Robust simulation based optimization with input uncertainty

Joint analysis of input and parametric uncertainties in watershed water quality modeling: A formal Bayesian approach

In this paper, a simulation-based optimization approach, named NHOCBA, for a typical resource allocation problem is presented. The hybrid algorithm based on neighborhood algorithm is applied to explore toward optimal direction in design space. For increasing efficiency, an optimal computing budget allocation (OCBA) is adopted to compute the optimal number of replications and to provide reliable evaluation of variance. In addition, we deal with the resource allocation problem which exist multiple global optima in design space. Therefore, a trim procedure which prevents to allocate extra numbers of replication to local optima has been proposed to enhance efficiency. Then, we use confidence interval at the end of algorithm procedure to find an optimal set instead of an optimal solution from design space. Finally, we compare the NHOCBA with different algorithms by experimentation study which shows that NHOCBA approach can perform better than the other algorithms under certain conditions.

We consider a pharmaceutical company that sources a biological product from a set of unreliable contract manufacturers. The likelihood of a manufacturer to successfully deliver the product is estimated via logistic regression as a function of the product attributes. The assignment of a product to the right contract manufacturers is of critical importance for the pharmaceutical company, and simulation-based optimization is used to identify the optimal sourcing decision. However, the input uncertainty due to the uncertain parameters of the logistic regression model often leads to poor sourcing decisions. We quantify the decrease in the expected profit due to input uncertainty as a function of the size of the historical data set, the level of dispersion in the historical data of a product attribute, and the number of products. We also introduce a sampling-based algorithm that reduces the expected decrease in the expected profit.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we investigate the capacity and capacity-achieving input probability distributions (IPDs) of finite-input–finite-output discrete memoryless channels (DMCs). In the general respect, we establish a novel and simple characterization for the capacity-achieving IPDs of a DMC, which is equivalent to the conventional Kuhn–Tucker conditions. We then prove a conjecture of Majani and Rumsey, which claims that every probability component of each capacity-achieving IPD of a DMC with positive capacity is less than <emphasis><formula formulatype="inline"><tex>$1-e^{-1}$</tex></formula></emphasis>, where <emphasis><formula formulatype="inline"><tex>$e=2.71828182\ldots $</tex></formula></emphasis> is the base of natural logarithms. It remains an open problem whether there exists an explicit closed-form solution for the capacity and capacity-achieving IPDs of a general finite-input–finite-output DMC, except for the two-input–two-output DMC. In the algebraic respect, we demonstrate that there does not, in general, exist an algebraic solution for the capacity-achieving IPDs of an <emphasis><formula formulatype="inline"><tex>$m$</tex></formula></emphasis>-input–<emphasis><formula formulatype="inline"><tex>$n$</tex></formula></emphasis>-output DMC for any <emphasis><formula formulatype="inline"><tex>$m\geq 2$</tex></formula></emphasis> and any <emphasis><formula formulatype="inline"><tex>$n\geq 3$</tex></formula></emphasis>. In the analytic respect, however, we can obtain an explicit closed-form analytic solution, represented as an infinite series, for the capacity-achieving IPD of a two-input–three-output DMC. We also provide a formula for the average capacity of weakly symmetric DMCs and show that the average capacity in nats per channel use of the <emphasis><formula formulatype="inline"><tex>$n$</tex></formula></emphasis>-input–<emphasis><formula formulatype="inline"><tex>$n$</tex></formula></emphasis>-output weakly symmetric DMCs increases for <emphasis><formula formulatype="inline"><tex>$n\geq 2$</tex> </formula></emphasis> but has a finite limit of <emphasis><formula formulatype="inline"> <tex>$1-\gamma$</tex></formula></emphasis> as <emphasis><formula formulatype="inline"> <tex>$n\to \infty$</tex></formula></emphasis>, where <emphasis><formula formulatype="inline"> <tex>$\gamma =0.57721566\ldots $</tex></formula></emphasis> is Euler's constant. In the algorithmic respect, the convergence of the Arimoto–Blahut algorithm is proved in a direct and elementary way. A new and simple iterative algorithm for calculating a capacity-achieving IPD is then proposed, which is provably convergent for all DMCs with positive transition probabilities. Finally, the characterization and determination of the set of all capacity-achieving IPDs of a DMC are addressed. </para>

