pith. sign in

arxiv: 1906.11111 · v1 · pith:YBTYGI3Hnew · submitted 2019-06-26 · 🧮 math.NA · cs.NA· stat.AP

Monte Carlo Integration with adaptive variance selection for improved stochastic Efficient Global Optimization

Felipe Carraro , Rafael Holdorf Lopez , Leandro Fleck Fadel Miguel , Andr\'e Jacomel Torii This is my paper

Pith reviewed 2026-05-25 15:15 UTC · model grok-4.3

classification 🧮 math.NA cs.NAstat.AP
keywords Monte Carlo integrationstochastic optimizationEfficient Global OptimizationStochastic Krigingadaptive varianceglobal optimizationrobust design
0
0 comments X

The pith

An adaptive target variance for Monte Carlo integration error improves stochastic Efficient Global Optimization by balancing cost and exploration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces an adaptive scheme that automatically selects the target variance of the Monte Carlo integration error at each step of a stochastic Efficient Global Optimization search. This variance is treated as an additional source of uncertainty inside a Stochastic Kriging surrogate, so the optimizer receives both the mean prediction and a controlled error level. By adapting the target rather than fixing it in advance, the method lets the designer influence how much computational effort is spent on each integral evaluation and how aggressively the search explores uncertain regions. On stochastic benchmark functions and a tuned mass damper design problem the adaptive version produced better final designs than either a fixed-variance version or a multi-start optimizer, and it remained usable even when the number of stochastic dimensions was large.

Core claim

The central claim is that the variance of Monte Carlo integration error can be set by the user through a chosen target value, that this value directly affects both the computational cost and the exploration behavior of sEGO, and that an automatic adaptation rule for the target produces consistently better results than a constant target or a multi-start baseline while extending the method to high-dimensional stochastic problems.

What carries the argument

The adaptive scheme for automatic selection of the target variance in Monte Carlo integration, supplied as an extra uncertainty term to the Stochastic Kriging model inside the sEGO loop.

If this is right

  • The method remains applicable when the number of stochastic dimensions is large.
  • It yields lower final objective values than fixed-variance MCI or multi-start optimization on the tested stochastic benchmark functions.
  • It also yields better designs than the two baselines on the tuned mass damper problem.
  • Performance degrades when the number of design variables becomes large because of the underlying sEGO and Kriging limits.
  • The chosen target variance directly trades off the cost of each integral evaluation against the amount of exploration performed by the optimizer.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same adaptive-variance idea could be transferred to other surrogate-based stochastic optimizers that already propagate integration or sampling error.
  • In engineering practice the method could reduce the total number of expensive simulations required for robust design by letting the algorithm decide when tighter integration is worth the cost.
  • A natural next test would be to apply the approach to problems that are simultaneously high-dimensional in both design variables and stochastic variables to locate the practical limits set by the Kriging surrogate.

Load-bearing premise

That the Monte Carlo integration error variance can be controlled through a user-chosen target value and that this choice strongly influences both the computational cost and the exploration ability of the sEGO process.

What would settle it

Run the adaptive and constant-target versions on the same stochastic benchmark functions for the same number of evaluations and measure final objective values and total wall-clock time; if the adaptive version does not produce lower objectives or lower total time in the majority of repeated trials, the claim is falsified.

Figures

Figures reproduced from arXiv: 1906.11111 by Andr\'e Jacomel Torii, Felipe Carraro, Leandro Fleck Fadel Miguel, Rafael Holdorf Lopez.

Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

In this paper, the minimization of computational cost on evaluating multi-dimensional integrals is explored. More specifically, a method based on an adaptive scheme for error variance selection in Monte Carlo integration (MCI) is presented. It uses a stochastic Efficient Global Optimization (sEGO) framework to guide the optimization search. The MCI is employed to approximate the integrals, because it provides the variance of the error in the integration. In the proposed approach, the variance of the integration error is included into a Stochastic Kriging framework by setting a target variance in the MCI. We show that the variance of the error of the MCI may be controlled by the designer and that its value strongly influences the computational cost and the exploration ability of the optimization process. Hence, we propose an adaptive scheme for automatic selection of the target variance during the sEGO search. The robustness and efficiency of the proposed adaptive approach were evaluated on global optimization stochastic benchmark functions as well as on a tuned mass damper design problem. The results showed that the proposed adaptive approach consistently outperformed the constant approach and a multi-start optimization method. Moreover, the use of MCI enabled the method application in problems with high number of stochastic dimensions. On the other hand, the main limitation of the method is inherited from sEGO coupled with the Kriging metamodel: the efficiency of the approach is reduced when the number of design variables increases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an adaptive scheme for selecting the target variance of Monte Carlo integration (MCI) error within a stochastic Efficient Global Optimization (sEGO) framework that employs Stochastic Kriging. The variance is treated as a controllable design parameter that trades off integration cost against exploration; an adaptive rule automatically adjusts the target during the search. The method is evaluated on stochastic benchmark functions and a tuned mass damper design problem, with the claim that the adaptive variant consistently outperforms both constant-variance MCI and a multi-start baseline while enabling application to problems with high stochastic dimension (the principal limitation being the number of design variables).

