Mesh-based Nelder–Mead algorithm for inequality constrained optimization

Audet, Charles; Tribes, Christophe

doi:10.1007/s10589-018-0016-0

Cited by 38 publications

(29 citation statements)

References 39 publications

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“…To overcome these difficulties, the gradient-free method known as the Nelder-Mead method [17] was used in this work. This method is based upon the comparison of the criterion values for various solutions, but not upon their numerical values.…”

Section: Optimization Routinementioning

confidence: 99%

Design Optimization of a Permanent-Magnet Flux-Switching Generator for Direct-Drive Wind Turbines

2019

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Due to the increasing need for direct-drive wind turbines, a large number of papers are dedicated to the optimization of low-speed wind generators. A permanent-magnet flux-switching machine can be a valuable option to use in such applications. This paper describes the optimization procedure of a direct-drive flux-switching wind generator. The average losses, the required converter power, and the cost of permanents magnets were chosen as the optimization objectives. To reduce the calculation efforts during the optimization, a method to construct the substituting load profiles is proposed. Two-mode and three-mode substituting profiles were constructed on the basis of the nine-mode initial profile. The losses calculated under the two-mode, three-mode, and nine-mode profiles accurately coincided, which supported the use of the low-mode substituting profiles instead of the initial one. During the optimization, the average losses decreased by 30%, which corresponded to an increase in the average efficiency by almost 6%. The required converter power was decreased by 10%. The total active material mass, cogging torque, and torque ripple were also slightly decreased.

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Section: Optimization Routinementioning

confidence: 99%

Design Optimization of a Permanent-Magnet Flux-Switching Generator for Direct-Drive Wind Turbines

2019

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“…Recently, the authors were aware of another hybrid variant of these two classes of optimization methods, developed in parallel with the current work by Audet and Tribes (2018) . While there are some similarities between the two approaches, since the Nelder-Mead Simplex algorithm is also used to define a search step in a Directional Direct-Search method, with similar conditions to define the search step as unsuccessful, constraints are addressed with a filter technique, which would not be possible in the context of the estimation of DEB models parameters.…”

Section: Discussionmentioning

confidence: 99%

Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods

Morais

Custódio²,

Marques

2018

J. Math. Biol.

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Dynamic Energy Budget (DEB) theory aims to capture the quantitative aspects of metabolism at the individual level, for all species. The parametrization of a DEB model is based on information obtained through the observation of natural populations and experimental research. Currently the DEB toolbox estimates these parameters using the Nelder-Mead Simplex method, a derivative-free direct-search method. However, this procedure presents some limitations regarding convergence and how to address constraints. Framed in the calibration of parameters in DEB theory, this work presents a numerical comparison between the Nelder-Mead Simplex method and the SID-PSM algorithm, a Directional Direct-Search method for which convergence can be established both for unconstrained and constrained problems. A hybrid version of the two methods, named as Simplex Directional Direct-Search, provides a robust and efficient algorithm, able to solve the constrained optimization problems resulting from the parametrization of the biological models. Support for J. V. Morais was provided by FCT/MCTES (PIDDAC) through project UID/EEA/50009/2013. Support for A. L. Custódio was provided by Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the project UID/MAT/00297/2013 (CMA).

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“…The meaning of the multiplication is that a 1% decrease in A is considered as valuable as a 1% decrease in B. To optimize the single-phase FRM and minimize the target function (2), the Matlab implementation of the Nelder-Mead method (function "fminsearch") was used [35], since it does not require a gradient calculation and is applicable to noisy objective functions. The Nelder-Mead method is an unconstrained algorithm, and the region of the allowed parameters are not required.…”

Section: Selection Of Optimization Criteria For a Single-phase Flux Rmentioning

confidence: 99%

Optimum Design of High-Speed Single-Phase Flux Reversal Motor with Reduced Torque Ripple

et al. 2020

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Single-phase motors are used in low-power, cost-effective, variable-speed applications. As a replacement to traditional single-phase synchronous motors with magnets on the rotor, single-phase flux reversal motors (FRMs) with a rugged and reliable toothed rotor are considered for the high-speed applications. However, torque pulsations of single-phase motors are high. The aim of this work is to minimize the torque ripple and increase its minimum instantaneous value, as well as to reduce FRM losses. To solve this problem, an asymmetric rotor is used, and an objective function is proposed, which includes parameters characterizing the pulsations of the torque and the loss of FRM for two load conditions. To optimize the single-phase FRM and minimize the objective function, the Nelder–Mead method was applied. The optimization criterion was selected to maximize the efficiency, to reduce the torque ripple, and to the avoid the negative torque in a wide range of powers at the fan load (quadric dependence of torque on speed). Two operating loading modes are considered. After two stages of optimization, the peak-to-peak torque ripple in the FRM in the rated loading mode decreased by 1.7 times, and in the mode with reduced load by 2.7 times. In addition, in the FRM before optimization, the torque has sections with negative values, and in the FRM after optimization, the torque is positive over the entire period. Although losses in the rated mode increased by 4%, when underloaded, they decreased by 11%, which creates an additional advantage for applications that work most of the time with underload.

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Mesh-based Nelder–Mead algorithm for inequality constrained optimization

Cited by 38 publications

References 39 publications

Design Optimization of a Permanent-Magnet Flux-Switching Generator for Direct-Drive Wind Turbines

Design Optimization of a Permanent-Magnet Flux-Switching Generator for Direct-Drive Wind Turbines

Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods

Optimum Design of High-Speed Single-Phase Flux Reversal Motor with Reduced Torque Ripple

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