Integrated Bayesian Multi-model approach to quantify input, parameter and conceptual model structure uncertainty in groundwater modeling

The indifference-zone (IZ) formulation of ranking and selection (R&S) is the foundation of many procedures that have been useful for choosing the best among a finite number of simulated alternatives. Of course, simulation models are imperfect representations of reality, which means that a simulation-based decision, such as choosing the best alternative, is subject to model risk. In this paper we explore the impact of model risk due to input uncertainty on IZ R&S. "Input uncertainty" is the result of having estimated ("fit") the simulation input models to observed real-world data. We find that input uncertainty may force the user to revise, or even abandon, their objectives when employing a R&S procedure, or it may have very little effect on selecting the best system even when the marginal input uncertainty is substantial.

Efficient calibration of microscopic car-following models for large-scale stochastic network simulators

This paper presents a new game-theoretic approach toward the validation of discrete-event air combat (AC) simulation models and simulation-based optimization. In this approach, statistical techniques are applied for estimating games based on data produced by a simulation model. The estimation procedure is presented in cases involving games with both discrete and continuous decision variables. The validity of the simulation model is assessed by comparing the properties of the estimated games to actual practices in AC. These games are also applied for simulation-based optimization in a two-sided setting in which the action of the opponent is taken into account. In optimization, the estimated games enable the study of effectiveness of AC tactics as well as aircraft, weapons, and avionics configurations. The game-theoretic approach enhances existing methods for the validation of discrete-event simulation models and techniques for simulation-based optimization by incorporating the inherent game setting of AC into the analysis. It also provides a novel game-theoretic perspective to simulation metamodeling which is used to facilitate simulation analysis. The utilization of the game-theoretic approach is illustrated by analyzing simulation data obtained with an existing AC simulation model.

An input model is a collection of distributions together with any associated parameters that are used as primitive inputs in a simulation model. Input model uncertainty arises when one is not completely certain what distributions and/or parameters to use. This tutorial attempts to provide a sense of why one should consider input uncertainty and what methods can be used to deal with it.

10525 Background: To evaluate the incremental short- and long-term benefits and harms of primary prevention with risk reducing medication in high-risk women receiving screening mammography. Methods: We adapted an established, validated Cancer Intervention and Surveillance Modeling Network (CISNET) breast cancer discrete event microsimulation model developed to synthesize data the impact of using risk-reducing medication and annual mammography among women with a 3% or higher five-year risk of developing breast cancer. We also examined the effects of supplemental MRI. The model follows a simulated cohort of millions of US women from birth to death. We used large observational and clinical trial data to derive input parameters for cohort-specific birth rates, breast cancer risk, incidence and stage, screening performance, survival by age, stage, and subtype, treatment efficacy, and other cause mortality. Breast cancer risk was modeled based on family history, breast density, age and history of past breast biopsy. We compared two strategies, annual 3D mammography alone vs. annual 3D mammography and a 5-year course of risk reducing medication at various starting ages, and adding MRI to each approach. Outcomes included the benefits of risk-reducing drugs (avoiding breast cancer) and screening (stage, breast cancer death). Harms included drug side effects and screening false positives and overdiagnosis. Sensitivity analysis tested the impact of uncertainty in model inputs and assumptions on results. Results: Compared to mammography alone, adding risk reducing medication could decrease invasive breast cancer incidence by 30%, and breast cancer deaths by 30% (Table). However, due to reduction in breast cancer incidence, risk reducing medication could result in a 3% increase in false positive results; adding MRI increases benefits but also increases false-positive results. Benefits and harms of risk reducing medication and breast cancer screening strategies for women at high-risk of developing breast cancer. Conclusions: Risk-reducing mediation reduces the risk of hormone-receptor positive breast cancer, and combining this with mammography (and/or MRI) improves earlier detection. Additional work is ongoing to incorporate adverse effects of therapy. Simulation modeling can be used to provide individualized data to facilitate discussions about breast cancer prevention and early detection among high-risk women seen in clinical practice.[Table: see text]

