynamic systems. Two examples are presented: a multiple server queue and a semiconductor manufacturing cluster tool. An interesting result was that the mathematical structure of the scheduling program gen-erated from a simulation of a cluster tool found in the literature leads to a different, more concise and illuminating cluster tool simulation model that would have been difficult to discover otherwise. The corresponding optimal scheduling problem is surprising in that it does not include explicit representation of the resource that is actually being scheduled!

Solving Stochastic Mathematical Programs with Complementarity Constraints Using Simulation
S. Ilker Birbil (Erasmus University Rotterdam) and Gul Gurkan and Ovidiu Listes (Tilburg University)

Monday 3:30:00 PM 5:00:00 PM
Efficient Simulation Budget Allocation

Chair: Chun-Hung Chen (George Mason University)

A Large Deviations Perspective on Ordinal Optimization
Peter Glynn (Stanford University) and Sandeep Juneja (Tata Institute of Fundamental Research)

We consider the problem of optimal allocation of computing budget to maximize probability of correct selection in ordinal optimization setting. This problem has been studied in literature in an approximate mathematical framework under assumption that the underlying random variables have a Gaussian distribution. We use large deviations theory to develop a mathematically rigorous framework to determine optimal allocation of computing resources even when the underlying variables have general, non-Gaussian distributions. Further, in a simple setting we show that when there exists an indifference zone, quick stopping rules may be developed that exploit exponential decay rates of the probability of false selection. In practice, the distributions of underlying variables are estimated from generated samples leading to performance degradation due to estimation errors. On a positive note, we show that corresponding estimates of optimal allocations converge to their true values as the number of generated samples increases to infinity.

Optimal Computing Budget Allocation for Multi-Objective Simulation Models
Loo Hay Lee, Ek Peng Chew, and Suyan Teng (National University of Singapore) and David Goldsman (Georgia Institute of Technology)

Simulation plays a vital role in identifying the best system design from among a set of competing designs. To improve simulation efficiency, ranking and selection techniques are often used to determine the number of simulation replications required so that a pre-specified level of correct selection is guaranteed at a modest possible computational expense. As most real-life systems are multi-objective in nature, in this paper, we consider a multi-objective ranking and selection problem, where the system designs are evaluated in terms of more than one performance measure. We incorporate the concept of Pareto optimality into the ranking and selection scheme, and try to find all of the non-dominated designs rather than a single best one. A simple sequential solution method is proposed to allocate the simulation replications. Computational results show that the proposed algorithm is efficient in terms of the total number of replications needed to find the Pareto set.

Optimal Computing Budget Allocation Under Correlated Sampling
Michael C. Fu (University of Maryland), Jian-Qiang Hu (Boston University), Chun-Hung Chen (George Mason University) and Xiaoping Xiong (University of Maryland)

We consider the optimal computing budget allocation (OCBA) problem where the simulated designs are correlated. The exact optimal allocation is presented for two designs, and an approximation proposed for more than two designs. Numerical experiments for several examples compare the approximation with some other allocation procedures. Results on convergence rates and the non-Gaussian setting are also discussed.

Tuesday 8:30:00 AM 10:00:00 AM
Adaptive Sampling

Chair: Shane Henderson (Cornell University)

Monte Carlo simulation techniques that use function approximations have been successfully applied to approximately price multi-dimensional American options. However, for many pricing problems the time required to get accurate estimates can still be prohibitive, and this motivates the development of variance reduction techniques. In this paper, we describe a zero-variance importance sampling measure for American options. We then discuss how function approximation may be used to approximately learn this measure; we test this idea in simple examples. We also note that the zero-variance measure is fundamentally connected to a duality result for American options. While our methodology is geared towards developing an estimate of an accurate lower bound for the option price, we observe that importance sampling also reduces variance in estimating the upper bound that follows from the duality.

An Adaptive Approach to Fast Simulation of Traffic Groomed Optical Networks
Chih-Chieh Hsu and Michael Devetsikiotis (North Carolina State University)

In this paper, we consider the fast simulation of traffic groomed optical networks, in which multiple sub-rate traffic streams may be carried on the same wavelength. For real-sized systems, call blocking probabilities may be rare events and require a large amount of CPU power to simulate. We present two importance sampling methods for fast simulation. For a light-load case, we prove that static IS using the Standard Clock (S-ISSC) method does indeed have bounded relative error (BRE) even in multi-class case. For a non-light-load case, we suggest, alternatively, \emph{adaptive ISSC} (A-ISSC) which calculates the relative possibility of reaching each target in every step of simulation. Using A-ISSC, biasing methods which are proven to be optimal or have bounded error can be extended to multi-dimensional cases while still retaining a very favorable performance.