Significance. If the reported outperformance is statistically robust, the work supplies a practical mechanism for controlling the accuracy-cost trade-off inside stochastic metamodel-based optimization. The explicit use of MCI variance as an external control input, rather than a hidden fitting parameter, is a clear methodological strength. The evaluation on both synthetic benchmarks and an engineering design problem, together with the explicit statement of the design-variable-dimension limitation, strengthens the practical relevance of the contribution.

major comments (2)
  1. [Abstract / Results] Abstract and results description: the central claim that the adaptive approach 'consistently outperformed' the constant-variance and multi-start baselines is asserted without any reported quantitative metrics, number of independent runs, error bars, or statistical tests. This information is load-bearing for the empirical contribution and must be supplied before the performance advantage can be assessed.
  2. [Method / Stochastic Kriging formulation] The description of how the target variance is mapped into the Stochastic Kriging nugget or noise term is not given in sufficient detail to verify that the adaptive rule does not inadvertently introduce bias into the surrogate or the expected-improvement criterion.
minor comments (2)
  1. [Introduction] The abstract states that MCI 'provides the variance of the error in the integration' but does not cite the standard Monte Carlo variance formula or the specific estimator used; a brief reference or equation would improve clarity.
  2. [Figures] Figure captions and axis labels should explicitly state whether plotted values are means over multiple runs or single-run trajectories.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and commit to revisions that strengthen the empirical claims and methodological clarity.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and results description: the central claim that the adaptive approach 'consistently outperformed' the constant-variance and multi-start baselines is asserted without any reported quantitative metrics, number of independent runs, error bars, or statistical tests. This information is load-bearing for the empirical contribution and must be supplied before the performance advantage can be assessed.

    Authors: We agree that the abstract and results sections require quantitative support to substantiate the performance claims. In the revised manuscript we will add explicit metrics (mean objective values and standard deviations), the number of independent runs (typically 30), error bars or confidence intervals, and statistical tests (e.g., Wilcoxon rank-sum) comparing the adaptive scheme against the constant-variance and multi-start baselines. These additions will appear in both the abstract and the results section. revision: yes

  2. Referee: [Method / Stochastic Kriging formulation] The description of how the target variance is mapped into the Stochastic Kriging nugget or noise term is not given in sufficient detail to verify that the adaptive rule does not inadvertently introduce bias into the surrogate or the expected-improvement criterion.

    Authors: The target MCI variance is supplied directly as the known observation noise variance and is inserted into the diagonal of the covariance matrix as the nugget term, following the standard Stochastic Kriging formulation. This augments the posterior variance without altering the mean predictor or introducing systematic bias beyond the controlled noise level; the expected-improvement criterion is then evaluated on the resulting noisy posterior. We acknowledge that the current text lacks explicit equations and will expand the methods section with the precise mapping (including the updated covariance expression and EI formula) to allow verification that the adaptive rule preserves the unbiasedness properties of the surrogate. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper introduces an adaptive target-variance rule for MCI inside sEGO and reports empirical outperformance versus constant-variance and multi-start baselines on stochastic benchmarks and a TMD design problem. No equations, self-citations, or uniqueness claims are shown that reduce the central performance result to a fitted parameter or prior self-work by construction; variance is treated as an external designer-controlled input whose effect is measured directly in the experiments. The derivation chain is therefore self-contained against the reported benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are identifiable. The approach inherits standard assumptions of Monte Carlo sampling and stochastic Kriging.

pith-pipeline@v0.9.0 · 5793 in / 1100 out tokens · 22382 ms · 2026-05-25T15:15:47.028617+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

85 extracted references · 85 canonical work pages

  1. [1]

