A restarted and modified simplex search for unconstrained optimization

Zhao, Qiu Hong; Urošević, Dragan; Mladenović, Nenad; Hansen, Pierre

doi:10.1016/j.cor.2009.03.005

Cited by 29 publications

(16 citation statements)

References 30 publications

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“…The different initial point brings the different registration results, and some initial points lead the local minima resulting in the registration error [6][7]. In the other hand, the optimal result is related with the size of the initial simplex.…”

Section: ) Optimal Search Algorithm Based On the Modified Simplexmentioning

confidence: 97%

Study of mutual information registration based on modified simplex optimization method

Wang

Zhang

et al. 2011

2011 IEEE International Instrumentation and Measurement Technology Conference

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A mutual information registration based on modified simplex optimization method is presented in this paper to improve the speed of medical image registration. For two MRI and PET images, the principal axis method is adopted to achieve the rough registration, and the modified simplex algorithm is employed to implement global search using the mutual information as similarity measure. Results indicate that the proposed registration method prevents the optimizing process from falling into local extremum and improves the convergence speed while keeping the precision. The accurate registration of multimodal image with different resolutions is achieved.

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Section: ) Optimal Search Algorithm Based On the Modified Simplexmentioning

confidence: 97%

Study of mutual information registration based on modified simplex optimization method

Wang

Zhang

et al. 2011

2011 IEEE International Instrumentation and Measurement Technology Conference

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show abstract

“…Typically, the algorithm is called several times in a row, with re-initialization with the previously found optimum. These successive calls improve the performance of the Nelder-Mead method and allow a better convergence toward the sought minimum (see for instance [32]).…”

Section: Weighted Least Squaresmentioning

confidence: 99%

Sensitivity analysis and reduction of a dynamic model of a bioproduction of fructo-oligosaccharides

Fekih-Salem

Dewasme

Castro

et al. 2019

Bioprocess Biosyst Eng

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Starting from a relatively detailed model of a bioprocess producing fructo-oligosaccharides, a set of experimental data collected in batch and fed-batch experiments is exploited to estimate the unknown model parameters. The original model includes the growth of the fungus Aureobasidium pullulans which produces the enzymes responsible for the hydrolysis and transfructosylation reactions, and as such contains 25 kinetic parameters and 16 pseudo-stoichiometric coefficients, which are not uniquely identifiable with the data at hand. The aim of this study is, therefore, to show how sensitivity analysis and quantitative indicators based on the Fisher information matrix can be used to reduce the detailed model to a practically identifiable model. Parametric sensitivity analysis can indeed be used to progressively simplify the model to a representation involving 15 kinetic parameters and 8 pseudo-stoichiometric coefficients. The reduced model provides satisfactory prediction and can be convincingly cross validated.

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“…To avoid this, a globalized Nelder-Mead method (GNMM) is proposed in this work, with two major modifications in the search heuristics. First, restarting the simplex is a common way to make the search stochastic [13,33]. Particularly, GNMM avoids shrinking the entire simplex towards the best vertex; instead, it keeps the best vertex and randomly restarts the rest around the initial estimation.…”

Section: Globalized Nelder-mead Optimizationmentioning

confidence: 99%

3D registration of laser range scenes by coincidence of coarse binary cubes

Martínez

Reina

Mandow

et al. 2011

Machine Vision and Applications

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Scene registration of a pair of three-dimensional (3D) range images is a 6D optimization problem usually required in mobile robotics. This problem is different from object registration, since all scan directions and depths may contain relevant data, and because farther regions are sampled with lower densities. The paper proposes an efficient scene matching method based on the concept of coarse binary cubes. An integer objective function is defined as the number of coincident cubes between both scans. This is a metric of the degree of overlap that does not employ point distances. Its value is obtained without actually using any 3D grid data structure, with a computational complexity of order O(n), where n represents the number of laser points. This objective function is optimized with a globalized version of the downhill Simplex algorithm to avoid local minima. Experimental results are presented from indoor and outdoor environments with different degrees of structuring. The effect of cube size and the number of vertices on registration performance has been analyzed. Besides, experiments show that the proposed method achieves similar accuracy as iterative closest points (ICP) and normal distribution transform (NDT), while it improves both computation time and robustness against initial misalignments.

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A restarted and modified simplex search for unconstrained optimization

Cited by 29 publications

References 30 publications

Study of mutual information registration based on modified simplex optimization method

Study of mutual information registration based on modified simplex optimization method

Sensitivity analysis and reduction of a dynamic model of a bioproduction of fructo-oligosaccharides

3D registration of laser range scenes by coincidence of coarse binary cubes

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