Robust Optimization in Simulation: Taguchi and Krige Combined

Dellino, Gabriella; Kleijnen, J.P.C.; Meloni, Carlo

doi:10.1287/ijoc.1110.0465

Cited by 74 publications

(34 citation statements)

References 49 publications

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“…Likewise, in simulation the optimum solution may be completely wrong when ignoring uncertainties in some inputs; e.g., the nominally optimal decision on the inventory control limits s (reorder level) and S (order-up-to level) may be completely wrong, because this solution ignores the uncertainty in the parameters assumed for the random demand and delivery time distributions. In Section 7.1, we …rst explain Taguchi's approach, updating and extending Dellino et al (2010); also see Dellino et al (2012). In Section 7.2, we brie ‡y discuss Ben-Tal's approach, summarizing Yan¬ko¼ glu et al (2013).…”

Section: Robust Optimizationmentioning

confidence: 99%

Response Surface Methodology

Kleijnen

2014

International Series in Operations Research &Amp; Management Science

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This chapter …rst summarizes Response Surface Methodology (RSM), which started with Box and Wilson's article in 1951 on RSM for real, non-simulated systems. RSM is a stepwise heuristic that uses …rst-order polynomials to approximate the response surface locally. An estimated polynomial metamodel gives an estimated local gradient, which RSM uses in steepest ascent (or descent) to decide on the next local experiment. When RSM approaches the optimum, the latest …rst-order polynomial is replaced by a second-order polynomial. The …tted second-order polynomial enables the estimation of the optimum. Furthermore, this chapter focuses on simulated systems, which may violate the assumptions of constant variance and independence. The chapter also summarizes a variant of RSM that is proven to converge to the true optimum, under speci…c conditions. The chapter presents an adapted steepest ascent that is scale-independent. Moreover, the chapter generalizes RSM to multiple random responses, selecting one response as the goal variable and the other responses as the constrained variables. This generalized RSM is combined with mathematical programming to estimate a better search direction than the steepest ascent direction. To test whether the estimated solution is indeed optimal, bootstrapping may be used. Finally, the chapter discusses robust optimization of the decision variables, while accounting for uncertainties in the environmental variables.

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Section: Robust Optimizationmentioning

confidence: 99%

Response Surface Methodology

Kleijnen

2014

International Series in Operations Research &Amp; Management Science

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“…Reformulating ( Myers et al (2009) and also in Dellino et al (2012) and Yaniko¼ glu et al (2015). Dellino et al (2012) combines the Taguchian world view and Kriging, so this approach replaces the polynomial in (59) To estimate the Kriging models for E(wjd) and (wjd) in (58), Dellino et al proposes the following two approaches: (i) Fit one Kriging model for E(wjd) and one Kriging model for (wjd)-estimating both models from the same simulation I/O data.…”

Section: Robust Optimization (Ro)mentioning

confidence: 99%

“…Dellino et al (2012) combines the Taguchian world view and Kriging, so this approach replaces the polynomial in (59) To estimate the Kriging models for E(wjd) and (wjd) in (58), Dellino et al proposes the following two approaches: (i) Fit one Kriging model for E(wjd) and one Kriging model for (wjd)-estimating both models from the same simulation I/O data. (ii) Fit one Kriging model to a relatively small number n of combinations of d and e, and use this metamodel to compute predictions for w for N n combinations of d and e, accounting for the distribution of e. We detail these approaches, as follows.…”

Section: Robust Optimization (Ro)mentioning

confidence: 99%

Regression and Kriging metamodels with their experimental designs in simulation: A review

Kleijnen

2017

European Journal of Operational Research

254

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This article reviews the design and analysis of simulation experiments. It focusses on analysis via either low-order polynomial regression or Kriging (also known as Gaussian process) metamodels. The type of metamodel determines the design of the experiment, which determines the input combinations of the simulation experiment. For example, a …rst-order polynomial metamodel requires a "resolution-III" design, whereas Kriging may use Latin hypercube sampling. Polynomials of …rst or second order require resolution III, IV, V, or "central composite" designs. Before applying either regression or Kriging, sequential bifurcation may be applied to screen a great many inputs. Optimization of the simulated system may use either a sequence of low-order polynomials known as response surface methodology (RSM) or Kriging models …tted through sequential designs including e¢ cient global optimization (EGO). The review includes robust optimization, which accounts for uncertain simulation inputs.

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“…Optimization methods can be applied directly to the metamodels to identify (potentially) good alternatives, but, as we discuss above, better results may be achieved when decision makers gain a broad understanding of the simulation's behaviour, rather than receive a specific recommendation. Robust design is often of interest for large-scale simulation studies, because decision makers may be interested in identifying combinations of the controllable decision factors that lead to good results across a variety of combinations of noise factors; see, for example, Kleijnen et al (2005), Dellino et al (2012), or . In this context, there is often less of a concern about the ability to identify noise factor contributions; even so, designs capable of handling large numbers of factors are necessary.…”

Section: Introductionmentioning

confidence: 99%

Efficient, nearly orthogonal-and-balanced, mixed designs: an effective way to conduct trade-off analyses via simulation

Vieira

Sanchez

Kienitz

et al. 2013

Journal of Simulation

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Designed experiments are powerful methodologies for gaining insights into the behaviour of complex simulation models. In recent years, many new designs have been created to address the large number of factors and complex response surfaces that often arise in simulation studies, but handling discrete-valued or qualitative factors remains problematic. We propose a framework for generating a design, of specified size, that is nearly orthogonal and nearly balanced for any mix of factor types (categorical, numerical discrete, and numerical continuous) and mix of factor levels. These new designs allow decision makers structured methods for trade-off analyses in situations that are not necessarily amenable to other methods for choosing alternatives, such as simulation optimization or ranking and selection approaches. These new designs also compare well to existing approaches for constructing custom designs for smaller experiments, and may also be of interest for exploring computer models in domains where fewer factors are involved.

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Robust Optimization in Simulation: Taguchi and Krige Combined

Cited by 74 publications

References 49 publications

Response Surface Methodology

Response Surface Methodology

Regression and Kriging metamodels with their experimental designs in simulation: A review

Efficient, nearly orthogonal-and-balanced, mixed designs: an effective way to conduct trade-off analyses via simulation

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