    Stochastic kriging for simulation metamodeling

    Bruce Ankenman, Barry L Nelson, and Jeremy Staum. Stochastic kriging for simulation metamodeling. Operations research, 58 0 (2): 0 371--382, 2010

    work page 2010

  2. [2]

    Ego method for diffusing s-duct shape design

    Hyo Gil Bae, Soo Hyung Park, and Jank Hyuk Kwon. Ego method for diffusing s-duct shape design. In International Conference on Computation Fluid Dynamics, volume 7, 2012

    work page 2012

  3. [3]

    Optimal performance-based design of non-linear stochastic dynamical rc structures subject to stationary wind excitation

    Andr \'e T Beck, Ioannis A Kougioumtzoglou, and Ketson R M dos Santos. Optimal performance-based design of non-linear stochastic dynamical rc structures subject to stationary wind excitation. Engineering Structures, 78: 0 145--153, 2014

    work page 2014

  4. [4]

    Beck , B

    J. Beck , B. M. Dia , L. F. R. Espath , Q. Long , and R. Tempone . Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain . Computer Methods in Applied Mechanics and Engineering, 334: 0 523--553, June 2018. doi:10.1016/j.cma.2018.01.053

    work page doi:10.1016/j.cma.2018.01.053 2018

  5. [5]

    Sarah Bobby, Seymour M. J. Spence, and Ahsan Kareem. Data-driven performance-based topology optimization of uncertain wind-excited tall buildings. Structural and Multidisciplinary Optimization, 54 0 (6): 0 1379--1402, Dec 2016. doi:10.1007/s00158-016-1474-6

    work page doi:10.1007/s00158-016-1474-6 2016

  6. [6]

    Capiez-Lernout and C

    E. Capiez-Lernout and C. Soize. Robust design optimization in computational mechanics. Journal of Applied Mechanics, Transactions ASME, 75 0 (2): 0 021001--1--021001--11, 2008

    work page 2008

  7. [7]

    Reliability based optimum design of tuned mass damper in seismic vibration control of structures with bounded uncertain parameters

    Subrata Chakraborty and Bijan Kumar Roy. Reliability based optimum design of tuned mass damper in seismic vibration control of structures with bounded uncertain parameters. Probabilistic Engineering Mechanics, 26 0 (2): 0 215--221, 2011

    work page 2011

  8. [8]

    Haftka, Peter Ifju, Kelvin Chang, Christopher Tyler, and Tony Schmitz

    Anirban Chaudhuri, Raphael T. Haftka, Peter Ifju, Kelvin Chang, Christopher Tyler, and Tony Schmitz. Experimental flapping wing optimization and uncertainty quantification using limited samples. Structural and Multidisciplinary Optimization, 51 0 (4): 0 957--970, Apr 2015. ISSN 1615-1488. doi:10.1007/s00158-014-1184-x

    work page doi:10.1007/s00158-014-1184-x 2015

  9. [9]

    Handbook of Structural Engineering, Second Edition

    W F Chen and E M Lui. Handbook of Structural Engineering, Second Edition. CRC Press, Boca Raton, FL, USA, 2005. ISBN 9781420039931

    work page 2005

  10. [10]

    Stochastic kriging with biased sample estimates

    Xi Chen and Kyoung-Kuk Kim. Stochastic kriging with biased sample estimates. ACM Transactions on Modeling and Computer Simulation (TOMACS), 24 0 (2): 0 8, 2014

    work page 2014

  11. [11]

    The effects of common random numbers on stochastic kriging metamodels

    Xi Chen, Bruce E Ankenman, and Barry L Nelson. The effects of common random numbers on stochastic kriging metamodels. ACM Transactions on Modeling and Computer Simulation (TOMACS), 22 0 (2): 0 7, 2012

    work page 2012

  12. [12]

    Enhancing stochastic kriging metamodels with gradient estimators

    Xi Chen, Bruce E Ankenman, and Barry L Nelson. Enhancing stochastic kriging metamodels with gradient estimators. Operations Research, 61 0 (2): 0 512--528, 2013

    work page 2013

  13. [13]

    Surrogate-based infill optimization applied to electromagnetic problems

    Ivo Couckuyt, Frederick Declercq, Tom Dhaene, Hendrik Rogier, and Luc Knockaert. Surrogate-based infill optimization applied to electromagnetic problems. International Journal of RF and Microwave Computer-Aided Engineering, 20 0 (5): 0 492--501, 2010

    work page 2010

  14. [14]

