Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Asynchronously parallel optimization solver for finding multiple minima

Journal Article · · Mathematical Programming Computation
 [1];  [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
+ Show Author Affiliations

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.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1466333
Journal Information:
Mathematical Programming Computation, Vol. 10, Issue 3; ISSN 1867-2949
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

References (21)

MPI for Python: Performance improvements and MPI-2 extensions journal May 2008
Lipschitzian optimization without the Lipschitz constant journal October 1993
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
Performance Modeling and Analysis of a Massively Parallel Direct—Part 2 journal February 2009
Stochastic global optimization methods part I: Clustering methods journal September 1987
Stochastic global optimization methods part II: Multi level methods journal September 1987
Theoretical Investigation of the Ground and Excited States of Coumarin 151 and Coumarin 120 journal October 2002
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
Design and implementation of a massively parallel version of DIRECT journal October 2007
Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch journal September 2017
Asynchronous Parallel Pattern Search for Nonlinear Optimization journal January 2001
Parallel Space Decomposition of the Mesh Adaptive Direct Search Algorithm journal January 2008
Parallel deterministic and stochastic global minimization of functions with very many minima journal August 2013
Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) journal March 2003
Benchmarking Derivative-Free Optimization Algorithms journal January 2009
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
Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization journal December 2003

Figures / Tables (15)

Table 1(p. 6)table Table 1
Fig. 1(p. 11)figure Fig. 1
Fig. 2(p. 14)figure Fig. 2
Fig. 3(p. 16)figure Fig. 3
Fig. 4(p. 20)figure Fig. 4
Fig. 5(p. 21)figure Fig. 5
Fig. 6(p. 22)figure Fig. 6
Fig. 7(p. 23)figure Fig. 7
Fig. 8(p. 24)figure Fig. 8
Fig. 9(p. 24)figure Fig. 9
Fig. 10(p. 25)figure Fig. 10
Fig. 11(p. 26)figure Fig. 11
Fig. 12(p. 27)figure Fig. 12
Fig. 13(p. 28)figure Fig. 13
Fig. 14(p. 29)figure Fig. 14

Similar Records

Related Subjects

97 MATHEMATICS AND COMPUTING
Concurrent Function Evaluations
Derivative-Free Optimization
Global Optimization
Multistart
Parallel Optimization Algorithms