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Title: Asynchronously parallel optimization solver for finding multiple minima

Abstract

This paper proposes and analyzes an asynchronously parallel optimization algorithm for finding multiple, high-quality minima of nonlinear optimization problems. Our multistart algorithm considers all previously evaluated points when determining where to start or continue a local optimization run. Theoretical results show that, under certain assumptions, the algorithm almost surely starts a finite number of local optimization runs and identifies, or has a single local optimization run converging to, every minimum. The algorithm is applicable to general optimization settings, but our numerical results focus on the case when derivatives are unavailable. In numerical tests, a PYTHON implementation of the algorithm is shown to yield good approximations of many minima (including a global minimum), and this ability scales well with additional resources. Our implementation’s time to solution is shown also to scale well even when the time to evaluate the function evaluation is highly variable.

Authors:
 [1];  [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1466333
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Mathematical Programming Computation
Additional Journal Information:
Journal Volume: 10; Journal Issue: 3; Journal ID: ISSN 1867-2949
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Concurrent Function Evaluations; Derivative-Free Optimization; Global Optimization; Multistart; Parallel Optimization Algorithms

Citation Formats

Larson, Jeffrey, and Wild, Stefan M. Asynchronously parallel optimization solver for finding multiple minima. United States: N. p., 2018. Web. doi:10.1007/s12532-017-0131-4.
Larson, Jeffrey, & Wild, Stefan M. Asynchronously parallel optimization solver for finding multiple minima. United States. doi:10.1007/s12532-017-0131-4.
Larson, Jeffrey, and Wild, Stefan M. Fri . "Asynchronously parallel optimization solver for finding multiple minima". United States. doi:10.1007/s12532-017-0131-4. https://www.osti.gov/servlets/purl/1466333.
@article{osti_1466333,
title = {Asynchronously parallel optimization solver for finding multiple minima},
author = {Larson, Jeffrey and Wild, Stefan M.},
abstractNote = {This paper proposes and analyzes an asynchronously parallel optimization algorithm for finding multiple, high-quality minima of nonlinear optimization problems. Our multistart algorithm considers all previously evaluated points when determining where to start or continue a local optimization run. Theoretical results show that, under certain assumptions, the algorithm almost surely starts a finite number of local optimization runs and identifies, or has a single local optimization run converging to, every minimum. The algorithm is applicable to general optimization settings, but our numerical results focus on the case when derivatives are unavailable. In numerical tests, a PYTHON implementation of the algorithm is shown to yield good approximations of many minima (including a global minimum), and this ability scales well with additional resources. Our implementation’s time to solution is shown also to scale well even when the time to evaluate the function evaluation is highly variable.},
doi = {10.1007/s12532-017-0131-4},
journal = {Mathematical Programming Computation},
number = 3,
volume = 10,
place = {United States},
year = {2018},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Table 1 Table 1: Logical conditions to determine when to start a local optimization run after $k$ evaluations.

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Works referenced in this record:

MPI for Python: Performance improvements and MPI-2 extensions
journal, May 2008

  • Dalcín, Lisandro; Paz, Rodrigo; Storti, Mario
  • Journal of Parallel and Distributed Computing, Vol. 68, Issue 5
  • DOI: 10.1016/j.jpdc.2007.09.005

Lipschitzian optimization without the Lipschitz constant
journal, October 1993

  • Jones, D. R.; Perttunen, C. D.; Stuckman, B. E.
  • Journal of Optimization Theory and Applications, Vol. 79, Issue 1
  • DOI: 10.1007/BF00941892

A particle swarm pattern search method for bound constrained global optimization
journal, February 2007


Performance Modeling and Analysis of a Massively Parallel Direct—Part 1
journal, February 2009

  • Jian He, ; Verstak, Alex; Watson, L. T.
  • The International Journal of High Performance Computing Applications, Vol. 23, Issue 1
  • DOI: 10.1177/1094342008098462

Performance Modeling and Analysis of a Massively Parallel Direct—Part 2
journal, February 2009

  • Jian He, ; Verstak, Alex; Sosonkina, M.
  • The International Journal of High Performance Computing Applications, Vol. 23, Issue 1
  • DOI: 10.1177/1094342008098463

Stochastic global optimization methods part I: Clustering methods
journal, September 1987

  • Rinnooy Kan, A. H. G.; Timmer, G. T.
  • Mathematical Programming, Vol. 39, Issue 1
  • DOI: 10.1007/BF02592070

Stochastic global optimization methods part II: Multi level methods
journal, September 1987

  • Rinnooy Kan, A. H. G.; Timmer, G. T.
  • Mathematical Programming, Vol. 39, Issue 1
  • DOI: 10.1007/BF02592071

Theoretical Investigation of the Ground and Excited States of Coumarin 151 and Coumarin 120
journal, October 2002

  • Cave, Robert J.; Burke, Kieron; Castner, Edward W.
  • The Journal of Physical Chemistry A, Vol. 106, Issue 40
  • DOI: 10.1021/jp026071x

GLODS: Global and Local Optimization using Direct Search
journal, August 2014


Algorithm 856: APPSPACK 4.0: asynchronous parallel pattern search for derivative-free optimization
journal, September 2006

  • Gray, Genetha A.; Kolda, Tamara G.
  • ACM Transactions on Mathematical Software, Vol. 32, Issue 3
  • DOI: 10.1145/1163641.1163647

Design and implementation of a massively parallel version of DIRECT
journal, October 2007

  • He, Jian; Verstak, Alex; Watson, Layne T.
  • Computational Optimization and Applications, Vol. 40, Issue 2
  • DOI: 10.1007/s10589-007-9092-2

Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch
journal, September 2017


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

Parallel Space Decomposition of the Mesh Adaptive Direct Search Algorithm
journal, January 2008

  • Audet, Charles; Dennis, J. E.; Digabel, Sébastien Le
  • SIAM Journal on Optimization, Vol. 19, Issue 3
  • DOI: 10.1137/070707518

Parallel deterministic and stochastic global minimization of functions with very many minima
journal, August 2013

  • Easterling, David R.; Watson, Layne T.; Madigan, Michael L.
  • Computational Optimization and Applications, Vol. 57, Issue 2
  • DOI: 10.1007/s10589-013-9592-1

Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES)
journal, March 2003

  • Hansen, Nikolaus; Müller, Sibylle D.; Koumoutsakos, Petros
  • Evolutionary Computation, Vol. 11, Issue 1
  • DOI: 10.1162/106365603321828970

Benchmarking Derivative-Free Optimization Algorithms
journal, January 2009

  • Moré, Jorge J.; Wild, Stefan M.
  • SIAM Journal on Optimization, Vol. 20, Issue 1
  • DOI: 10.1137/080724083

New Sequential and Parallel Derivative-Free Algorithms for Unconstrained Minimization
journal, January 2002


A batch, derivative-free algorithm for finding multiple local minima
journal, October 2015


Calculating all local minima on liquidus surfaces using the FactSage software and databases and the Mesh Adaptive Direct Search algorithm
journal, September 2011

  • Gheribi, Aimen E.; Robelin, Christian; Digabel, Sébastien Le
  • The Journal of Chemical Thermodynamics, Vol. 43, Issue 9
  • DOI: 10.1016/j.jct.2011.03.021

Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization
journal, December 2003

  • Gaviano, Marco; Kvasov, Dmitri E.; Lera, Daniela
  • ACM Transactions on Mathematical Software, Vol. 29, Issue 4
  • DOI: 10.1145/962437.962444