Adaptive Control Variates
Sujin Kim and Shane G. Henderson (Cornell University)

Adaptive Monte Carlo methods are specialized Monte Carlo simulation techniques where the methods are adaptively tuned as the simulation progresses. The primary focus of such techniques has been in adaptively tuning importance sampling distributions to reduce the variance of an estimator. We instead focus on adaptive control variate schemes, developing asymptotic theory for the performance of two adaptive control variate estimators. The first estimator is based on a stochastic approximation scheme for identifying the optimal choice of control variate. It is easily implemented, but its performance is sensitive to certain tuning parameters, the selection of which is nontrivial. The second estimator uses a sample average approximation approach. It has the advantage that it does not require any tuning parameters, but it can be computationally expensive and requires the availability of nonlinear optimization software.

Function-Approximation-Based Importance Sampling for Pricing American Options
Nomesh Bolia and Sandeep Juneja (Tata Institute of Fundamental Research) and Paul Glasserman (Columbia Business School)

Tuesday 10:30:00 AM 12:00:00 PM
Ranking and Selection

Chair: Barry Nelson (Northwestern University)

We present a new sequential, eliminating procedure for selecting the best system in a single-factor Bernoulli-response experiment with an odds-ratio indifference zone, where best refers to the system with the largest probability of success on any given trial. Analytical results show that the proposed procedure is more efficient than existing procedures in that it requires fewer observations to identify the best system when only two systems are being considered. Empirical results show that the procedure is more efficient for comparing up to five systems when the specified odds-ratio indifference zone is greater than two.

Better Selection of the Best
Huaiyu Harry Ma and Thomas R. Willemain (Rensselaer Polytechnic Institute)

We present a new method of selecting the best of several competing system designs on the basis of expected steady-state performance. The method uses a new form of time-series bootstrap in a sequential hypothesis testing frame-work. We illustrate the efficiency of the new method by comparing its results against the current state of the art in a series of simulation experiments. The new method achieves equal or greater probability of correct selection of the best system with substantial savings in the number of simulation observations required for the decision.

Combined Pattern Search and Ranking and Selection for Simulation Optimization
Todd A. Sriver and James W. Chrissis (Air Force Institute of Technology)

A new algorithm class is presented for optimization of stochastic simulation models. The algorithms, which combine generalized pattern search (GPS) with ranking and selection (R&S), require "black-box" simulation evaluations and are applicable to problems with mixed variables (continuous, discrete numeric, and categorical). Implementation of the Mixed-variable Generalized Pattern Search with Ranking and Selection (MGPS-RS) algorithm with three different R&S procedures is demonstrated and tested on a small set of standard test functions. Results of this preliminary performance evaluation are summarized and compared with existing search methods.

An Odds-Ratio Indifference-Zone Selection Procedure for Bernoulli Populations
Jamie R. Wieland and Barry L. Nelson (Northwestern University)

Tuesday 1:30:00 PM 3:00:00 PM
Output Analysis I

Chair: Emily Lada (North Carolina State University)

Confidence intervals for the median of estimators or other quantiles were proposed as a substitute for usual confidence intervals in terminating and steady-state simulation. This is adequate since for many estimators the median and the expectation are close together or coincide, particularly if the sample size is large. Grouping data into batches is useful for median confidence intervals. The novel confidence intervals are easy to obtain, the variance of the estimator is not used. They are well suited for correlated simulation output data, apply to functions of estimators, and in simulation they seem to be particularly accurate, namely they follow the confidence level better than other confidence intervals. This paper states their accuracy which is the difference between the nominal confidence level and the actual coverage. The accuracy is evaluated with analytical models and simulation. For the estimation of quantiles by order statistics, the new confidence intervals are exact.