    Statistics for spatial data, volume 15

    Noel Cressie. Statistics for spatial data, volume 15. Wiley, New York, 1993

    work page 1993

  15. [15]

    Pattern classification

    Richard O Duda, Peter E Hart, and David G Stork. Pattern classification. John Wiley & Sons, 2012

    work page 2012

  16. [16]

    Kriging-based optimization applied to flow control

    R \'e gis Duvigneau and Praveen Chandrashekar. Kriging-based optimization applied to flow control. International Journal for Numerical Methods in Fluids, 69 0 (11): 0 1701--1714, 2012

    work page 2012

  17. [17]

    Failure probability minimization of buildings through passive friction dampers

    Miguel Letícia Fleck Fadel, Miguel Leandro Fleck Fadel, and Lopez Rafael Holdorf. Failure probability minimization of buildings through passive friction dampers. The Structural Design of Tall and Special Buildings, 25 0 (17): 0 869--885, 2016

    work page 2016

  18. [18]

    Engineering design via surrogate modelling: a practical guide

    Alexander Forrester, Andras Sobester, and Andy Keane. Engineering design via surrogate modelling: a practical guide. John Wiley & Sons, Chichester, West Sussex, United Kingdom, 2008

    work page 2008

  19. [19]

    A kriging constrained efficient global optimization approach applied to low-energy building design problems

    E Gengembre, Bruno Ladevie, Olivier Fudym, and A Thuillier. A kriging constrained efficient global optimization approach applied to low-energy building design problems. Inverse Problems in Science and Engineering, 20 0 (7): 0 1101--1114, 2012

    work page 2012

  20. [20]

    Multilevel monte carlo path simulation

    Michael B Giles. Multilevel monte carlo path simulation. Operations Research, 56 0 (3): 0 607--617, 2008

    work page 2008

  21. [21]

    Hafkta, and Wei Shyy

    Tushar Goel, Raphael T. Hafkta, and Wei Shyy. Comparing error estimation measures for polynomial and kriging approximation of noise-free functions. Structural and Multidisciplinary Optimization, 38 0 (5): 0 429, Aug 2008. ISSN 1615-1488. doi:10.1007/s00158-008-0290-z

    work page doi:10.1007/s00158-008-0290-z 2008

  22. [22]

    Gomes, André T

    Wellison J.S. Gomes, André T. Beck, Rafael H. Lopez, and Leandro F.F. Miguel. A probabilistic metric for comparing metaheuristic optimization algorithms. Structural Safety, 70: 0 59 -- 70, 2018. ISSN 0167-4730

    work page 2018

  23. [23]

    Optimization under unknown constraints

    RB Gramacy and HKH Lee. Optimization under unknown constraints. In Proceedings of the sixth Valencia international meeting, USA, 2010. Oxford University Press

    work page 2010

  24. [24]

    Haftka, Diane Villanueva, and Anirban Chaudhuri

    Raphael T. Haftka, Diane Villanueva, and Anirban Chaudhuri. Parallel surrogate-assisted global optimization with expensive functions -- a survey. Structural and Multidisciplinary Optimization, 54 0 (1): 0 3--13, Jul 2016. ISSN 1615-1488. doi:10.1007/s00158-016-1432-3

    work page doi:10.1007/s00158-016-1432-3 2016

  25. [25]

    Multi-index monte carlo: when sparsity meets sampling

    Abdul-Lateef Haji-Ali, Fabio Nobile, and Ra \'u l Tempone. Multi-index monte carlo: when sparsity meets sampling. Numerische Mathematik, 132 0 (4): 0 767--806, 2016

    work page 2016

  26. [26]

    General principles of the monte carlo method

    John Michael Hammersley and David Christopher Handscomb. General principles of the monte carlo method. In Monte Carlo Methods, pages 50--75. Springer, 1964

    work page 1964

  27. [27]

    Adaptive gradient-enhanced kriging model for variable-stiffness composite panels using isogeometric analysis

    Peng Hao, Shaojun Feng, Ke Zhang, Zheng Li, Bo Wang, and Gang Li. Adaptive gradient-enhanced kriging model for variable-stiffness composite panels using isogeometric analysis. Structural and Multidisciplinary Optimization, pages 1--16, 2018. doi:10.1007/s00158-018-1988-1

    work page doi:10.1007/s00158-018-1988-1 2018

  28. [28]

