SDO : A Statistical Method for Global Optimization

By D. Dennis, Coxy, Susan, JohnzAbstractAn. 1997

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Citations in the corpus

An evaluation of adaptive surrogate modeling based optimization with two benchmark problems (2014, methodology): “There are many adaptive sampling approaches, including “Minimizing an Interpolating Surface (MIS)” (Jones, 2001), “Minimizing a Statistical Lower Bound (MSL)” (Cox and John, 1997), “Maximizing the Probability of Improvement (MPI)” (Stuckman, 1988) and “Maximizing Expected Improvement (MEI)” (Schonla”
Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting (2009, methodology): “Among competing criteria for GP optimization (see Section I), variants of the - rule (with only heuristically defined ) have been introduced and demonstrated to be effective for this application [7], [27].”
Design and Analysis of Computer Experiments in Multidisciplinary Design Optimization: A Review of How Far We Have Come - Or Not (2008, methodology): “30,31,32,33,34 For instance, the Variable Complexity Response Surface Modeling (VCRSM) method developed predominantly at Virginia Tech, 35,36 uses analyses of varying fidelity to reduce the design space to the region of interest and build response surface models of increasing accuracy.”
On Sequential Sampling for Global Metamodeling in Engineering Design (2002, unknown): “For metamodel-based design optimization, based on different criteria for a balanced search (sequential sampling), various optimization approaches have been developed, e.g., Efficient Global Optimization (EGO) [17], Surrogate Management Framework (SMF) [5], Sequential Design Optimization (SDO) [18], ”
Portfolio Allocation for Bayesian Optimization (2010, background): “Upper conﬁdence bound (UCB & GP-UCB): Cox and John [11] introduce an algorithm they call “Sequential Design for Optimization”, or SDO .”
Bayesian optimization for learning gaits under uncertainty (2015, background): “UCB [28] is deﬁned as The choice of the free parameter κ is crucial as it determines the trade-oﬀ rate between exploration and exploitation.”
A benchmark of kriging-based infill criteria for noisy optimization (2013, background): “This criterion can be found in [5] or [38].”
Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. (2002, methodology): “Cox and John used an approach whereby a lower bounding function was mini- mized at each iteration [20], [21]. min x ŷ(x)− bσ̂(x), (2.14) where b is a user-controlled parameter that defines how globally or locally to search.”
Building Efficient Response Surfaces of Aerodynamic Functions with Kriging and Cokriging (2008, methodology): “The surrogate management framework [6] and trust-region framework [7] are generally the most favored methods, but refining the response surface at its predicted optimum is also efficient particularly when taking into account uncertainty (Expected Improvement or Lower Confidence Bounding Function cri”
Derivative-free optimization: a review of algorithms and comparison of software implementations (2012, methodology): “Sequential design for optimization (SDO) Assuming that f̂ (x) is a random variable with standard deviation predictor s(x), the SDO algorithm [36] proposes the minimization of the statistical lower bound of the function f̂ (x∗) − τ s(x∗) for some τ ≥ 0.”
Efficient Global Optimization of Expensive Black-Box Functions (1998, methodology): “Cox and John [9] use a statistical model, but they optimize the figure of merit by complete enumeration over a fine grid – a procedure obviously limited to one or two dimensions.”
Surrogate-based methods for black-box optimization (2017, methodology): “Here y min is the current best function value and the minimum is taken over all possible remaining candidate points [16].”
An experimental methodology for response surface optimization methods (2011, background): “…surface methods has been steady over the past 40 years (Kushner 1964; Perttunen et al. 1989; Stuckman 1989; Mockus 1989; Sacks et al. 1989; Elder 1992; Cox and John 1995; Schonlau 1997; Jones and Schonlau 1998; Gutmann 2001; Sasena 2002; Santner et al. 2003; Boyle 2006; Regis 2007; Lizotte 2008).”
Parallelizing Exploration-Exploitation Tradeoffs with Gaussian Process Bandit Optimization (2012, methodology): “…such as Maximum Expected Improvement (Jones et al., 1998), Maximum Probability of Improvement (Mockus, 1989), and upperconfidence based methods (Cox & John, 1997), have been developed to balance exploration with exploitation and successfully applied in learning problems (Lizotte et al., 2007).”