Mode-pursuing sampling method for global optimization on expensive black-box functions

Wang, Liqun; Shan, Songqing; Wang, G. Gary

doi:10.1080/03052150410001686486

Cited by 176 publications

(60 citation statements)

References 6 publications

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“…(7), is a surrogate engineering problem which is a well-known example for evaluating the global optimisation plans (Wang et al 2004). This function has a complex shape with six local optima and two global optima of −1.0316 at (0.0898, −0.7127) and (−0.0898, 0.7127).…”

Section: Theoretical Validation Via Benchmark Problem: the Six Hump Cmentioning

confidence: 99%

Application of permutation genetic algorithm for sequential model building–model validation design of experiments

2015

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The work presented in this paper is motivated by a complex multivariate engineering problem associated with engine mapping experiments, which require efficient design of experiments (DoE) strategies to minimise expensive testing. The paper describes the development and evaluation of a Permutation Genetic Algorithm (PermGA) to enable an exploration-based sequential DoE strategy for complex reallife engineering problems. A known PermGA was implemented to generate uniform OLH DoEs, and substantially extended to support generation of model building-model validation (MB-MV) sequences, by generating optimal infill sets of test points as OLH DoEs that preserve good spacefilling and projection properties for the merged MB + MV test plan. The algorithm was further extended to address issues with non-orthogonal design spaces, which is a common problem in engineering applications. The effectiveness of the PermGA algorithm for the MB-MV OLH DoE sequence was evaluated through a theoretical benchmark problem based on the Six-Hump-Camel-Back function, as well as the Gasoline Direct Injection engine steady-state engine mapping problem that motivated this research. The case studies show that the algorithm is effective in delivering quasi-orthogonal spacefilling DoEs with good properties even after several MB-MV iterations, while the improvement in model adequacy and accuracy can be monitored by the engineering analyst. The Communicated by

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Section: Theoretical Validation Via Benchmark Problem: the Six Hump Cmentioning

confidence: 99%

Application of permutation genetic algorithm for sequential model building–model validation design of experiments

2015

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“…Instead it balances exploration and exploitation by on the one hand looking for neighbors of the best few current samples and on the other hand looking to move towards the boundary of the design space. Wang et al (2004) developed the mode-pursuing sampling approach (MPS), which generates a probability function that samples points preferentially where the surrogate has low values, but has a non-zero probability of sampling even when the values are high. The original MPS used a linear spline function as global surrogate with local quadratic surrogates in regions of high point density (promising regions).…”

Section: Distance-based and Other Criteriamentioning

confidence: 99%

“…The mode-pursuing sampling method (Wang et al 2004) creates local quadratic surrogates for promising regions, where the sampling approach tends to generate dense samples. Hu et al (2008) pursued this idea further, using particle swarm optimization to refine the sampling.…”

Section: Global-local Approachesmentioning

confidence: 99%

Parallel surrogate-assisted global optimization with expensive functions – a survey

Haftka

Villanueva

Chaudhuri

2016

Struct Multidisc Optim

204

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Surrogate assisted global optimization is gaining popularity. Similarly, modern advances in computing power increasingly rely on parallelization rather than faster processors. This paper examines some of the methods used to take advantage of parallelization in surrogate based global optimization. A key issue focused on in this review is how different algorithms balance exploration and exploitation. Most of the papers surveyed are adaptive samplers that employ Gaussian Process or Kriging surrogates. These allow sophisticated approaches for balancing exploration and exploitation and even allow to develop algorithms with calculable rate of convergence as function of the number of parallel processors. In addition to optimization based on adaptive sampling, surrogate assisted parallel evolutionary algorithms are also surveyed. Beyond a review of the present state of the art, the paper also argues that methods that provide easy parallelization, like multiple parallel runs, or methods that rely on population of designs for diversity deserve more attention.

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“…A PDF can thus be considered as a special sampling guidance function. The variation of the objective function in MPS [18] is also a sampling guidance function.…”

Section: Sampling Guidance Functionmentioning

confidence: 99%

“…more points in the area that has high probability and fewer points in the area that has low probability, as defined by the PDF. Inspired by such sampling, the authors developed a Mode Pursuing Sampling (MPS) method before [18], which used a variation of the objective function to act as a PDF so that more points are generated in areas having lower objective function value and fewer in other areas. In brief, for an expensive black-box objective function, MPS first constructs an approximation model from a few sample points.…”

Section: Sampling Guidance Functionmentioning

confidence: 99%

An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions

Shan

Wang

2004

Journal of Mechanical Design

Self Cite

101

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Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multi-objective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursuing (PSP) method is developed.By developing sampling guidance functions based on approximation models, this approach progressively provides a designer with a rich and evenly distributed set of Pareto optimal points. This work describes PSP procedures in detail. From testing and design application, PSP demonstrates considerable promises in efficiency, accuracy, and robustness. Properties of PSP and differences between PSP and other approximation-based methods are also discussed. It is believed that PSP has a great potential to be a practical tool for multi-objective optimization problems.

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Mode-pursuing sampling method for global optimization on expensive black-box functions

Cited by 176 publications

References 6 publications

Application of permutation genetic algorithm for sequential model building–model validation design of experiments

Application of permutation genetic algorithm for sequential model building–model validation design of experiments

Parallel surrogate-assisted global optimization with expensive functions – a survey

An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions

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