    Simulation-based optimal bayesian experimental design for nonlinear systems

    Xun Huan and Youssef M Marzouk. Simulation-based optimal bayesian experimental design for nonlinear systems. Journal of Computational Physics, 232 0 (1): 0 288--317, 2013

    work page 2013

  29. [29]

    Global optimization of stochastic black-box systems via sequential kriging meta-models

    Deng Huang, Theodore T Allen, William I Notz, and Ning Zeng. Global optimization of stochastic black-box systems via sequential kriging meta-models. Journal of global optimization, 34 0 (3): 0 441--466, 2006

    work page 2006

  30. [30]

    Optimal design of aeroengine turbine disc based on kriging surrogate models

    Zhangjun Huang, Chengen Wang, Jian Chen, and Hong Tian. Optimal design of aeroengine turbine disc based on kriging surrogate models. Computers & structures, 89 0 (1): 0 27--37, 2011

    work page 2011

  31. [31]

    Forrester, Andy J Keane, and Neil W Bressloff

    Alexander I J. Forrester, Andy J Keane, and Neil W Bressloff. Design and analysis of "noisy" computer experiments. AIAA journal, 44 0 (10): 0 2331--2339, 2006

    work page 2006

  32. [32]

    Comparison of kriging-based algorithms for simulation optimization with heterogeneous noise

    Hamed Jalali, Inneke Van Nieuwenhuyse, and Victor Picheny. Comparison of kriging-based algorithms for simulation optimization with heterogeneous noise. European Journal of Operational Research, 261 0 (1): 0 279 -- 301, 2017. ISSN 0377-2217. doi:https://doi.org/10.1016/j.ejor.2017.01.035

    work page doi:10.1016/j.ejor.2017.01.035 2017

  33. [33]

    A Taxonomy of Global Optimization Methods Based on Response Surfaces

    Donald Jones. A Taxonomy of Global Optimization Methods Based on Response Surfaces . Journal of Global Optimization, 21 0 (4): 0 345--383, 2001. doi:doi: 10.1023/a:1012771025575

    work page doi:10.1023/a:1012771025575 2001

  34. [34]

    Efficient Global Optimization of Expensive Black-Box Functions

    Donald R Jones, Matthias Schonlau, and J William. Efficient Global Optimization of Expensive Black-Box Functions . Journal of Global Optimization, 13: 0 455--492, 1998. ISSN 09255001. doi:10.1023/a:1008306431147

    work page doi:10.1023/a:1008306431147 1998

  35. [35]

    Kalos and P.A

    M.H. Kalos and P.A. Whitlock. Monte Carlo Methods, Volume 1: Basics. Monte Carlo Methods. Wiley, 1986. ISBN 9780471898399

    work page 1986

  36. [36]

    A method for the updating of stochastic kriging metamodels

    Bogumi Kami \'n ski. A method for the updating of stochastic kriging metamodels. European Journal of Operational Research, 247 0 (3): 0 859--866, 2015

    work page 2015

  37. [37]

    Semi-empirical formula for the seismic characteristics of the ground

    Kiyoshi Kanai. Semi-empirical formula for the seismic characteristics of the ground. 35, 07 1957

    work page 1957

  38. [38]

    Efficient global optimization applied to multi-objective design optimization of lift creating cylinder using plasma actuators

    Masahiro Kanazaki, T Matsumo, Kengo Maeda, and Mitsuhiro Kawazoe. Efficient global optimization applied to multi-objective design optimization of lift creating cylinder using plasma actuators. In Proceedings of the 18th Asia Pacific symposium on intelligent and evolutionary systems, volume 1, pages 663--677, 2015

    work page 2015

  39. [39]

    Estimating the variance of the predictor in stochastic kriging

    Jack P C Kleijnen and Ehsan Mehdad. Estimating the variance of the predictor in stochastic kriging. Simulation Modelling Practice and Theory, 66: 0 166--173, 2016

    work page 2016

  40. [40]

    Daniel G. Krige. A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand . Journal of the Chemical, Metallurgical and Mining Society of South Africa, 52 0 (6): 0 119--139, December 1951. doi:10.2307/3006914

    work page doi:10.2307/3006914 1951

  41. [41]

