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Title: SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

Abstract

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases themore » efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.« less

Authors:
; ;
Publication Date:
Research Org.:
Cornell Univ., Ithaca, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1328968
Alternate Identifier(s):
OSTI ID: 1425456
Grant/Contract Number:  
SC000 6791; SC0006791
Resource Type:
Published Article
Journal Name:
Journal of Global Optimization
Additional Journal Information:
Journal Name: Journal of Global Optimization Journal Volume: 66 Journal Issue: 3; Journal ID: ISSN 0925-5001
Publisher:
Springer Science + Business Media
Country of Publication:
Netherlands
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Krityakierne, Tipaluck, Akhtar, Taimoor, and Shoemaker, Christine A. SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems. Netherlands: N. p., 2016. Web. doi:10.1007/s10898-016-0407-7.
Krityakierne, Tipaluck, Akhtar, Taimoor, & Shoemaker, Christine A. SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems. Netherlands. doi:10.1007/s10898-016-0407-7.
Krityakierne, Tipaluck, Akhtar, Taimoor, and Shoemaker, Christine A. Tue . "SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems". Netherlands. doi:10.1007/s10898-016-0407-7.
@article{osti_1328968,
title = {SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems},
author = {Krityakierne, Tipaluck and Akhtar, Taimoor and Shoemaker, Christine A.},
abstractNote = {This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.},
doi = {10.1007/s10898-016-0407-7},
journal = {Journal of Global Optimization},
number = 3,
volume = 66,
place = {Netherlands},
year = {2016},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1007/s10898-016-0407-7

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Cited by: 1 work
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Works referenced in this record:

Globally-biased Disimpl algorithm for expensive global optimization
journal, April 2014

  • Paulavičius, Remigijus; Sergeyev, Yaroslav D.; Kvasov, Dmitri E.
  • Journal of Global Optimization, Vol. 59, Issue 2-3
  • DOI: 10.1007/s10898-014-0180-4

Watershed calibration using multistart local optimization and evolutionary optimization with radial basis function approximation
journal, June 2007

  • Shoemaker, Christine A.; Regis, Rommel G.; Fleming, Ryan C.
  • Hydrological Sciences Journal, Vol. 52, Issue 3
  • DOI: 10.1623/hysj.52.3.450

Parallel Stochastic Global Optimization Using Radial Basis Functions
journal, August 2009

  • Regis, Rommel G.; Shoemaker, Christine A.
  • INFORMS Journal on Computing, Vol. 21, Issue 3
  • DOI: 10.1287/ijoc.1090.0325

Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection
journal, February 2015


Combining radial basis function surrogates and dynamic coordinate search in high-dimensional expensive black-box optimization
journal, May 2013


Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models
journal, March 2006


Global optimization of expensive black box functions using potential Lipschitz constants and response surfaces
journal, March 2015


Efficient global optimization algorithm assisted by multiple surrogate techniques
journal, March 2012

  • Viana, Felipe A. C.; Haftka, Raphael T.; Watson, Layne T.
  • Journal of Global Optimization, Vol. 56, Issue 2
  • DOI: 10.1007/s10898-012-9892-5

Local Function Approximation in Evolutionary Algorithms for the Optimization of Costly Functions
journal, October 2004

  • Regis, R. G.; Shoemaker, C. A.
  • IEEE Transactions on Evolutionary Computation, Vol. 8, Issue 5
  • DOI: 10.1109/TEVC.2004.835247

A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions
journal, November 2007

  • Regis, Rommel G.; Shoemaker, Christine A.
  • INFORMS Journal on Computing, Vol. 19, Issue 4
  • DOI: 10.1287/ijoc.1060.0182

A parallel updating scheme for approximating and optimizing high fidelity computer simulations
journal, June 2004

  • S�bester, A.; Leary, S. J.; Keane, A. J.
  • Structural and Multidisciplinary Optimization, Vol. 27, Issue 5
  • DOI: 10.1007/s00158-004-0397-9

Improved evolutionary optimization from genetically adaptive multimethod search
journal, January 2007

  • Vrugt, Jasper A.; Robinson, Bruce A.
  • Proceedings of the National Academy of Sciences, Vol. 104, Issue 3
  • DOI: 10.1073/pnas.0610471104

Algorithmic construction of optimal symmetric Latin hypercube designs
journal, September 2000


A rigorous framework for optimization of expensive functions by surrogates
journal, February 1999

  • Booker, A. J.; Dennis, J. E.; Frank, P. D.
  • Structural Optimization, Vol. 17, Issue 1
  • DOI: 10.1007/BF01197708

Asynchronous Parallel Pattern Search for Nonlinear Optimization
journal, January 2001

  • Hough, Patricia D.; Kolda, Tamara G.; Torczon, Virginia J.
  • SIAM Journal on Scientific Computing, Vol. 23, Issue 1
  • DOI: 10.1137/S1064827599365823

Multiple-optima search method based on a metamodel and mathematical morphology
journal, February 2015


Comparison of Optimization Methods for Ground-Water Bioremediation
journal, January 1999


On the Design of Optimization Strategies Based on Global Response Surface Approximation Models
journal, September 2005

  • Sóbester, András; Leary, Stephen J.; Keane, Andy J.
  • Journal of Global Optimization, Vol. 33, Issue 1
  • DOI: 10.1007/s10898-004-6733-1