Sensitivity and Uncertainty

In a highway asset maintenance management system involving more than one highway asset type, identifying an equitable optimal allocation of available budget to individual asset systems is a major challenge. This is because the following outcomes are desirable: (1) the maintenance needs of all assets are adequately addressed, (2) the objectives of individual asset systems are optimally satisfied in an equitable manner, and (3) the objectives of the overall highway asset system are achieved optimally. To achieve these desirable outcomes, this paper proposes a two-stage approach in solving the dual-level multiasset, multiobjective pavement network maintenance optimal budget allocation problem. Stage I of the approach analyzes the individual multiobjective asset systems independently to establish for each a family of optimal Pareto solutions. Minimization of maintenance cost is selected as a common objective for the individual asset systems. This serves as the link for interaction with the Stage II analysis. Stage II adopts an optimal algorithm to allocate budget to individual assets by performing a cross-asset trade-off to achieve the optimal budget solution for the given overall system-level objectives. By defining a minimum performance threshold level for each asset type, the Stage II optimization analysis aims to achieve an equitable allocation of budget by maintaining equivalent amounts of performance improvements for the individual asset systems above their respective minimum threshold levels. The conceptual framework of the proposed approach is presented in this paper with a numerical example to illustrate the detailed working of the procedure.

While the popularity of the numerical simulation approach (such as the Monte Carlo) for probabilistic reserves estimation has never been higher among geoscientists and reservoir engineers, comparatively little attention has been paid to the techniques needed to correctly model the required petrophysical input parameters. Petrophysical well analyses typically end in the presentation of average reservoir property values for porosity, water saturation and net-to-gross but these lone averages, while adequate for deterministic reserves estimates, obviously fail to account for the inherent reservoir petrophysical properties uncertainty within a probabilistic reserves estimate. Of more importance for probabilistic reserves estimation is a statistical model comprising Probability Distribution Functions (or PDFs) of the aerial uncertainty in reservoir properties resulting from a larger reservoir being sampled by a relatively small discrete well population. Monte Carlo simulations are typically used to estimate probabilistic reserves but the accuracy of these are strongly correlated to the quality of the input probability distributions. Many errors in the outputs of reserves models could be traced back to assigning incorrect values to the descriptive parameters of a distribution, and indeed the selection of an appropriate distribution. Therefore, if probability distributions are to be used to represent statistical assumptions of petrophysical properties in reserves estimates, then the way petrophysical averages data is analysed and transformed into PDFs becomes of crucial importance. Hence, the purpose of this paper is to present practical ideas for achieving the definition of probability distributions that best represent the petrophysical property input into probabilistic reserves estimates. The focus on petrophysical properties in this paper is not arbitrary or accidental but, instead, reflects the centrality of petrophysical input as a driver of accuracy in reserves estimates.

In stochastic simulation, we construct mathematical models to imitate the behavior of real systems, use computers to sample behavioral histories (sample paths) of these models, and exploit those samples to improve decision making with the real system. The imitation part can be very challenging, in particular for modeling uncertainty. Fitting univariate probability distribution to data is far from sufficient. Modeling the dependence is very important and much more challenging. It involves multivariate distributions, copulas, stochastic processes, and other complicated stochastic objects. Simulating the model on a computer also involves an imitation game, to simulate the realizations of random variables and stochastic processes with deterministic algorithms on a computer. Random number generation involves writing deterministic computer programs that can imitate simple probabilistic models such as independent uniform random variables uniformly distributed over the interval (0, 1). An "exact" algorithmic implantation of such models is theoretically impossible, so we settle for a reasonable fake. The talk will give snapshots and expose ideas collected from the author's journey thought stochastic simulation. The tour will start with random number generation and visit some challenging problems such as stochastic modeling, simulation-based optimization, rare events, simulation on parallel processors, and future challenges.

A repairable system with N failure modes and one standby unit : Mitsuo Yamashiro. Microelectron. Reliab.20, 831 (1980)