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Ranking&selection (R&S) procedures are simulation-optimization algorithms for making one-time decisions among a finite set of alternative system designs or feasible solutions with a statistical assurance of a good selection. R&S with covariates (R&S+C) extends the paradigm to allow the optimal selection to depend on contextual information that is obtained just prior to the need for a decision. The dominant approach for solving such problems is to employ offline simulation to create metamodels that predict the performance of each system or feasible solution as a function of the covariate. This paper introduces a fundamentally different approach that solves individual R&S problems offline for various values of the covariate, and then treats the real-time decision as a classification problem: given the covariate information, which system is a good solution? Our approach exploits the availability of efficient R&S procedures, requires milder assumptions than the metamodeling paradigm to provide strong guarantees, and can be more efficient. 

Many tutorials and survey papers have been written on ranking & selection because it is such a useful tool for simulation optimization when the number of feasible solutions or “systems” is small enough that all of them can be simulated. Cheap, ubiquitous, parallel computing has greatly increased the “all of them can be simulated” limit. Naturally these tutorials and surveys have focused on the underlying theory of R&S and have provided pseudocode procedures. This tutorial, by contrast, emphasizes applications, programming and interpretation of R&S, using the R programming language for illustration. Readers (and the audience) can download the code and follow along with the examples, but no experience with R is needed. 

The Rapid Gaussian Markov Improvement Algorithm (rGMIA) solves discrete optimization via simulation problems by using a Gaussian Markov random field and complete expected improvement as the sampling and stopping criterion. rGMIA has been created as a sequential sampling procedure run on a single processor. In this paper, we extend rGMIA to a parallel computing environment when q+1 solutions can be simulated in parallel. To this end, we introduce the q-point complete expected improvement criterion to determine a batch of q+1 solutions to simulate. This new criterion is implemented in a new object-oriented rGMIA package. 

Disruption is a serious and common problem for the airline industry. High utilisation of aircraft and airport resources mean that disruptive events can have large knock-on effects for the rest of the schedule. The airline must rearrange their schedule to reduce the impact. The focus in this paper is on the Aircraft Recovery Problem. The complexity and uncertainty involved in the industry makes this a difficult problem to solve. Many deterministic modelling approaches have been proposed, but these struggle to handle the inherent variability in the problem. This paper proposes a multi-fidelity modelling framework, enabling uncertain elements of the environment to be included within the decision making process. We combine a deterministic integer program to find initial solutions and a novel simulation optimisation procedure to improve these solutions. This allows the solutions to be evaluated whilst accounting for the uncertainty of the problem. The empirical evaluation suggests that the combination consistently finds good rescheduling options. 

When working with models that allow for many candidate solutions, simulation practitioners can benefit from screening out unacceptable solutions in a statistically controlled way. However, for large solution spaces, estimating the performance of all solutions through simulation can prove impractical. We propose a statistical framework for screening solutions even when only a relatively small subset of them is simulated. Our framework derives its superiority over exhaustive screening approaches by leveraging available properties of the function that describes the performance of solutions. The framework is designed to work with a wide variety of available functional information and provides guarantees on both the confidence and consistency of the resulting screening inference. We provide explicit formulations for the properties of convexity and Lipschitz continuity and show through numerical examples that our procedures can efficiently screen out many unacceptable solutions. 

In their 2004 seminal paper, Glynn and Juneja formally and precisely established the rate-optimal, probability of incorrect-selection, replication allocation scheme for selecting the best of k simulated systems. In the case of independent, normally distributed outputs this allocation has a simple form that depends in an intuitively appealing way on the true means and variances. Of course the means and (typically) variances are unknown, but the rate-optimal allocation provides a target for implementable, dynamic, data-driven policies to achieve. In this paper we compare the empirical behavior of four related replication-allocation policies: mCEI from Chen and Rzyhov and our new gCEI policy that both converge to the Glynn and Juneja allocation; AOMAP from Peng and Fu that converges to the OCBA optimal allocation; and TTTS from Russo that targets the rate of convergence of the posterior probability of incorrect selection. We find that these policies have distinctly different behavior in some settings. 

