A modification to Jones' global optimization algorithm for fast local convergence

Nelson, Sigurd A.; Papalambros, Panos Y.

doi:10.2514/6.1998-4751

Cited by 7 publications

(8 citation statements)

References 10 publications

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“…A number of variants of DIRECT have been described 28–32. Several authors have noted that the final (local) convergence of the DIRECT algorithm often is rather slow.…”

Section: The Outer Problemmentioning

confidence: 99%

Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits

Ljungberg

Mishchenko²,

Holmgren

2010

AABC

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We present a two-phase strategy for optimizing a multidimensional, nonconvex function arising during genetic mapping of quantitative traits. Such traits are believed to be affected by multiple so called quantitative trait loci (QTL), and searching for d QTL results in a d-dimensional optimization problem with a large number of local optima. We combine the global algorithm DIRECT with a number of local optimization methods that accelerate the final convergence, and adapt the algorithms to problem-specific features. We also improve the evaluation of the QTL mapping objective function to enable exploitation of the smoothness properties of the optimization landscape. Our best two-phase method is demonstrated to be accurate in at least six dimensions and up to ten times faster than currently used QTL mapping algorithms.

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“…A number of variants of DIRECT have been described 28–32. Several authors have noted that the final (local) convergence of the DIRECT algorithm often is rather slow.…”

Section: The Outer Problemmentioning

confidence: 99%

Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits

Ljungberg

Mishchenko²,

Holmgren

2010

AABC

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“…Several modifications to DIRECT (Nelson et al 1998, Gablonsky et al 2001b, Cox et al 2002, Finkel et al 2004a et al 2006) have been proposed to speed up the convergence. Additionally, combining DIRECT with other methods has been found to be fairly successful to address this issue (Nelson et al 1998, Zwolak et al 2005, Panning et al 2006.…”

Section: Overview Of Directmentioning

confidence: 99%

“…Additionally, combining DIRECT with other methods has been found to be fairly successful to address this issue (Nelson et al 1998, Zwolak et al 2005, Panning et al 2006. The emphasis of the present work is on the performance analysis of the parallel design, so the original DIRECT with ǫ = 0 and additional stopping rules is considered.…”

Section: Overview Of Directmentioning

confidence: 99%

Performance Modeling and Analysis of a Massively Parallel Direct—Part 2

Verstak

Sosonkina

et al. 2009

The International Journal of High Performance Computing Applica

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Modeling and analysis techniques are used to investigate the performance of a massively parallel version of DIRECT, a global search algorithm widely used in multidisciplinary design optimization applications. Several high-dimensional benchmark functions and real world problems are used to test the design effectiveness under various problem structures. Theoretical and experimental results are compared for two parallel clusters with different system scale and network connectivity. The present work aims at studying the performance sensitivity to important parameters for problem configurations, parallel schemes, and system settings.The performance metrics include the memory usage, load balancing, parallel efficiency, and scalability. An analytical bounding model is constructed to measure the load balancing performance under different schemes. Additionally, linear regression models are used to characterize two major overhead sources-interprocessor communication and processor idleness, and also applied to the isoefficiency functions in scalability analysis. For a variety of high-dimensional problems and large scale systems, the massively parallel design has achieved reasonable performance. The results of the performance study provide guidance for efficient problem and scheme configuration. More importantly, the generalized design considerations and analysis techniques are beneficial for transforming many global search algorithms to become effective large scale parallel optimization tools.

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“…Several implementations have incorporated a local optimizer into DIRECT, either at the end of the optimization 2 or periodically during the DIRECT optimization, 6 which has partially solved this problem. This has worked well for smooth functions with widely separated local optima where a local optimizer can quickly move to the only optimum in the immediate vicinity.…”

Section: Introductionmentioning

confidence: 99%

DIRECT Algorithm with Box Penetration for Improved Local Convergence

Cox¹,

Hart²,

Haftka³

et al. 2002

9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization

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We describe DIRECT-BP, a modi cation to the DIRECT algorithm that attempts to perform a more balanced search about the best point found in each iteration. DIRECT ensures the division of one of the largest boxes in each iteration, which asymptotically guarantees convergence to a global optimum. We demonstrate that DIRECT can fail to e ectively perform local search about the best point found even though it globally optimizes. DIRECT-BP modi es the DIRECT algorithm to ensure more e ective local convergence. DIRECT-BP forces a subset of the boxes neighboring the best box to divide, and it provides a mechanism for the local search to move from one box to another. This allows continuous progress towards a local optimum without relying on the global aspects of DIRECT.

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A modification to Jones' global optimization algorithm for fast local convergence

Cited by 7 publications

References 10 publications

Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits

Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits

Performance Modeling and Analysis of a Massively Parallel Direct—Part 2

DIRECT Algorithm with Box Penetration for Improved Local Convergence

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