Direct Search Methods

Lewis, Robert; Torczon, Virginia

doi:10.1002/9780470400531.eorms0517

Cited by 6 publications

(2 citation statements)

References 72 publications

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“…In recent years, direct search methods have received renewed interest due to new mathematical analysis, their suitability for parallel and distributed computing, and their utility in addressing optimization problems that involve complex computer simulations (Lewis & Torczon, 2011). Direct search methods as one of the earliest numerical optimization methods, formally proposed in the late 1950s and early 1960s, have remained popular with users due to their (Macklem, 2006;Lewis et al, 2000;Lewis & Torczon, 2011): (i) ease of implementation and formulation requiring setting of only few parameters, (ii) flexibility, reliability and practical success in solving a wide range of non-continual, non-differentiable and multimodal optimization problems, (iii) features unique to direct search methods often avoid the pitfalls that can plague more sophisticated approaches, (iv) robustness in locating at least local optimal solutions. Historically direct search methods can be classified into pattern search (PS) methods, simplex methods, and methods with adaptive sets of search directions (Lewis et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

“…The development and results of Torczon's multidirectional search (Torczon, 1989), generalized pattern search (Torczon, 1997), generating set search (Kolda et al, 2003) and mesh adaptive direct search (Audet and Dennis, 2006) renewed interest in the application of direct search methods for solving nonlinear optimization problems. Direct search methods neither compute nor approximate derivatives, instead, they work directly with values of the objective function to drive the search for an optimal point (Lewis & Torczon, 2011). They generate search points according to a pattern, around the current point, and accept points, which improve the objective function.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of machining processes using pattern search algorithm

Madić¹,

Radovanović²

2014

10.5267/j.ijiec

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Optimization of machining processes not only increases machining efficiency and economics, but also the end product quality. In recent years, among the traditional optimization methods, stochastic direct search optimization methods such as meta-heuristic algorithms are being increasingly applied for solving machining optimization problems. Their ability to deal with complex, multi-dimensional and ill-behaved optimization problems made them the preferred optimization tool by most researchers and practitioners. This paper introduces the use of pattern search (PS) algorithm, as a deterministic direct search optimization method, for solving machining optimization problems. To analyze the applicability and performance of the PS algorithm, six case studies of machining optimization problems, both single and multi-objective, were considered. The PS algorithm was employed to determine optimal combinations of machining parameters for different machining processes such as abrasive waterjet machining, turning, turn-milling, drilling, electrical discharge machining and wire electrical discharge machining. In each case study the optimization solutions obtained by the PS algorithm were compared with the optimization solutions that had been determined by past researchers using meta-heuristic algorithms. Analysis of obtained optimization results indicates that the PS algorithm is very applicable for solving machining optimization problems showing good competitive potential against stochastic direct search methods such as meta-heuristic algorithms. Specific features and merits of the PS algorithm were also discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimization of machining processes using pattern search algorithm

Madić¹,

Radovanović²

2014

10.5267/j.ijiec

View full text Add to dashboard Cite

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Characterizing the optimal pivots for efficient similarity searches in vector space databases with Minkowski distances

Gómez-Tostón

Barrena

Cortés

2018

Applied Mathematics and Computation

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On the use of hybrid models in wedge trust region

Yang

Zhou

Fei

et al. 2013

11th International Symposium on Operations Research and Its Applications in Engineering, Technology and Management 2013 (ISORA

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In this paper, we have constructed a new algorithm for unconstrained optimizations based on the wedge trust region method. It is designed for solving problems in which the gradient of the object function is not available and the number of variables is moderate. After reviewing the separate contributions of the linear models and the quadratic models, here we propose a hybrid model to update the wedge trust region radius. Comparison of the new algorithm with both version of interpolation methods are reported in this paper. Numerical results show the applicability of our new algorithm to practical problems.

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Direct Search Methods

Cited by 6 publications

References 72 publications

Optimization of machining processes using pattern search algorithm

Optimization of machining processes using pattern search algorithm

Characterizing the optimal pivots for efficient similarity searches in vector space databases with Minkowski distances

On the use of hybrid models in wedge trust region

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