    Rodolphe Le Riche and Raphael T. Haftka. On global optimization articles in smo. Structural and Multidisciplinary Optimization, 46 0 (5): 0 627--629, Nov 2012. ISSN 1615-1488. doi:10.1007/s00158-012-0785-5. URL https://doi.org/10.1007/s00158-012-0785-5

    work page doi:10.1007/s00158-012-0785-5 2012

  42. [42]

    A review of comparative studies of spatial interpolation methods in environmental sciences: performance and impact factors

    Jin Li and Andrew D Heap. A review of comparative studies of spatial interpolation methods in environmental sciences: performance and impact factors. Ecological Informatics, 6 0 (3-4): 0 228--241, 2011

    work page 2011

  43. [43]

    Locatelli

    M. Locatelli. Bayesian algorithms for one-dimensional global optimization. Journal of Global Optimization, 10 0 (1): 0 57--76, 1997. ISSN 1573-2916. doi:10.1023/A:1008294716304

    work page doi:10.1023/a:1008294716304 1997

  44. [44]

    Lopez, Leandro F

    Rafael H. Lopez, Leandro F. F. Miguel, and Andr \'e T. Beck. Tuned Mass Dampers for Passive Control of Structures Under Earthquake Excitations, pages 3814--3823. Springer Berlin Heidelberg, Berlin, Heidelberg, 2015. ISBN 978-3-642-35344-4. doi:10.1007/978-3-642-35344-4_215

    work page doi:10.1007/978-3-642-35344-4_215 2015

  45. [45]

    Lopez, T.G

    R.H. Lopez, T.G. Ritto, Rubens Sampaio, and J.E. Souza de Cursi. A new algorithm for the robust optimization of rotor-bearing systems. Engineering Optimization, 46 0 (8): 0 1123--1138, 2014. doi:10.1080/0305215X.2013.819095

    work page doi:10.1080/0305215x.2013.819095 2014

  46. [46]

    Luersen, R

    M.A. Luersen, R. Le Riche, and F. Guyon. A constrained, globalized, and bounded nelder--mead method for engineering optimization. Structural and Multidisciplinary Optimization, 27 0 (1): 0 43--54, May 2004

    work page 2004

  47. [47]

    Globalized nelder--mead method for engineering optimization

    Marco A Luersen and Rodolphe Le Riche. Globalized nelder--mead method for engineering optimization. Computers & structures, 82 0 (23): 0 2251--2260, 2004

    work page 2004

  48. [48]

    Optimum design of multiple friction tuned mass dampers under seismic excitations

    Giancarlo Zibetti Mantovani, Leandro Fleck Fadel Miguel, Rafael Holdorf Lopez, Letícia Fleck Fadel Miguel, and Andre J Torii. Optimum design of multiple friction tuned mass dampers under seismic excitations. Proceedings of the 6th international symposium on solid mechanics, Joinville, pages 521--535, 2017

    work page 2017

  49. [49]

    The Mathworks, Inc., Natick, Massachusetts, 2015

    MATLAB version 8.6.0.267246 (R2015b). The Mathworks, Inc., Natick, Massachusetts, 2015

    work page 2015

  50. [50]

    R. E. Melchers and A. T. Beck. Structural Reliability Analysis and Prediction. John Wiley & Sons, 2018

    work page 2018

  51. [51]

    Miguel, Rafael H

    Leandro F.F. Miguel, Rafael H. Lopez, André J. Torii, Letícia F.F. Miguel, and André T. Beck. Robust design optimization of tmds in vehicle–bridge coupled vibration problems. Engineering Structures, 126: 0 703 -- 711, 2016. ISSN 0141-0296

    work page 2016

  52. [52]

    A hybrid approach for damage detection of structures under operational conditions

    Leandro Fleck Fadel Miguel, Rafael Holdorf Lopez, and Letícia Fleck Fadel Miguel. A hybrid approach for damage detection of structures under operational conditions. Journal of Sound and Vibration, 332 0 (18): 0 4241 -- 4260, 2013. ISSN 0022-460X

    work page 2013

  53. [53]

    Designing optimal multiple tuned mass dampers using genetic algorithms ( GA s) for mitigating the seismic response of structures

    Mohtasham Mohebbi, Kazem Shakeri, Yavar Ghanbarpour, and Hossein Majzoub. Designing optimal multiple tuned mass dampers using genetic algorithms ( GA s) for mitigating the seismic response of structures. Journal of Vibration and Control, 19 0 (4): 0 605--625, 2013

    work page 2013

  54. [54]

