DIRECT Algorithm with Box Penetration for Improved Local Convergence

Cox, Steven; Hart, William E.; Haftka, Raphael T.; Watson, Luke

doi:10.2514/6.2002-5581

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…Classical Lipschitzian Optimization requires an appropriate setting for the Lipshitz constant. DIRECT does not require estimation of the Lipshitz constant, and searches for optimum solutions using all possible constants [7] [8].…”

Section: Optimization Algorithms a Direct Algorithmmentioning

confidence: 99%

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Hybrid optimization using DIRECT, GA, and SQP for global exploration

Hiwa

Hiroyasu

Miki

2007

2007 IEEE Congress on Evolutionary Computation

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Abstract-As there are many good optimization algorithms each with its own characteristics, it is very difficult to choose the best method for optimization problems. Thus, it is important to select and apply the appropriate algorithms according to the complexities of the problem. However, it is difficult to solve very complicated problems with only a single algorithm, and a hybrid optimization approach, which combines multiple optimization algorithms, is necessary. To develop an efficient hybrid optimization algorithm, it is necessary to determine how the optimization process is performed. This paper focuses on the balance between local and broad searches. Multiple optimization methods are controlled to derive both the optimum point and the information of the landscape. To achieve the proposed optimization strategy, three distinguished optimization algorithms are introduced: DIRECT (DIviding RECTangles), GAs (Genetic Algorithms), and SQP (Sequential Quadratic Programming). To integrate these three algorithms, each algorithm, especially DIRECT, was modified and developed. This paper describes a new hybrid method using these three algorithms. The performance of the proposed hybrid algorithm was examined through numerical experiments. From these experiments, not only the optimum point but also the information of the landscape was determined. The information of the landscape verified the reliability of optimization results.

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Section: Optimization Algorithms a Direct Algorithmmentioning

confidence: 99%

“…One of the shortcomings of DIRECT is the lack of an obvious terminal criterion [8] [16] [17]. Although Jones' original DIRECT uses the iteration limit as the termination rule, it is unsuitable for the proposed hybrid optimization algorithm, in which DIRECT should be stopped after completing the global exploration of the search space.…”

Section: Sqpmentioning

confidence: 99%

Hybrid optimization using DIRECT, GA, and SQP for global exploration

Hiwa

Hiroyasu

Miki

2007

2007 IEEE Congress on Evolutionary Computation

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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%

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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Traditional and Hybrid Derivative-Free Optimization Approaches for Black Box Functions

Gray

Fowler

2011

Computational Optimization, Methods and Algorithms

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DIRECT Algorithm with Box Penetration for Improved Local Convergence

Cited by 6 publications

References 5 publications

Hybrid optimization using DIRECT, GA, and SQP for global exploration

Hybrid optimization using DIRECT, GA, and SQP for global exploration

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

Traditional and Hybrid Derivative-Free Optimization Approaches for Black Box Functions

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