Evaluation of Methods Used to Detect Warm-Up Period in Steady State Simulation
Prasad S. Mahajan and Ricki G. Ingalls (Oklahoma State University)

This paper reviews the performance of various methods used to detect the warm up length in steady state discrete event simulation. An evaluation procedure is used to com-pare the methods. The methods are applied to the output generated by a simple job shop model. The performance of the methods is tested at different levels of utilizations. Various measures of goodness are used to assess the effec-tiveness of the methods.

Steady-State Simulation Analysis Using Asap3
Natalie M. Steiger (University of Maine), Emily K. Lada (Statistical and Applied Mathematical Sciences Institute), James R. Wilson and Jeffrey A. Joines (North Carolina State University) and Christos Alexopoulos and David Goldsman (Georgia Institute of Technology)

We discuss ASAP3, a refinement of the batch means algorithms ASAP and ASAP2. ASAP3 is a sequential procedure designed to produce a confidence-interval estimator for the expected response of a steady-state simulation that satisfies user-specified precision and coverage-probability requirements. ASAP3 operates as follows: the batch size is increased until the batch means pass the Shapiro-Wilk test for multivariate normality; and then ASAP3 fits a first-order autoregressive (AR(1)) time series model to the batch means. If necessary, the batch size is further increased until the autoregressive parameter in the AR(1) model does not significantly exceed 0.8. Next ASAP3 computes the terms of an inverse Cornish-Fisher expansion for the classical batch means t-ratio based on the AR(1) parameter estimates; and finally ASAP3 delivers a correlation-adjusted confidence interval based on this expansion. ASAP3 compared favorably with other batch means procedures (namely, ABATCH, ASAP2, ASAP, and LBATCH) in an extensive experimental performance evaluation.

The Accuracy of a New Confidence Interval Method
Johann Christoph Strelen (Universität Bonn)

Tuesday 3:30:00 PM 5:00:00 PM
Output Analysis II

Chair: E. Chen (BASF Corporation)

We consider the steady state output analysis problem for a process that satisfies a functional central limit theorem. We construct asymptotically valid confidence intervals for the steady-state mean using normalized excursions of the simulated process. An alternative approach splits the output at the last zero of the normalized path. The methods use a bounded memory of size determined by the user.

Experimental Performance Evaluation of Histogram Approximation for Simulation Output Analysis
E. Jack Chen (BASF Corporation) and W. David Kelton (University of Cincinnati)

We summarize the results of an experimental performance evaluation of using an empirical histogram to approximate the steady-state distribution of the underlying stochastic process. We use a runs test to determine the required sample size for simulation output analysis and construct a histogram by computing sample quantiles at certain grid points. The algorithm dynamically increases the sample size so that histogram estimates are asymptotically unbiased. Characteristics of the steady-state distribution, such as the mean and variance, can then be estimated through the empirical histogram. The preliminary experimental results indicate that the natural estimators obtained based on the empirical distribution are fairly accurate.

Performance Evaluation of a Wavelet-based Spectral Method for Steady-state Simulation Analysis
Emily K. Lada (Statistical and Applied Mathematical Sciences Institute), James R. Wilson (North Carolina State University), Natalie M. Steiger (University of Maine) and Jeffrey A. Joines (North Carolina State University)

We summarize the results of an experimental performance evaluation of WASSP, an automated wavelet-based spectral method for constructing an approximate confidence interval on the steady-state mean of a simulation output process so that the delivered confidence interval satisfies user-specified requirements on absolute or relative precision as well as coverage probability. We applied WASSP to test problems designed specifically to explore its efficiency and robustness in comparison with ASAP3 and the Heidelberger-Welch algorithm, two sequential procedures based respectively on the methods of nonoverlapping batch means and spectral analysis. Concerning efficiency, WASSP compared favorably with its competitors, often requiring smaller sample sizes to deliver confidence intervals with the same nominal levels of precision and coverage probability. Concerning robustness against the statistical anomalies commonly encountered in simulation studies, WASSP outperformed its competitors, delivering confidence intervals whose actual half-lengths and coverage probabilities were frequently closer to the corresponding user-specified nominal levels.