    Applied statistics and probability for engineers

    Douglas C Montgomery and George C Runger. Applied statistics and probability for engineers. John Wiley & Sons, New York, USA, 2010

    work page 2010

  55. [55]

    A simplex method for function minimization

    John A Nelder and Roger Mead. A simplex method for function minimization. The computer journal, 7 0 (4): 0 308--313, 1965

    work page 1965

  56. [56]

    An improved hybrid optimization algorithm for vibration based-damage detection

    Idilson António Nhamage, Rafael Holdorf Lopez, and Leandro Fleck Fadel Miguel. An improved hybrid optimization algorithm for vibration based-damage detection. Advances in Engineering Software, 93: 0 47 -- 64, 2016. ISSN 0965-9978. doi:https://doi.org/10.1016/j.advengsoft.2015.12.003

    work page doi:10.1016/j.advengsoft.2015.12.003 2016

  57. [57]

    Gaussian processes for global optimization

    Michael A Osborne, Roman Garnett, and Stephen J Roberts. Gaussian processes for global optimization. In 3rd international conference on learning and intelligent optimization (LION3), pages 1--15, 2009

    work page 2009

  58. [58]

    Noisy kriging-based optimization methods: a unified implementation within the diceoptim package

    Victor Picheny and David Ginsbourger. Noisy kriging-based optimization methods: a unified implementation within the diceoptim package. Computational Statistics & Data Analysis, 71: 0 1035--1053, 2014

    work page 2014

  59. [59]

    Quantile-based optimization of noisy computer experiments with tunable precision

    Victor Picheny, David Ginsbourger, Yann Richet, and Gregory Caplin. Quantile-based optimization of noisy computer experiments with tunable precision. Technometrics, 55 0 (1): 0 2--13, 2013 a

    work page 2013

  60. [60]

    A benchmark of kriging-based infill criteria for noisy optimization

    Victor Picheny, Tobias Wagner, and David Ginsbourger. A benchmark of kriging-based infill criteria for noisy optimization. Structural and Multidisciplinary Optimization, 48 0 (3): 0 607--626, 2013 b

    work page 2013

  61. [61]

    Building accurate emulators for stochastic simulations via quantile kriging

    Matthew Plumlee and Rui Tuo. Building accurate emulators for stochastic simulations via quantile kriging. Technometrics, 56 0 (4): 0 466--473, 2014

    work page 2014

  62. [62]

    Gradient extrapolated stochastic kriging

    Huashuai Qu and Michael C Fu. Gradient extrapolated stochastic kriging. ACM Transactions on Modeling and Computer Simulation (TOMACS), 24 0 (4): 0 23, 2014

    work page 2014

  63. [63]

    T. G. Ritto, R. H. Lopez, R. Sampaio, and J. E. Souza De Cursi. Robust optimization of a flexible rotor-bearing system using the campbell diagram. Engineering Optimization, 43 0 (1): 0 77--96, 2011

    work page 2011

  64. [64]

    R. Y. Rubinstein. Simulation and the Monte Carlo Method. John Wiley & Sons, 2007

    work page 2007

  65. [65]

    Welch, Toby J

    Jerome Sacks, William J. Welch, Toby J. Mitchell, and Henry P. Wynn. Design and analysis of computer experiments. Statist. Sci., 4 0 (4): 0 409--423, 11 1989. doi:10.1214/ss/1177012413

    work page doi:10.1214/ss/1177012413 1989

  66. [66]

    Kriging-based convex subspace single linkage method with path-based clustering technique for approximation-based global optimization

    Sei-ichiro Sakata, Fumihiro Ashida, and Hiroyoshi Tanaka. Kriging-based convex subspace single linkage method with path-based clustering technique for approximation-based global optimization. Structural and Multidisciplinary Optimization, 44 0 (3): 0 393--408, Sep 2011. ISSN 1615-1488. doi:10.1007/s00158-011-0643-x

    work page doi:10.1007/s00158-011-0643-x 2011

  67. [67]

    The correlated knowledge gradient for simulation optimization of continuous parameters using gaussian process regression

    Warren Scott, Peter Frazier, and Warren Powell. The correlated knowledge gradient for simulation optimization of continuous parameters using gaussian process regression. SIAM Journal on Optimization, 21 0 (3): 0 996--1026, 2011

    work page 2011

  68. [68]

