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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]
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  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)
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.
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Larson, Jeffrey, & Wild, Stefan M. Asynchronously parallel optimization solver for finding multiple minima. United States. https://doi.org/10.1007/s12532-017-0131-4
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Larson, Jeffrey, and Wild, Stefan M. Fri . "Asynchronously parallel optimization solver for finding multiple minima". United States. https://doi.org/10.1007/s12532-017-0131-4. https://www.osti.gov/servlets/purl/1466333.
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@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 = {Fri Feb 16 00:00:00 EST 2018},
month = {Fri Feb 16 00:00:00 EST 2018}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1007/s12532-017-0131-4
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Figures / Tables:

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