Inference-based optimization via simulation, which substitutes Gaussian process (GP) learning for the structural properties exploited in mathematical programming, is a powerful paradigm that has been shown to be remarkably effective in problems of modest feasible-region size and decision-variable dimension. The limitation to “modest” problems is a result of the computational overhead and numerical challenges encountered in computing the GP conditional (posterior) distribution on each iteration. In this paper, we substantially expand the size of discrete-decision-variable optimization-via-simulation problems that can be attacked in this way by exploiting a particular GP—discrete Gaussian Markov random fields—and carefully tailored computational methods. The result is the rapid Gaussian Markov Improvement Algorithm (rGMIA), an algorithm that delivers both a global convergence guarantee and finite-sample optimality-gap inference for significantly larger problems. Between infrequent evaluations of the global conditional distribution, rGMIA applies the full power of GP learning to rapidly search smaller sets of promising feasible solutions that need not be spatially close. We carefully document the computational savings via complexity analysis and an extensive empirical study. Summary of Contribution: The broad topic of the paper is optimization via simulation, which means optimizing some performance measure of a system that may only be estimated by executing a stochastic, discrete-event simulation. Stochastic simulation is a core topic and method of operations research. The focus of this paper is on significantly speeding-up the computations underlying an existing method that is based on Gaussian process learning, where the underlying Gaussian process is a discrete Gaussian Markov Random Field. This speed-up is accomplished by employing smart computational linear algebra, state-of-the-art algorithms, and a careful divide-and-conquer evaluation strategy. Problems of significantly greater size than any other existing algorithm with similar guarantees can solve are solved as illustrations. 

Often in manufacturing systems, scenarios arise where the demand for maintenance exceeds the capacity of maintenance resources. This results in the problem of allocating the limited resources among machines competing for them. This maintenance scheduling problem can be formulated as a Markov decision process (MDP) with the goal of finding the optimal dynamic maintenance action given the current system state. However, as the system becomes more complex, solving an MDP suffers from the curse of dimensionality. To overcome this issue, we propose a two-stage approach that first optimizes a static condition-based maintenance (CBM) policy using a genetic algorithm (GA) and then improves the policy online via Monte Carlo tree search (MCTS). The static policy significantly reduces the state space of the online problem by allowing us to ignore machines that are not sufficiently degraded. Furthermore, we formulate MCTS to seek a maintenance schedule that maximizes the long-term production volume of the system to reconcile the conflict between maintenance and production objectives. We demonstrate that the resulting online policy is an improvement over the static CBM policy found by GA. 

This paper studies computational improvement of the Gaussian Markov improvement algorithm (GMIA) whose underlying response surface model is a Gaussian Markov random field (GMRF). GMIA’s computational bottleneck lies in the sampling decision, which requires factorizing and inverting a sparse, but large precision matrix of the GMRF at every iteration. We propose smart GMIA (sGMIA) that performs expensive linear algebraic operations intermittently, while recursively updating the vectors and matrices necessary to make sampling decisions for several iterations in between. The latter iterations are much cheaper than the former at the beginning, but their costs increase as the recursion continues and ultimately surpass the cost of the former. sGMIA adaptively decides how long to continue the recursion by minimizing the average per-iteration cost. We perform a floating-point operation analysis to demonstrate the computational benefit of sGMIA. Experiment results show that sGMIA enjoys computational efficiency while achieving the same search effectiveness as GMIA. 

The nonstationary Poisson process (NSPP) is a workhorse tool for modeling and simulating arrival processes with time-dependent rates. In many applications only a single sequence of arrival times are observed. While one sample path is sufficient for estimating the arrival rate or integrated rate function of the process—as we illustrate in this paper—we show that testing for Poissonness, in the general case, is futile. In other words, when only a single sequence of arrival data are observed then one can fit an NSPP to it, but the choice of “NSPP” can only be justified by an understanding of the underlying process physics, or a leap of faith, not by testing the data. This result suggests the need for sensitivity analysis when such a model is used to generate arrivals in a simulation.