    Enhancing stochastic kriging for queueing simulation with stylized models

    Haihui Shen, L Jeff Hong, and Xiaowei Zhang. Enhancing stochastic kriging for queueing simulation with stylized models. IISE Transactions, 0 (just-accepted), 2018

    work page 2018

  69. [69]

    Soize, E

    C. Soize, E. Capiez-Lernout, and R. Ohayon. Robust updating of uncertain computational models using experimental modal analysis. Mechanical Systems and Signal Processing, 22 0 (8): 0 1774--1792, 2008

    work page 2008

  70. [70]

    Performance-based design and optimization of uncertain wind-excited dynamic building systems

    Seymour M J Spence and Ahsan Kareem. Performance-based design and optimization of uncertain wind-excited dynamic building systems. Engineering Structures, 78: 0 133--144, 2014

    work page 2014

  71. [71]

    Better simulation metamodeling: The why, what, and how of stochastic kriging

    Jeremy Staum. Better simulation metamodeling: The why, what, and how of stochastic kriging. In Proceedings of the 2009 Winter Simulation Conference (WSC), pages 119--133, Austin, TX, USA, 2009. IEEE

    work page 2009

  72. [72]

    A statistical method of determining the maximum response of a building structure during an earthquake

    Hiroshi Tajimi. A statistical method of determining the maximum response of a building structure during an earthquake. In Proceedings of the 2nd World Conference on Earthquake Engineering, pages 781--797, Tokyo, Japan, 1960

    work page 1960

  73. [73]

    Evaluation and optimisation of groundwater observation networks using the kriging methodology

    Nicolaos Theodossiou and Pericles Latinopoulos. Evaluation and optimisation of groundwater observation networks using the kriging methodology. Environmental Modelling & Software, 21 0 (7): 0 991--1000, 2006

    work page 2006

  74. [74]

    A local-restart coupled strategy for simultaneous sizing and geometry truss optimization

    André Jacomel Torii, Rafael Holdorf Lopez, and Marco Antônio Luersen. A local-restart coupled strategy for simultaneous sizing and geometry truss optimization . Latin American Journal of Solids and Structures , 8: 0 335 -- 349, 09 2011. ISSN 1679-7825. doi:10.1590/S1679-78252011000300008

    work page doi:10.1590/s1679-78252011000300008 2011

  75. [75]

    On the use of gradients in kriging surrogate models

    Selvakumar Ulaganathan, Ivo Couckuyt, Tom Dhaene, Eric Laermans, and Joris Degroote. On the use of gradients in kriging surrogate models. In Simulation Conference (WSC), 2014 Winter, pages 2692--2701. IEEE, 2014

    work page 2014

  76. [76]

    Adaptive efficient global optimization of systems with independent components

    Samee Ur Rehman and Matthijs Langelaar. Adaptive efficient global optimization of systems with independent components. Structural and Multidisciplinary Optimization, 55 0 (4): 0 1143--1157, Apr 2017. ISSN 1615-1488. doi:10.1007/s00158-017-1663-y

    work page doi:10.1007/s00158-017-1663-y 2017

  77. [77]

    Global optimization based on noisy evaluations: an empirical study of two statistical approaches

    Emmanuel Vazquez, Julien Villemonteix, Maryan Sidorkiewicz, and Eric Walter. Global optimization based on noisy evaluations: an empirical study of two statistical approaches. In Journal of Physics: Conference Series, volume 135, page 012100. IOP Publishing, 2008

    work page 2008

  78. [78]

    An informational approach to the global optimization of expensive-to-evaluate functions

    Julien Villemonteix, Emmanuel Vazquez, and Eric Walter. An informational approach to the global optimization of expensive-to-evaluate functions. Journal of Global Optimization, 44 0 (4): 0 509, 2009

    work page 2009

  79. [79]

    A new stochastic kriging method for modeling multi-source exposure--response data in toxicology studies

    Kai Wang, Xi Chen, Feng Yang, Dale W Porter, and Nianqiang Wu. A new stochastic kriging method for modeling multi-source exposure--response data in toxicology studies. ACS sustainable chemistry & engineering, 2 0 (7): 0 1581--1591, 2014

    work page 2014

  80. [80]

    Asymmetric kriging emulator for stochastic simulation

    Qiong Zhang and Wei Xie. Asymmetric kriging emulator for stochastic simulation. In Proceedings of the 2017 Winter Simulation Conference, page 137. IEEE Press, 2017

    work page 2017

Showing first 80 references.