Simulation Output Analysis Based on Excursions
James M. Calvin (New Jersey Institute of Technology)

Wednesday 8:30:00 AM 10:00:00 AM
Simulation Analysis I

Chair: John Fowler (Arizona State University)

Discrete event simulation modelling has been extensively used in modelling complex systems. Although it offers great conceptual-modelling flexibility, it is both computationally expensive and data intensive. There are several examples of simulation models that generate millions of observations to achieve satisfactory point and confidence interval estimations for the model variables. In these cases, it is exceptionally cumbersome to conduct the required output and sensitivity analysis in a spreadsheet or statistical package. In this paper, we highlight the advantages of employing data warehousing techniques for storing and analyzing simulation output data. The proposed data warehouse environment is capable of providing the means for automating the necessary algorithms and procedures for estimating different parameters of the simulation. These include initial transient in steady-state simulations and point and confidence interval estimations. Previously developed models for evaluating patient flow through hospital departments are used to demonstrate the problem and the proposed solutions.

An Efficient Screening Methodology for a Priori Assessed Non-Influential Factors
Thomas M. Cioppa (US Army Training and Doctrine Command Analysis Center)

The choice of which factors to choose to vary in a simula-tion to effect a change in the measure of interest is diffi-cult. Many factors are a priori judged not to effect the measure of interest. There is often no subsequent analysis of whether this judgment is valid or not. The proposed methodology outlines a sequence of limited runs to assess the accuracy of the a priori belief of non-influential fac-tors. These runs can either identify if an influential fac-tor(s) has been omitted or confirm a priori beliefs. Execut-ing these sequences of runs before focusing on the suspected influential factors can contribute to subsequent analysis by confirming that suspected non-influential fac-tors do not significantly impact the measure of interest. An example of the methodology using an agent based model is presented.

Variance-Based Sampling for Cycle Time - Throughput Confidence Intervals
Rachel T. Johnson (Arizona State Univeristy) and Sonia E. Leach, John W. Fowler, and Gerald T. Mackulak (Arizona State University)

In the analysis of a manufacturing system, the analyst is often interested in the change in mean cycle time as a func-tion of different throughput (start rate) levels. Since the variance of the mean cycle time generally increases as the start rate increases, an equal allocation of simulation effort at each simulated throughput level will result in confidence intervals of different widths. This paper discusses an ap-proach for generating nearly equal sized mean cycle time confidence intervals at selected throughput levels when the computing budget is fixed (limited). The simulation effort allocation procedure described in this paper determines the proportion of the fixed budget to allocate at each through-put level based on the asymptotic variance.

A Data Warehouse Environment for Storing and Analyzing Simulation Output Data
Christos Vasilakis, Elia El-Darzi, and Panagiotis Chountas (University of Westminster)

Wednesday 10:30:00 AM 12:00:00 PM
Simulation Analysis II

Chair: Donald Gross (George Mason University)

Calvin and Nakayama previously introduced permuting as a way of improving existing standardized time series methods. The basic idea is to split a simulated sample path into non-overlapping segments, permute the segments to construct a new sample path, and apply a standardized time series scaling function to the new path. Averaging over all permuted paths yields the permuted estimator. This paper discusses applying permutations to the weighted area estimator of Goldsman and Schruben. Empirical results seem to indicate that compared to not permuting, permuting can reduce the length and variability of the resulting confidence interval half widths but with additional computational overhead and some degradation in coverage; however, the decrease in coverage is not as bad as with batching.

Input Modeling Using Quantile Statistical Methods
Abhishek Gupta and Emanuel Parzen (Texas A&M University)

This paper applies quantile data analysis to input modeling in simulation. We introduce the use of QIQ plots to identify suitable distributions fitting the data and comparison distribution P-P plots to test the fit. Two examples illustrate the utility of these quantile statistical methods for input modeling. Popular distribution fitting software often give confusing results, which is usually a set of distributions differing marginally in the test statistic value. The methods discussed in this paper can be used for further analysis of the software results.

Overlapping Variance Estimators for Simulations
Christos Alexopoulos and David Goldsman (Georgia Institute of Technology), Nilay Tanik Argon (University of Wisconsin-Madison) and Gamze Tokol (Decision Analytics, LLC)

We examine properties of overlapped versions of the standardized time series area and Cramér-von Mises estimators for the variance parameter of a stationary stochastic process, e.g., a steady-state simulation output process. We find that the overlapping estimators have the same bias properties as, but lower variance than, their nonoverlapping counterparts; the new estimators also perform well against the benchmark batch means estimator. We illustrate our findings with analytical and Monte Carlo examples.

Permuted Weighted Area Estimators
James M. Calvin and Marvin K. Nakayama (New Jersey Institute of Technology)